Determine the equivalent system for the given system of equations.


4x − 5y = 2
10x − 21y = 10

a. 4x − 5y = 2
3x − y = 4
b. 4x − 5y = 2
24x − 47y = 22
c. 4x − 5y = 2
10x + 3y = 15
d. 4x − 5y = 2
14x + 26y = 12

Answers

Answer 1

Answer:

B

Step-by-step explanation:

4x-5y=2 ...(1)

10x-21y=10   ...(2)

(1)+2(2)  gives

24x-47y=22

Answer 2

The equivalent system for the given system of equations is 4x − 5y = 2, and 10x − 21y = 10 is 4x − 5y = 2  and 24x − 47y = 22

We have to determine, the equivalent system for the given system of equations is 4x − 5y = 2, and 10x − 21y = 10.

According to the question,

System of equation; 4x − 5y = 2, and 10x − 21y = 10.

To determine the equivalent relation following all the steps given below.

From equation 1,

[tex]4x - 5y = 2\\\\4x = 2 +5y\\\\x = \dfrac{2+5y}{4}[/tex]

Substitute the value of x in equation 2,

[tex]10(\dfrac{2+5y}{4} )- 21y= 10\\\\10 + 25y - 42y = 10 \times 2\\\\10 -17y = 20\\\\-17y = 20-10\\\\-17y = 10\\\\ y = \dfrac{-10}{17}[/tex]

Substitute the value of y in equation 1,

[tex]4x - 5(\dfrac{-10}{17}) = 2\\\\68x + 50 = 34\\\\68x = 34-50\\\\68x = -16\\\\x = \dfrac{-16}{68}\\\\x = \dfrac{-4}{17}[/tex]

The equation is equivalent to given relation which satisfies the value of x and y is,

[tex]-47(\dfrac{-10}{17} )+24 (\dfrac{-4}{17})= 22\\\\\dfrac{470-96}{17} = 22\\\\\dfrac{374}{17} = 22\\\\22 = 22[/tex]

Hence, The equivalent system for the given system of equations is 4x − 5y = 2, and 10x − 21y = 10 is 4x − 5y = 2  and 24x − 47y = 22.

To know more about Equation click the link given below.

https://brainly.com/question/2925460


Related Questions

Two new drugs are to be tested using a group of 60 laboratory mice, each tagged with a number for identification purposes. Drug A is to be given to 21 mice, drug B is to be given to another 21 mice, and the remaining 18 mice are to be used as controls. How many ways can the assignment of treatments to mice be made? (A single assignment involves specifying the treatment for each mouse—whether drug A, drug B, or no drug.) (Enter the exact number or an equivalent algebraic expression.)

Answers

Final answer:

To find out the number of ways the mice can be assigned to receive the two different drugs or no drug, we use the combination formula. The total number of ways is given by the product of the combinations C(60, 21) * C(39, 21) * 1.

Explanation:

In this problem, we are given a group of 60 mice and we need to find the number of ways the mice can be assigned to receive drug A, drug B, or no drug. This is a problem of combinatorics, specifically a problem of combinations.

We have 60 mice and we want to choose 21 for the drug A. The number of ways to do this is given by the combination formula C(n, k) = n! / [k!(n-k)!], where 'n' is the total number of items, 'k' is the number of items to choose, and '!' represents the factorial function. So for drug A, it will be C(60, 21).

Then, from the remaining 39 mice, we need to choose 21 for drug B. The number of ways we can do this is C(39, 21).

Finally, the remaining 18 mice will serve as the control group. Given that there's no need to specifically choose which mice are in the control group (since all the remaining ones default to it), we only have 1 way for this selection.

 Therefore, the total number of ways the assignment can be made is the product of the number of ways we can form each group, which is C(60, 21) * C(39, 21) * 1.

Learn more about Combinations here:

https://brainly.com/question/30646507

#SPJ11

The number of ways the assignment of treatments to the mice can be made is 10278857927713471414080000.

To determine how many ways the treatments can be assigned to the 60 laboratory mice (21 for drug A, 21 for drug B, and 18 as controls), we need to calculate the number of permutations of the assignments.

The total number of mice is 60, consisting of:

- 21 mice for drug A

- 21 mice for drug B

- 18 mice as controls

The number of ways to assign treatments is the number of permutations of these groups within the total set of mice. This can be calculated using the multinomial coefficient:

[tex]\[ \frac{60!}{21! \times 21! \times 18!} \][/tex]

Where:

- 60!  is the factorial of 60 (total number of mice)

- 21! is the factorial of 21 (number of mice for drug A)

- 21! is again the factorial of 21 (number of mice for drug B)

- 18! is the factorial of 18 (number of control mice)

Let's compute this step-by-step:

1. Calculate 60!:

[tex]\[ 60! = 60 \times 59 \times 58 \times \ldots \times 2 \times 1 \][/tex]

2. Calculate 21!:

[tex]\[ 21! = 21 \times 20 \times \ldots \times 2 \times 1 \][/tex]

3. Calculate 18!:

[tex]\[ 18! = 18 \times 17 \times \ldots \times 2 \times 1 \][/tex]

Now, plug these into the formula:

[tex]\[ \frac{60!}{21! \times 21! \times 18!} = \frac{60 \times 59 \times \ldots \times 2 \times 1}{(21 \times 20 \times \ldots \times 2 \times 1) \times (21 \times 20 \times \ldots \times 2 \times 1) \times (18 \times 17 \times \ldots \times 2 \times 1)} \][/tex]

[tex]\[ \frac{60!}{21! \times 21! \times 18!} = \frac{83209871127413901442763411832233643807541726063612459524492776964096000000000000000}{51090942171709440000} \][/tex]

[tex]\[ \frac{60!}{21! \times 21! \times 18!} = 10278857927713471414080000 \][/tex]

Martin has a combination of 33 quarters and dimes worth a total of $6. Which system of linear equations can be used to find the number of quarters, q, and the number of dimes, d, Martin has?A) q + d = 625q + 10d = 33B) q + d = 60.25q + 0.1d = 33C) q + d = 3325q + 10d = 6D) q + d = 330.25q + 0.1d = 6

Answers

Answer:

D) q + d = 330

0.25q + 0.1d = 6

Step-by-step explanation:

Let q= numbers of quarters

d = number of dimes

q + d = 33 ...........(1)

q = 33 - d

xq + yd = 6 ..........(2)

We will consider the options to know the correct answer

From option A

q +d = 6

25q + 10d = 33

This is wrong

Option B

q + d = 60

0.25q + 0.1d = 33

This is also wrong

Option C

q+d = 33

25q + 10d = 6

Put q = 33 -d in equation 2

25(33 - d) + 10q = 6

825 - 25d + 10d = 6

825 - 15d = 6

-15d = 6-825

-15d = -819

d = -819/-15

d= 54.6

This is also wrong because d exceeds the combination.

Option D

q+d = 33

0.25q + 0.1d = 6

Put q = 33 -d in equation 2

0.25(33 - d) + 0.1d = 6

8.25 - 0.25d + 0.1d = 6

8.25 - 0.15d = 6

-0.15d = 6 - 8.25

-0.15d = -2.25

d = -2.25/ -0.15

d = 15

q = 33 - 15

q = 18

This is correct

Answer:

It's D.

Step-by-step explanation:

Edge 2020;)

A carnival booth made $88 selling popcorn in one day . It made 22 times as much selling cotton candy how much money did the carnival booth make selling popcorn and cotton candy?

Answers

Answer:

Total money made by carnival booth selling popcorn and cotton candy = $2024

Step-by-step explanation:

Money made by carnival booth selling popcorn = $88

Money made by selling cotton candy was 22 times the money made by selling popcorn.

Thus, money made selling cotton candy = [tex]22\times \$88=\$1936[/tex]

Total money made by carnival booth selling popcorn and cotton candy = [tex]\$88+\$1936=\$2024[/tex]

A square is inscribed in a right triangle so that they have a common right angle. The legs of the triangle are 6 in and 8 in long. Find the length of the side of the square.

Answers

Answer:

  24/7 = 3 3/7 inches

Step-by-step explanation:

The triangle can be represented by a line in the first quadrant with y-intercept 8 and x-intercept 6. Then its equation is ...

  x/6 +y/8 = 1 . . . . . intercept form of the equation of the line

  4x + 3y = 24 . . . . multiply by 24 to get standard form

Since the square will have the origin as one corner, and all sides are the same length, the opposite corner will lie on the line y=x. Then we're solving the system ...

  4x +3y = 24

  y = x

to find the side length.

__

By substitution for y, this becomes ...

  4x +3x = 24

  7x = 24

  x = 24/7 = 3 3/7

The length of the side of the square is 3 3/7 inches.

Final answer:

The question involved finding the side length of a square inscribed in a right triangle. The correct approach uses additional geometry to set up a system of equations resulting from segments on the legs of the triangle equal to the side length of the square. Solving these equations reveals that the side length of the square is 2 inches.

Explanation:

The student is seeking to find the length of the side of a square inscribed in a right triangle with legs measuring 6 inches and 8 inches. To determine this, one can use the Pythagorean theorem which relates the legs of a right triangle to its hypotenuse. However, in this scenario, the side of the square also acts as a 'leg' of two smaller right triangles within the original triangle. The length of the square, let's call it 's', plus the square's length (again 's') will equal the longer leg of the triangle (8 inches); similarly, 's' plus the length from the corner of the square to the right angle of the triangle (which is also 's') will equal the shorter leg (6 inches).

Therefore, we have two equations: 2s = 8 and 2s = 6. Since both cannot be true with the same value of 's', we realize that the premise of the question must be reconsidered. The actual process involves a bit more geometry, using the fact that the segments along the legs that are not part of the square must be equal respectively, leading to a system of equations to solve for the length of the side of the square. Let's denote these segments as 'x'; hence the equations are s + x = 6 and s + x = 8. Subtracting these equations from the original leg lengths gives us x = 6 - s and x = 8 - s. As these segments are equal, we can set them equal to each other, getting 6 - s = 8 - s, which simplifies to s = 2 inches.

Please Help!! I'm soo confused.
A line contains the points (-30, 42) and (-27, -30) what is the slope of the line in simplest form?

if you need any other information let me know!!
:))

Answers

We can use the points (-30, 42) and (-27, -30) to solve.

Slope formula: y2-y1/x2-x1

= -30-42/-27-(-30)

= -72/3

= -24 (Answer)

Best of Luck!

Only questions 8 and 9 help please!!!

Answers

Answer:

Step-by-step explanation:

Perpendicular slopes are the opposite reciprocals of the slopes given.  Our slope in 8 is -2.  That means that the perpendicular slope is 1/2.  If the line goes through (2, -1), then

[tex]y-(-1)=\frac{1}{2}(x-2)[/tex] and

[tex]y+1=\frac{1}{2}x-1[/tex] and

[tex]y=\frac{1}{2}x-2[/tex]

9 is a tiny bit trickier because we don't have the slope, the x term, on the opposite side of the equals sign from the y.  Let's do that and then we can determine the slope of that given line.  Moving over the 3x and isolating the y:

y = -3x + 5

So the slope is -3.  That means that the perpendicular slope is 1/3.  If the line goes through (-9, 3), then

[tex]y-3=\frac{1}{3}(x-(-9))[/tex] and

[tex]y-3=\frac{1}{3}(x+9)[/tex] and

[tex]y-3=\frac{1}{3}x+3[/tex] so

[tex]y=\frac{1}{3}x+6[/tex]

Answer:

Step-by-step explanation:

8) y = -2x + 1 and the line passes through (2, - 1)

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

y= -2x + 1

Comparing with the slope intercept form, slope = - 2

If two line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of that of the given line. Therefore, the slope of the line passing through (2,-1) is 1/2

To determine the intercept, we would substitute m = 1/2, x = 2 and y = -1 into y = mx + c. It becomes

- 1 = 1/2 × 2 + c = 1 + c

c = - 1 - 1 = - 2

The equation becomes

y = x/2 - 2

9) 3x + y = 5 and the line passes through (-9, 3)

The equation of the given line is

3x + y = 5

y = -3x + 5

Comparing with the slope intercept form, slope = - 3

If two line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of that of the given line. Therefore, the slope of the line passing through (- 9, 3) is 1/3

To determine the intercept, we would substitute m = 1/3, x = -9 and y = 3 into y = mx + c. It becomes

3 = 1/3 × -9 + c = - 3 + c

c = 3 + 3 = 6

The equation becomes

y = x/3 + 6

PLEASE HELP SOS
What type of exponential function is f(x) = 0.3(2.6)^x?
What is the function's percent rate of change?
Select from the drop-down menus to correctly complete each statement.

Answers

Answer:

Part a) Is a growth function

Part b) The function's percent rate of change is 160%

Step-by-step explanation:

we have

[tex]f(x)=0.3(2.6^x)[/tex]

This is a exponential function of the form

[tex]f(x)=a(b^x)[/tex]

where

a is the initial value or y-intercept

b is the base of the exponential function

If b> 1---> we have a growth function

if b< 1---> is a decay function

r is the percent rate of change

b=(1+r)

In this problem we have

[tex]a=0.3[/tex]

[tex]b=2.6[/tex]

The value of b >1

so

Is a growth function

Find the value of r

[tex]r=b-1=2.6-1=1.6[/tex]

convert to percentage

[tex]r=1.6*100=160\%[/tex]

If n and y are positive integers and 450y = n³, which of the following must be an integer?"
I. [tex]\frac{y}{3*2^2*5}[/tex]
II. [tex]\frac{y}{3^2*2*5}[/tex]
III. [tex]\frac{y}{3*2*5^2}[/tex]
(A) None
(B) I only
(C) II only
(D) III only
(E) I, II, and III

Answers

Answer:

(B) I only

Step-by-step explanation:

450y = n³

y = n³ / 450 = n³ / (3² * 2 * 5²)

in order to keep y and n be positive integer, the minimal requirement for n³ is n³ = (3³ * 2³ * 5³)

y = n³ / 450

  = n³ / (3² * 2 * 5²)

  = (3³ * 2³ * 5³) / (3² * 2 * 5²)

  = 3*2²*5

∴ I. y / (3*2²*5) =  ((3³ * 5³ * 2³) / (3² * 5² * 2)) / (3*2²*5) = 1 ... that keep answer as the smallest positive integer .... Correct answer

II.   y / (3²*2*5) =  ((3³ * 5³ * 2³) / (3² * 5² * 2)) / (3²*2*5) = 2/3 ...not integer

III.  y / (3²*2*5) =  ((3³ * 5³ * 2³) / (3² * 5² * 2)) / (3*2*5²) = 2/5 ...not integer

Answer: The correct answer is neither

Step-by-step explanation:

for DeltaMath.

What is the value of x in the inequality start fraction seven minus two x over negative four end fraction plus two less than negative x ?


A. x less than start fraction one over six end fraction

B. x less than negative start fraction one over six end fraction

C. x greater than negative start fraction one over six end fraction

D. x < 6

Answers

Answer:

[tex]x<-\frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\frac{7-2x}{-4} +2<-x[/tex]

Subtract 2 from both sides

[tex]\frac{7-2x}{-4} <-x-2[/tex]

mutliply both sides by -4, flip the inequality

[tex]7-2x >4x+8[/tex]

Add 2x on both sideds

[tex]7>6x+8[/tex]

Subtract 8 from both sides

[tex]-1>6x[/tex]

Divide both sides by 6

[tex]x<-\frac{1}{6}[/tex]

Final answer:

To solve for x, the given inequality (7 - 2x) / (-4) + 2 < -x can be simplified by isolating the variable on one side of the inequality. The value of x is found to be x < -15/2, making option C) x greater than negative one over six the correct answer choice.

Explanation:

The given inequality is:



(7 - 2x) / (-4) + 2 < -x



To solve for x, we need to isolate it on one side of the inequality. Let's simplify the equation step by step:



(7 - 2x) / (-4) + 2 < -x



7 - 2x + 8 < -4x (Added 2 to both sides)



15 - 2x < -4x



15 < 2x - 4x (Moved -2x to the right side)



15 < -2x



-15/2 > x



So the value of x in the inequality is x < -15/2. Therefore, the correct answer is option C) x greater than negative start fraction one over six end fraction.

tyler is 4 years older than tiffany in ten years he will be twicse as old a tifinay.

Answers

For this case we have to:

x: Variable that represents Tyler's age

y: Variable that represents Tiffany's age

According to the data of the statement we can propose the following equations:

[tex]x = y + 4\\x + 10 = 2y[/tex]

To solve we substitute the first equation in the second equation:

[tex]y + 4 + 10 = 2y\\14 = 2y-y\\14 = y[/tex]

So, Tiffany is 14 years old.

Then Tyler has:

[tex]x = 14 + 4\\x = 18[/tex]

Tyler is 18 years old.

Answer:

Tyler: 18 years old

Tiffany: 14 years old

Andrew's bowling scores are approximately normally distributed with mean 130 and standard deviation 21, while Pam's scores are normally distributed with mean 125 and standard deviation 12. If Andrew and Pam each bowl one game, then assuming that their scores are independent random variables, approximate the probability that the total of their scores is above 265

Answers

Answer:

2

Step-by-step explanation:

In Fig .1 2-40,one end of a uniform beam of weight 222N is hinged to a wall ;the other end is sup -ported by a wire that makes angles 6 =30.0with both wall and beam .Find (a)thetension in the wire and the ( b)horizontaland (c)verticalcompo -nents of the force of the hinge on the beam .

Answers

Answer:

  (a) 74√3 N

  (b) 37√3 N

  (c) 111 N

Step-by-step explanation:

(a) The moment about the hinge produced by the beam is the product of the weight of the beam and the distance of its center from the wall. The tension in the wire counteracts that moment.

The tension in the wire acts at a horizontal distance from the wall that is twice the distance to the beam's center, so the tension's vertical component is only half the weight of the beam.

Since the wire is at a 30° angle to the wall, the horizontal component of the tension is 1/√3 times the vertical component. Altogether, the tension in the wire is (2/√3) times half the beam's weight, or 74√3 N.

__

(b) The horizontal force at the hinge counteracts the horizontal component of the tension in the wire, so is 111/√3 N = 37√3 N.

__

(c) The vertical component of the force at the hinge is half the beam weight, so is 111 N.

a) The tension in the wire is 192.3 N. b) The horizontal component of the force of the hi-nge on the beam is 96.1 N. c) Vertical component of the force of the hi-nge on the beam is 55.5 N.

(a) To find the tension in the wire, we can use a torque balance around the hi-nge. The torques due to the weight of the beam and the tension in the wire are equal and opposite, so we have:

T * L * cos(30°) = W * L/2

where:

T is the tension in the wire

L is the length of the beam

W is the weight of the beam

Solving for T, we get:

T = W * cos(30°) / 2

Substituting the known values, we get:

T = 222 N * cos(30°) / 2

= 192.3 N

Therefore, the tension in the wire is 192.3 N.

(b) The horizontal component of the force of the hi-nge on the beam is equal to the tension in the wire multiplied by the sine of the angle between the wire and the beam. This angle is 30°, so we have:

[tex]F_h[/tex] = T * sin(30°)

Substituting the known values, we get:

[tex]F_h[/tex] = 192.3 N * sin(30°)

= 96.1 N

Therefore, the horizontal component of the force of the hi-nge on the beam is 96.1 N.

(c) The vertical component of the force of the hi-nge on the beam is equal to the weight of the beam minus the tension in the wire multiplied by the cosine of the angle between the wire and the beam. This angle is 30°, so we have:

[tex]F_v[/tex] = W - T * cos(30°)

Substituting the known values, we get:

[tex]F_v[/tex] = 222 N - 192.3 N * cos(30°)

= 55.5 N

Therefore, the vertical component of the force of the hi-nge on the beam is 55.5 N.

To learn more about horizontal component here:

https://brainly.com/question/32317959

#SPJ3

Given the function ƒ(x) = 8(x - 4) - 18, determine the value of x such that ƒ(x) = 22. Select one: A. 3 B. 6 C. 9 D. 12

Answers

Answer:

C. 9

Step-by-step explanation:

it's multiple choice so plug each value in

A = -26

B = -34

C = 22

D = 46

so the answer is c

Match the terms to their definition.
Part A
1. intersection of sets A and B is defined as any elements that are in either set A or set B
2. union of sets A and B is defined as any elements that are in both set A and set B
3. a statement formed by two or more inequalities
4. a member of a set
5. a collection or group of objects indicated by braces, { }
Part B
a. compound inequality
b. element
c. set
d. union
e. intersection

Answers

Final answer:

The correct matches are the intersection for common elements in both sets, union for all elements in either set, compound inequality for multiple inequalities, element for a set member, and set for a grouped collection of objects.

Explanation:

To match the terms with their definitions, we need to understand the concepts represented by each term. Here is the correct matching:

Intersection of sets A and B (e. intersection) is defined as any elements that are in both set A and set B.Union of sets A and B (d. union) is defined as any elements that are in either set A or set B.A compound inequality (a. compound inequality) is a statement formed by two or more inequalities.A member of a set (b. element) is a specific entity within that set.A collection or group of objects indicated by braces, { } (c. set).

These definitions are essential to understanding basic concepts in set theory, a foundation for probability and other areas of mathematics. Recognizing these definitions helps in identifying the relationships between sets and the outcomes of events, especially when working with Venn diagrams and calculating probabilities.

Today robbie is carrying his history textbook and his lunch in his backpack. If the history textbook weighs 2 5/6 pounds and his lunch weighs 1 2/3 pounds, how much weight is in robbies backpack?

Answers

Answer:

37/9 pounds

Step-by-step explanation:

+ them together

Answer:

Step-by-step explanation:

robbie is carrying his history textbook and his lunch in his backpack today.

The history textbook weighs 2 5/6 pounds. Converting 2 5/6 pounds to improper fraction, it becomes

17/6 pounds.

His lunch weighs 1 2/3 pounds. Converting 1 2/3 pounds to improper fraction, it becomes

5/3 pounds.

Total weight of the back backpack today would be the sum of the weight of his history textbook and his lunch. It becomes

17/6 + 5/3 = 27/6 = 4 1/2 pounds

Find the area of a rhombus with side length 6 and an interior angle with measure $120^\circ$.

Answers

Answer:

The area of a rhombus is [tex]18\sqrt{3}[/tex] square units.

Step-by-step explanation:

Side length of rhombus = 6 units.

Interior angle of rhombus = 120°

another Interior angle of rhombus = 180°-120° = 60°.

Draw an altitude.

In a right angled triangle

[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]

[tex]\sin (60)=\frac{h}{6}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{h}{6}[/tex]

Multiply both sides by 6.

[tex]3\sqrt{3}=h[/tex]

The height of the rhombus is [tex]3\sqrt{3}[/tex].

Area of a rhombus is

[tex]Area=base\times height[/tex]

[tex]Area=6\times 3\sqrt{3}[/tex]

[tex]Area=18\sqrt{3}[/tex]

Therefore, the area of a rhombus is [tex]18\sqrt{3}[/tex] square units.

Area of Rhombus is 31.176 unit² (Approx.)

Given that;

Length of rhombus side = 6 unit

Angle = 120°

Find:

Area of Rhombus

Computation:

Area of Rhombus = Side²(Sin θ)

Area of Rhombus = 6²(Sin 120)

Area of Rhombus = 36(0.866)

Area of Rhombus = 31.176 unit² (Approx.)

Learn more:

https://brainly.com/question/3234540?referrer=searchResults

An aerial photograph from a U-2 spy plane is taken of a building suspected of housing nuclear warheads. When the photograph is taken, the angle of elevation of the sun is 30∘. By comparing the shadow cast by the building in question to the shadows of other objects of known size in the photograph, scientists determine that the shadow of the building in question is 98 feet long.How tall is the bulding? (Round your answer to two decimal places.)

Answers

Answer:

Building is 56.58 feet long.

Step-by-step explanation:

Consider the provided information.

An aerial photograph from a U-2 spy plane is taken of a building suspected of housing nuclear warheads.

When the photograph is taken, the angle of elevation of the sun is 30°.

By comparing the shadow cast by the building in question to the shadows of other objects of known size in the photograph, scientists determine that the shadow of the building in question is 98 feet long.

As we know: [tex]\tan\theta=\frac{opp}{adj}[/tex]

The value of tan 30 degrees is [tex]\frac{1}{\sqrt{3} }[/tex]

[tex]\tan30=\frac{h}{98}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{h}{98}[/tex]

[tex]h=\frac{98}{\sqrt{3}}[/tex]

[tex]h=56.58[/tex]

Hence, Building is 56.58 feet long.

Answer:

56.58 feet long

Step-by-step explanation:

Consider the provided information.

An aerial photograph from a U-2 spy plane is taken of a building suspected of housing nuclear warheads.

When the photograph is taken, the angle of elevation of the sun is 30°.

By comparing the shadow cast by the building in question to the shadows of other objects of known size in the photograph, scientists determine that the shadow of the building in question is 98 feet long.

As we know:

The value of tan 30 degrees is

Hence, Building is 56.58 feet long.

Explain how to find n, the number of copies the machine can print in one minute. I need an algebraic expression for the answer.

Once the first part is done, I need help with this question.

Working at the same rate, how long will it take the machine to print 5,200 copies? Explain how you found your answer.

Answers

Answer:

It prints 65 copies in 1  minute.

It takes 80 minutes to print 5200 copies.

Step-by-step explanation:

In 5 minutes the machine prints 325 copies and it can print at that steady state.

We have to find the number of copies it prints in  1 minute.

So ,number of copies in 1 minute = [tex]\frac{number of copies in 5 minute}{5}[/tex]

                                          = [tex]\frac{325}{5}[/tex]

                                           = 65

Hence it prints 65 copies in 1  minute.

The time taken to print 5200 copies = [tex]time to make 1 copy \times 5200[/tex]

                                            = [tex]\frac{1}{65} \times 5200[/tex]

                                             = 80 minutes

Only questions 10-12!! Help please!!

Answers

Answer:

Step-by-step explanation:

10) The opposite sides of a parallelogram are equal. It means that

a + 15 = 3a + 11

3a - a = 15 - 11

2a = 4

a = 4/2 = 2

Also,

3b + 5 = b + 11

3b - b = 11 - 5

2b = 4

b = 4/2 = 2

11) The opposite angles of a parallelogram are congruent and the adjacent angles are supplementary. This means that

2x + 11 + x - 5 = 180

3x + 6 = 180

3x = 180 - 6 = 174

x = 174/3 = 58

Therefore,

2x + 11 = 2×58 + 11 = 127 degrees

The opposite angles of a parallelogram are congruent, therefore,

2y = 127

y = 127/2 = 63.5

12) The diagonals of a parallelogram bisect each other. This means that each diagonal is divided equally at the midpoint. Therefore

3y - 5 = y + 5

3y - y = 5 + 5

2y = 10

y = 10/2 = 5

Also,

z + 9 = 2z + 7

2z - z = 9 - 7

z = 2

How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?

A. 35
B. 40
C. 50
D. 65
E. 70

Answers

Answer:  The correct option is

(E) 70.

Step-by-step explanation:  We are given to find the number of  triangles and quadrilaterals altogether that can be formed using the vertices of a 7-sided regular polygon.

To form a triangle, we need any 3 vertices of the 7-sided regular polygon. So, the number of triangles that can be formed is

[tex]n_t=^7C_3=\dfrac{7!}{3!(7-3)!}=\dfrac{7\times6\times5\times4!}{3\times2\times1\times4!}=35.[/tex]

Also, to form a quadrilateral, we need any 4 vertices of the 7-sided regular polygon. So, the number of quadrilateral that can be formed is

[tex]n_q=^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!\times3\times2\times1}=35.[/tex]

Therefore, the total number of triangles and quadrilaterals is

[tex]n=n_t+n_q=35+35=70.[/tex]

Thus, option (E) is CORRECT.

State the horizontal asymptote is the rational function. F(x)=x+9/x^2+8x+8
None
Y=x
Y=9
Y=0

Answers

Answer:

y = 0

Step-by-step explanation:

When the degree of the denominator of a rational function is greater than the degree of the numerator, then the equation of the horizontal asymptote is

y = 0

here degree of numerator is 1 and degree of denominator is 2

Degree of denominator > degree of numerator, thus

y = 0 ← equation of horizontal asymptote

An 85-foot rope from the top of a tree house to the ground forms a 45 degree angle of elevation from the ground. How high is the top of the tree house?

Answers

Answer:

(about) 61.1

Step-by-step explanation:

To find the height, or H, we can use

sin (45 degree angle) =H/85

rearrange as H=85* sin (45 degrees) =(about) 61.1

What is the tens digit of the positive integer r ? 1) The tens digit of r/10 is 3. 2) The hundreds digit of 10r is 6.

Answers

Answer:6

Step-by-step explanation:

Let digit be r=abc

if tens digit of [tex]\frac{r}{10}[/tex] is 3.2

i.e. [tex]\frac{r}{10}[/tex] is written as ab.c

so tens digit is a=3

If the hundreds digit of 10r is 6

i.e. 10r is written as abc0

its hundreds digit is b=6

thus tens digit of abc is b=6

                   

Final answer:

To find the tens digit of the integer r, we use the information that the hundreds digit of 10r is 6, indicating that the tens digit of r is also 6.

Explanation:

The question is asking to determine the tens digit of a positive integer r. To solve this, we need to analyze the given facts separately:

The tens digit of r/10 is 3. If we divide the integer r by 10 and find that its tens digit is 3, this implies that in the original number r, the ones digit was 3.The hundreds digit of 10r is 6. By multiplying r by 10, we essentially shift each digit one place to the left, meaning the tens digit of r becomes the hundreds digit of 10r. Therefore, if the hundreds digit of 10r is 6, the tens digit of r is also 6.

From statement 2 alone, we can determine that the tens digit of the positive integer r is 6.

What is the area of the new trapezoid formed by dilating the original by a factor of 3

Answers

Answer:

[tex]A_{new}=9A_{original}[/tex]

Step-by-step explanation:

The are of a trapezoid is:

[tex]A_{original}=\frac{(a+b)}{2}h[/tex]

where:

a and b are basesh is the height

When a geometric figure dilates, every coordinate of the original figure must be multiplied by the scale factor of this dilatation. In our case this factor is 3, therefore we will have:

[tex]A_{new}=\frac{(3a+3b)}{2}3h[/tex]

[tex]A_{new}=9\frac{(a+b)}{2}h[/tex]

[tex]A_{new}=9A_{original}[/tex]

The new area is 9 times the original one.

I hope it helps you!

Patrician saves $ 1.20 everyday while her sister Nicole saves $ 2.80 daily. The two girls saved $ 150.00 together. How much of this amount was saved by Nicole?

Answers

Amount saved by Nicole is $ 105

Solution:

Given that Patrician saves $ 1.20 everyday and Nicole saves $ 2.80 daily

The two girls saved $ 150.00 together

To find: Amount saved by Nicole

Let "x" be the number of days for which Patrician and Nicole saved money

Given that they both saved $ 150.00 together

So we can frame a equation as:

[tex]\text{(amount saved by patrician + amount saved by nicole) } \times x = 150.00[/tex]

[tex](1.20 + 2.80) \times x = 150\\\\4x = 150\\\\x = 37.5[/tex]

Therefore amount saved by nicole:

Nicole has saved $ 2.80 daily for "x" days

[tex]\text{ Amount saved by Nicole } = x \times 2.80\\\\\text{ Amount saved by Nicole } = 37.5 \times 2.80 = 105[/tex]

Thus amount saved by Nicole is $ 105

Sayuri's Asian Café makes the best pot stickers in town. The kitchen's production is usually between 20 and 22 pot stickers per hour. Sayuri buys a new machine to help the team make pot stickers faster. She tracks production over the course of seven days. On which day does the machine make a positive impact on production?

Answers

The question is not complete without a picture depicting the pot stickers production. I found a similar question with a table for the production of pot stickers which is attached to this answer. If the actual table is different from the table in this answer, you can still answer your question accordingly using my working and reasoning.

Answer:

Day 6

Step-by-step explanation:

It was given that the usual production of the kitchen is between 20 to 22 pot stickers per hour. Day 1 to 3, the production is within the range given.

However on day 4 and 5, the production is dropped to 10 and 15 - probably due to the workers unfamiliar with the machine.

On day 6 and 7, the production increases to 50 and 55. Therefore the day the machine makes positive impact is on day 6 where the production starts to make a significant increase.

Final answer:

We cannot determine the exact day when the new machine makes a positive impact on production at Sayuri's Asian Café.

Explanation:

The question asks on which day the new machine makes a positive impact on production at Sayuri's Asian Café. To determine this, we need to compare the production before and after the machine was introduced. Unfortunately, the statement provided does not mention the production levels before the machine. Therefore, we cannot determine the exact day when the machine makes a positive impact.

What is the measure of an interior angle in a regular triangle? Write your answer as an integer or as a decimal rounded to the nearest tenth.

Answers

Answer:

The measure of an interior angle in a regular triangle is 60 degrees

Step-by-step explanation:

we know that

A regular triangle has three equal sides and three equal interior angles

Remember that the sum of the interior angles in a triangle must be equal to 180 degrees

so

Divide 180 by 3 to determine the measure of each interior angle

[tex]\frac{180^o}{3}=60^o[/tex]

A regular triangle is called equilateral triangle

therefore

The measure of an interior angle in a regular triangle is 60 degrees

Lina wants to find the least common denominator of 4/32 and 5/8 so that she can add the fractions.What is the least common denominator?Rewrite the fractions with a common denominator.Explain your reasoning

Answers

Answer:

Least common denominator = 32

Step-by-step explanation:

We are given the following in the question:

Lina wants to find the least common denominator of two fractions so she can add them.

[tex]\dfrac{4}{32}\text{ and }\dfrac{5}{8}[/tex]

To find the LCM of the fractions:

[tex]8 = 2\times 2\times 2\\32 = 2\times 2\times 2\times 2\times 2\\\text{Common factors = }2\times 2\times 2\\LCM = 2\times 2\times 2\times 2\times 2 = 32[/tex]

The fractions can be added in the following manner:

[tex]\dfrac{4}{32} + \dfrac{5}{8}\\\\=\dfrac{4\times 1}{32\times 1} + \dfrac{5\times 4}{8\times 4}\\\\= \dfrac{4}{32} + \dfrac{20}{32}\\\\=\dfrac{4+20}{32}\\\\=\dfrac{24}{32}[/tex]

6. If X is the midpoint of WY, WX = 3x - 1 and
WY = 10x - 26, find XY.

Answers

XY = 17

Step-by-step explanation:

It is given that x is the mid-point of WY, so it divides WY in two equal parts

WX and XY so the sum of both lengths will constitute the length of WY

[tex]WY = WX+XY\\XY = WY - WX[/tex]

putting values

[tex]XY = 10x-26 -(3x-1)\\= 10x-26-3x+1\\= 7x-25[/tex]

As X is the mid-point,

[tex]WX = XY\\3x-1 = 7x-25\\3x-1-3x = 7x-25-3x\\-1 = 4x-25\\-1+25 = 4x-25+25\\24 = 4x[/tex]

Dividing both sides by 4

[tex]\frac{4x}{4} = \frac{24}{4}\\x = 6[/tex]

XY = 7x-25

[tex]=7(6) -25\\= 42-25\\=17[/tex]

So,

XY = 17

Verification:

WX = XY

[tex]3x-1 = 7x-25\\3(6)-1 = 7(6)-25\\18-1 = 42-25\\17 = 17[/tex]

Keywords: Linear equations, polynomials

Learn more about polynomials at:

brainly.com/question/5758530brainly.com/question/573729

#LearnwithBrainly

Joe wants to find out volume of his marble . He fills a beaker with 100ml of water and then drops his marble in the breaker. His new reading is 147ml of water . The volume of the water is ??

Answers

Answer:

The volume of the marble is 47 ml

The volume of the water is 100 ml

Step-by-step explanation:

we know that

The volume of the marble is equal to the change in water level

so

To find out the volume of the marble subtract 100 ml from 147 ml

[tex]147-100=47\ ml[/tex]

The volume of the water no change

The volume of the water is 100 ml

Other Questions
Which of the following is true regarding the use of instance variable j in class B1?A) It is directly accessible only in B1B) It is directly accessible only in B2C) It is directly accessible only in B3D) It is directly accessible in B1 and B2E) It is directly accessible in B1, B2, and B3 Brainliest!!!Draw a tree diagram to show the sample space for each event.a shirt with style choices crew-neck and v-neck and colors blue, yellow, or green one half the cost of a dress decreased by $12 is the same as 2/5 the cost of a dress. What is the cost of the dress? N2 is non-reactive, however, if you can get it to react with H2, it does so in a 1:3 mole ratio (N2:H2) and releases 92.0 kJ of thermal energy. That means which if these statements are true? A. This reaction is exothermic. B. This reaction has a negative enthalpy of reaction. C. All of the above are true. D. This reaction has a negative enthalpy of reaction. 10.) A soccer team plays 104 tournaments in twoyears, playing the same number of tournaments eachyear. In each tournament they play 3 games. If theywon a total of 55 games in first year and 103 gamesin the second year,A. how many games did they lose inboth years? B.Is the number of games won greater thanThe number of games lost? Show your work below tojustify your anwser.. The Texas Government Code allows jurisdictions to draw upon which source(s) for jury selection? pls help me to match the word with the correct definition ______is a basic, innate emotional disposition that emerges very early in life and affects behavior throughout childhood. A square and a circle intersect so that each side of the square contains a chord of the circle equal in length to the radius of the circle. What is the ratio of the area of the square to the area of the circle? Express your answer as a common fractin in terms of Pie. There is a bag filled with marbles: 5 red, 8 blue, 4 yellow, and 3 green.You want to draw a red then a blue marble. Do you have a better chance of drawing a red then a blue marble with or without replacing the first marble? Explain your answer.please give an explanation. i seriously don't understand this question. have a wonderful day and happy holidays! What is the approximate wavelength of visible light?(A) 7 10 7 m(B) 7 m(C) 1 10 7 m(D) 70 m A box with a square base and open top must have a volume of 32,000 cm3. Find the dimensions of the box that minimize the amount of material used.(a) Sides of base (cm)(b) Height (cm) There are many new religious movements that have come about in the last 200 years. Select one not mentioned in the text to expand on and present here on the Discussion Forum. Present its origins, basic beliefs, and what its current numbers are. You can choose one that is historical, small in number, or in any part of the world. Examples might be, but are not limited to: Wiccan, Druidism, any of the New Age religions, Shakers, Theosophy, etc. You can also select little known or mentioned sects of established religions: Pentecostal snake churches, People's Temple, etc. In ____, in which cultural change occurs more rapidly, adults continue to socialize their children, but peers play a greater role in socializing each other. a) prefigurative cultures b) figurative cultures c) cofigurative cultures d) postfigurative cultures. Select the best answer for the question17. A local supermarket sells shrimp for $4.50 per pound and lobster for $7.25 per pound.You have a total budget of $95.75. If you buy 7 pounds of lobster, how many pounds of shrimpcan you purchase? If 10 minutes is how long it took Lisa to walk 1/4 of the way home, how long does it take to walk 2/3 of the way home? Which three statements describe the direct effects of apartheid?Black South Africans faced difficulties in uniting in the struggle against apartheid.Great Britain and Dutch led military involvement in South Africa.White South Africans retained control of the government and the economy.Black South Africans were forced into poverty and unemployment.Black South Africans create Bantustans to separate from South Africa.Submit Based on Daniel Kahnemans research, the use of predictive advertising would fall under which system of decision making? The vapor pressure of water at 25 degrees Celsius is 23.8 torr, and the heat of vaporization of water at 25 degrees Celsius is 43.9 kJ/mol. Calculate the vapor pressure of water at 50 degrees Celsius. John AdamsWhen Adams became President, the war between the French and British was causing great difficulties for the United States on the high seas and intense partisanship [taking of sides] among contending factions within the Nation.His administration focused on France, where the Directory, the ruling group, had refused to receive the American envoy and had suspended commercial relations.Adams sent three commissioners to France, but in the spring of 1798 word arrived that the French Foreign Minister Talleyrand and the Directory had refused to negotiate with them unless they would first pay a substantial bribe. Adams reported the insult to Congress, and the Senate printed the correspondence, in which the Frenchmen were referred to only as "X, Y, and Z."President Adams did not call for a declaration of war, but hostilities began at sea. At first, American shipping was almost defenseless against French privateers, but by 1800 armed merchantmen and U.S. warships were clearing the sea-lanes. WhiteHouse.govBased on the information in the excerpt, what can be inferred about the effect the war between France and England had on the United States? A.) Congress became united in wanting to attack the French.B.) The refusal to pay the bribe resulted in a suspension in French trade that deeply altered the American economy.C.) The negotiations led to further disputes among the French Directory members regarding British trade policy.D.) The attacks on U.S. ships led to strengthening the through building more frigates.Please explain why! I will give brainly if the answer is correct! Steam Workshop Downloader