1. During a field trip, 60 students are put into equal-sized groups.
- Describe two ways to interpret 60:5 in this context.
- Find the quotient.
- Explain what the quotient would mean in each of the two interpretations you
described.


Help me plzz

The expression for distance AB is :389 tan 88.60°. The angle D is 88.35°.The value of angle CAD in radians is 0.0532 rad.

Step-by-step explanation:

Given the information, you can sketch triangle ACB with ∠C=88.60° and a perpendicular bisector of segment CD as AB that forms 90° at B where the diatnace from C to B given as 389 ft you can find the length of the perpendicular bisector AB which is the distance between tower A and B.

Apply the tangent of an angle rule, where tangent of angle = opposite side length/adjacent side length

tan 88.60°=O/A

tan 88.60°=AB/389

AB=389 tan 88.60° = 15916.87 ⇒ 15917 (nearest foot)

B.

Given distance BD as 459 ft and the distance between tower A and B as 15917 ft you can calculate the value of angle ∠D by applying the tangent of an angle formula.

tan Ф=O/A where Ф=∠D

tan ∠D =15917/459

tan ∠D =34.6772834701

tan⁻(34.6772834701) =88.35°

C.

Finding angle ∠A in radians will be;

Applying the sum of angles in a triangle theorem

∠A=180°-(88.60°+88.35°) = 180°-176.95°=3.05°

Changing degrees to radians, multiply value of degrees by π/180°

3.05×π/180 =0.05323254 ⇒ 0.0532 rad

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Keywords : horizontal distance,towers, elevation, perpendicular line, distance, equation, expression,hundredth

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Answer:

90+x=30-3[x]

Step-by-step explanation:

collect like terms

x+3x=30-90

4x=-260

divide both sides by 4

x=-60/4

x=-4*3*5/4

x=-[3*5/1]

x=-[3*5]

x=-15

Answer:

The number is 60.

Step-by-step explanation:

Let x = unknown number.

Now we translate the sentence into an equation, one piece at a time.

When 90 is added to a number it equals 30 less than 3 times the number.

x + 90

When 90 is added to a number it equals 30 less than 3 times the number.

x + 90 = 3x - 30

We now solve the equation for x.

Subtract 3x from both sides.

-2x + 90 = -30

Subtract 90 from both sides.

-2x = -120

Divide both sides by -2.

x = 60

The number is 60.

Check:

When 90 is added to a number it equals 30 less than 3 times the number.

Add 90 to 60:

90 + 60 = 150

We get 150.

When 90 is added to a number it equals 30 less than 3 times the number.

Now multiply 60 by 3 and subtract 30.

3(60) - 30 = 180 - 30 = 150

We also get 150.

That means our answer of 60 is correct.

Answer: 60

Answer: at new cost increase is 30%

               after additional $4.50 fee  increase  would be 45%

Step-by-step explanation:

use equation

30:100=39:x

30x=3900

x=3900/30

x=130

130-100=30%

39+4.50=43.5

30:100=43.5:x

30x=4350

x=4350/30

x=145

145-100=45%

The increase percent will be 30%

And, The percent increase if the ticket agent charges an additional​ $4.50 fee with the new ticket​ price is 45%.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

The old cost of the tickets = $30

And, New cost of the ticket = $39

Now,

The increase percent is calculate as;

Increase percent = (39 - 30) / 30 x 100

                           = 9/30 x 100

                           = 30%

And, When the ticket agent charges an additional $4.50 fee with the new ticket price.

Then, The new cost of the tickets = $39 + $4.50

                                                    = $43.50

Thus, The percent increase if the ticket agent charges an additional $4.50 fee with the new ticket price is calculated as;

Increase percent = (43.50 - 30) / 30  x 100

                          = 13.50/30  x 100

                          = 45%

Therefore, The increase percent will be 30%.

And, The percent increase if the ticket agent charges an additional​ $4.50 fee with the new ticket​ price is 45%.

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Answer:

13/14 is greater

Step-by-step explanation:

Find the lcm for both:

9 x 7     = 63

10 x 7        70

13 x 5    = 65

14 x 5        70

so therefore 13/14 is greater since it has a greater value when finding the lcm

Answer:

The value of x is 3 ,

The measure of each side is 55 units .

Step-by-step explanation:

Given as :

The sides of the equilateral Triangle are pq , qr , pr

The measure of side pq = 18 x + 1

The measure of side qr = 24 x - 17

The measure of side pr = 15 x + 10

∵ The triangle is equilateral then all sides are equal

i.e pq = qr = pr

So, 18 x + 1 = 24 x - 17

Or, 24 x - 18 x = 17 + 1

Or, 6 x = 18

∴  x = [tex]\dfrac{18}{6}[/tex]

i.e x = 3

So, Putting the value of x

The measure of side pq = 18 × 3 + 1 = 55 unit

The measure of side qr = 24 × 3 - 17 = 55 unit

The measure of side pr = 15 × 3 + 10 = 55 unit

Hence The value of x is 3 ,

And The measure of each side is 55 units . Answer

Answer:

x = 3.

Measure of each side is 55 units.

Step-by-step explanation:

In an equilateral triangle, the length of all the three sides are equal.

Therefore, Side PQ = QR = PR.

⇒ 18X + 1 = 24X - 17

⇒ 24X - 18X = 18

⇒ 6X = 18

⇒ X = 3

Substituting the value of X, we get:

PQ = 18(3) + 1 = 55 Units.

QR = 24(3) - 17 = 55 units.

PR = 15(3) + 10 = 55 units.

We see the length of all the sides are equal.

What numbers??? You need to either add a picture or just write the numbers

Answer:

1) A. Not a direct variation 2) D. Direct Variation, constant of variation is -2 C) B. Direct Variation, constant of variation is ½

Step-by-step explanation:

Direct Variation requires that [tex]y=kx[/tex] with k≠0. K its constant of variation and its slope. It is a linear function with b =0

1) Examining 2y =5x + 1. Rewriting it as standard form:

[tex]2y =5x + 1\\\\y=\frac{5}{2}x+\frac{1}{2} \\\\[/tex]

Since this function cannot be written as y=kx as b ≠ 0 (b=1) then we can say that this is not a direct variation.

A. Not a direct variation

2) [tex]2). -12x=6y \Rightarrow y=-2x[/tex]

This linear function has no linear parameter. And its line goes through the origin varying directly. The constant k is equal to -2. So,

D. Direct Variation, constant of variation is -2

3) [tex]0.7x-1.4y=0\\\\-1.4y=-0.7x* (-1)\\y=0.5 \:or\,y=\frac{1}{2}[/tex]

The Constant of Variation is 1/2 and K>0. There is a direct variation between x and y of 1/2. So it's B.

B. Direct Variation, constant of variation is ½

The equation 2y = 5x + 1 represents a direct variation with a constant of variation of 5/2. The equation -12x = 6y represents a direct variation with a constant of variation of -2. The equation 0.7x - 1.4y = 0 represents a direct variation with a constant of variation of 0.5.

For the equation 2y = 5x + 1, we need to determine if it represents a direct variation. In a direct variation, y is directly proportional to x, meaning that when x increases, y also increases or when x decreases, y also decreases. To check if it's a direct variation, we can rearrange the equation to y = mx + b form, where m is the constant of variation. In this case, rearranging the equation gives us y = (5/2)x + 1/2, so the constant of variation is 5/2. Therefore, the equation represents a direct variation and the constant of variation is 5/2.

For the equation -12x = 6y, we can rearrange it to y = (-12/6)x = -2x. Since the constant of variation is -2, the equation represents a direct variation.

For the equation 0.7x - 1.4y = 0, we can rearrange it to y = (0.7/1.4)x = 0.5x. Since the constant of variation is 0.5, the equation represents a direct variation.

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x+y≤525 and 9x+5y≤1200 represents the scenario.

Step-by-step explanation:

Given,

Room for people at summer camp = 525 people

Maximum budget = $1200

Cost per adult = $9

Cost per camper = $5

It means that there cannot be spent more than $1200.

x represents the number of adults.

y represents the number of campers.

x+y≤525      

9x+5y≤1200

x+y≤525 and 9x+5y≤1200 represents the scenario.

Keywords: inequality, budget

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Answer:  

x+y≤525      

9x+5y≤1200

Step-by-step explanation:

Answer: 0

Step-by-step explanation: The answer would be 0 since if y = -4, the graph of the line would just be a horizontal line through the point (0,-4). This would be like saying that y = 0x-4. Hope this helped!

Answer:

slope = 0

Step-by-step explanation:

The equation of a horizontal line parallel to the x- axis is

y = c

where c is the value of the y- coordinates the line passes through.

y = - 4 ← is therefore a horizontal line

with slope = 0

Answer:

The correct option is (a).

Step-by-step explanation:

See the diagram attached.

Whatever be the translation done on a figure the dimensions of the figure will remain unchanged and only the coordinates of the vertices will change according to the rule of translation.

Therefore, if a rectangle FGHJ is translated by 6 units right and one unit up to produce a rectangle F'G'H'J', then the length F'G' = FG = 3 units and G'H' = GH = 5 units.  

So, the correct option is (a). (Answer)

Rectangle F'G'H'J' will have sides, F'G' = J'H' = 3 units, and, F'J'=G'H'=6 units.

Given to us,

Rectangle FGHJ, with sides, FG = JH = 3 units, and, FJ=GH=6 units.

Now, as given to us, Rectangle FGHJ has translated 6 units up to produce rectangle F’G’H’J', but even if the rectangle is translated it will still be a rectangle making no changes in its sides.

Therefore, Rectangle F'G'H'J' will have sides, F'G' = J'H' = 3 units, and, F'J'=G'H'=6 units.

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Answer:

The new coordinate of the image will be (4, 0) when the point (-4,0) is rotated 180 degrees counterclockwise using center (0,0).

i.e. [(-4,0)→(4,0)]

Step-by-step explanation:

The rule for rotation a point 180° counterclockwise about the origin states that when a point (x, y) is rotated 180° counterclockwise about the origin, the new position of the coordinates of point P(x, y) becomes (-x, -y).

Hence,

So, when the given point  (-4,0) is rotated 180 degrees counterclockwise using center (0,0), the new coordinates of the image will be:

Therefore, the new coordinate of the image will be (4, 0) when the point (-4,0) is rotated 180 degrees counterclockwise using center (0,0).

i.e. [(-4,0)→(4,0)]

Keywords: rotation, origin, image

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In order to find \( f(x+h) \) given the function \( f(x) = \fraction{x²}{x+3} \), we need to replace every instance of \( x \) in the function with \( x+h \). Here are the steps to do so:

1. Write down the original function:
  \( f(x) = \fraction{x²}{x+3} \)

2. Substitute \( x+h \) for \( x \) in the function to get \( f(x+h) \):
  \( f(x+h) = \fraction{(x+h)²}{(x+h)+3} \)

3. Now expand the numerator and simplify the expression:
  \( (x+h)² = x² + 2xh + h² \)
  Therefore, \( f(x+h) = \fraction{x² + 2xh + h²}{x+h+3} \)

That is the expression for \( f(x+h) \) given the function \( f(x) = \fraction{x²}{x+3} \). Note that you could further simplify the expression depending on the context or the specific question asked, but as it stands, this is the correct substitution and form of \( f(x+h) \).

Answer:

1. 24          2. 21:15          3. 36:21

Step-by-step explanation:

18:27 is 2:3 and 24 is 16/2*3

7:5 is also 21:15

36:21 fully simplified is 12:7 not 9:7

Answer:

1:24 2: 21:15 3: 36:21

Step-by-step explanation:

Hope this helps!!!

Answer:

The initial value of the function is 3.

The range of the function is y > 0.

The simplified base value of the function is 8.

Step-by-step explanation:

The given function is [tex]f(x) = 3(16)^{\frac{3}{4}x }[/tex]

Therefore, the simplified function will be [tex]f(x) = 3(16^{\frac{3}{4} } )^{x} = 3(8)^{x}[/tex] ........ (1)

Now, at x = 0, f(x) = 3.

Hence, the initial value of the function is 3. (Answer)

The value of x in the equation (1) can be any real value but for any value of x, the f(x) value will be greater than 0.

Hence, y > 0 that is the range that the function has. (Answer)

Again, from equation (1) we get the simplified base value of the function is 8. (Answer)  

Answer:

A, C, E

Step-by-step explanation:

Egde 2020

Final answer:

The value of 17 tens can be written in standard form as 170, in expanded form as (1 × 10²) + (7 × 10¹), and in unit form as '1 hundred 7 tens 0 ones'.

Explanation:

When asked to write the value of 17 tens three different ways, we first recognize that '17 tens' is essentially the number 170, since 17 tens are 17 multiplied by 10.

Standard Form

The standard form is simply writing the number as it is, so in this case, it would be 170.

Expanded Form

The expanded form breaks down the number into its place value components. Since 170 comprises 1 hundred, 7 tens, and 0 ones, it can be written as:
(1 × 10²) + (7 × 10¹) + (0 × 10°)

Unit Form

Last, the unit form expresses each digit's value according to its place value, which for 170 is '1 hundred 7 tens 0 ones'.

Answer:

The Two Column Proof is given below.

Step-by-step explanation:

Given:

[tex]\overline{MP} \cong \overline{MN}[/tex]

[tex]\overline{PO} \cong \overline{NO}[/tex]

To Prove:

∠ P ≅ ∠ N

Proof:

In  Δ MPO  and Δ MNO

STATEMENT                                              REASONS  

1. MP ≅ MN                                   1. Given

2. PO ≅ NO                                  2. Given

3. MO ≅ MO                                 3. Reflexive property

4. ΔMPO ≅ ΔMNO                       4. Side-Side-Side congruence test}

5. ∠MPO ≅∠MNO                        5. Corresponding parts of congruent Triangles

i.e ∠ P ≅ ∠ N                                 ..................Proved

Answer:

(x − 5) (x + 4)

Step-by-step explanation:

x² − x − 20

Factor using AC method:

1 × -20 = -20

Factors of -20 that add up to -1: -5 and 4

Divide by 1 and reduce: -5/1 and 4/1

(x − 5) (x + 4)

Answer:

[tex]\displaystyle [x + 4][x - 5][/tex]

Step-by-step explanation:

Find two quantities that when differed to −1, they also multiply to −20, and those numbers are 4 and −5.

I am joyous to assist you anytime.

Answer:4

Step-by-step explanation: since he has 24

Yaneliz has 24 X 1/6 = 4

Answer: y = 24 x 1/6

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

Marcos: $24

Yaneliz: 1/6 of the amount of money Marcos has

So, to write an expression we have to multiply the amount of money Marcos has (24) by 1/6.

Mathematically speaking

Y = 24 x 1/6  

Where "y" is the amount of money Yaneliz has.

Solving:

24 x 1/6 = 4

Yaneliz has $4.

Feel free to ask for more if needed or if you did not understand something.

1. Is the actual equation, so this is Given

2. removing the parenthesis is the Distributive Property

3. Combining like terms.

4. They add 6x to both sides, this would be the Addition Property of Equality

5. Subtract 4 from both sides, this is the Subtraction Property of Equality.

6. Divide both sides by 8, this would be the Division Property of Equality.

Answer:

1. Given

2. Distributive property

3. Combining like Terms

4. Addition property of Equality

5. Subtraction property of equality

6. Division Property of Equality

Question:

Ming took a cab across town. His fare was $22 and he leaves an 18%, percent tip. What is the total amount Ming pays the cab driver?

Answer:

Ming pays the $25.96 to cab driver

Step-by-step explanation:

Given:

the fare of the car =  $22

Percentage of tip paid by the Ming = 18%

To Find:

Total amount Ming pays the cab driver=?

Solution:

The total amount of the tip paid by the Ming to the cab driver be x

then

x = car fare + 18% of cab fare

substituting the values we get

x = 22 + 18% of 22

x = 22 +  [tex]\frac{18}{100} \times 22[/tex]

x = 22 +  [tex]\frac{18}{100} \times 22[/tex]

x = 22 +  [tex]0.18 \times 22[/tex]

x = 22 + 3.96

x = 25.96

Answer: [tex]\frac{25}{6} a^{9} b^{10}[/tex]

Step-by-step explanation:

Assuming the described expression is:

[tex]\frac{(5ab)^{3}}{30 a^{-6} b^{-7}}[/tex]

And knowing the condition [tex]a \neq 0[/tex] and [tex]b \neq 0[/tex]

We cansimplify it following the rules related to the exponents with the same base:

[tex]\frac{25}{6} a^{3} b^{3} a^{6} b^{7}[/tex]

Finally:

[tex]\frac{25}{6} a^{9} b^{10}[/tex]

Answer:

Answer: \frac{25}{6} a^{9} b^{10}

Step-by-step explanation:

100% on ed

Answer:

I have no idea

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find out the area just compare the amount of green space and yellow space then calculate the numbers.

Answer:

The answer is D

Step-by-step explanation:

[tex]sector = \frac{θ}{360} \times π {r}^{2} [/tex]

Given that θ = 75° and r = 3in, so use the formula to find the shaded region :

A = (75/360)×π×3²

= (15/8)π

Question:

The park district is paying to enlarge the area of a square-shaped dock at a local lake. The area of the dock will increase by 16 square feet. Complete the equation below that can be used to find the area, x, of the original dock if the side length of the new dock is 20 feet.

So, the square root of what (?) equals(=) 20

Answer:

The complete equation is square root of(x + 16) = 20

Solution:

Given that Dock has a shape of square

[tex]\text{ area of square }= (side)^2[/tex]

From question, it is given that side length of new dock is 20 feet

Therefore, area of new dock is given as:

[tex]\text{ area of new dock}= (20)^2[/tex]

Taking square root on both sides,

square root of (new area ) = 20  --- eqn 1

Let "x" be the area of original dock

The area of the dock will increase by 16 square feet

New area = original area + 16

New area = x + 16 ---- eqn 2

From eqn 1,

square root of (new area ) = 20

From eqn 2

square root of(x + 16) = 20

Thus the complete equation is: square root of(x + 16) = 20

Final answer:

To find the area of the original dock, the equation x + 16 = 20^2 can be used, where x is the original area. By solving the equation, we find that x equals 384 square feet.

Explanation:

The area of the original square-shaped dock can be found using the equation for the area of a square, with the area being equal to the side length squared. Given that the new square dock has a side length of 20 feet, and the area is increased by 16 square feet, we can set up an equation to find the original area, x.

The equation is x + 16 = 20^2, where 20^2 is the area of the new, larger dock, and x is the original area of the dock before the enlargement. Therefore, the side length of the original dock is the square root of x. To find x, we can solve the equation:

x + 16 = 400
x = 400 - 16
x = 384

So the area of the original dock is 384 square feet.

Answer:

Step-by-step explanation:

sales - expenses = profit

lets x represent number of shirts sold

12x - (3x + 150) > = 300

12x - 3x - 150 > = 300

9x - 150 > = 300

9x > = 300 + 150

9x > = 450

x > = 450/9

x > = 50 <== they would need to sell at least 50 shirts

Answer:

20748

Step-by-step explanation:

546 times 38

Answer:

The sum of - 2 and - 5 is - 7.

[tex]1\frac{2}{3} + 3\frac{1}{2} = 5\frac{1}{6}[/tex]

Step-by-step explanation:

The sum of - 2 and - 5 is [- 2 + (- 5)] = - 2 - 5 = - 7. (Answer)

Let two mixed fractions are [tex]1\frac{2}{3}[/tex] and [tex]3\frac{1}{2}[/tex] that we have to add with steps.

Now, we have to sum the mixed numbers after converting then into improper fractions.

So,  [tex]1\frac{2}{3} = \frac{5}{3}[/tex] and  

[tex]3\frac{1}{2} = \frac{7}{2}[/tex]

Hence, [tex]1\frac{2}{3} + 3\frac{1}{2}[/tex]

= [tex]\frac{5}{3} + \frac{7}{2}[/tex]

= [tex]\frac{5\times 2 + 7 \times 3}{6}[/tex] {Because the  L.C.M. of 2 and 3 is 6}

= [tex]\frac{ 10 + 21}{6}[/tex]

= [tex]\frac{31}{6}[/tex]

= [tex]5\frac{1}{6}[/tex] (Answer)

Answer:

Hi im on odyssey ware and i had this question too, Just remember that the fractions are pictures, so they wont go on the question. Another way to write fractions is like this 4/8 so the actual question is, find the sum of -2 9/10 and -5 4/15. Then, in two or more complete sentences, explain the steps you used to add the mixed numbers.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Later area of Pyramid =  2 * 1/2 * 9 * 12.3  + 2*1/2*11*11.9

                                     = 9*12.3 + 11*11.9

                                      =  110.7 +130.9

                                      = 241.60 sq.feet