The sum of two numbers is 61.61. if three times three times the smaller number is subtracted from the larger? number, the result is 5.5. find the two numbers.

Answers

Answer 1

x + y = 61
y - 3x = 5...y = 3x + 5

x + (3x + 5) = 61
4x + 5 = 61
4x = 61 - 5
4x = 56
x = 56/4
x = 14

y - 3x = 5
y - 3(14) = 5
y - 42 = 5
y = 42 + 5
y = 47

ur 2 numbers are 14 and 47

Related Questions

let i be the first of four consecutive integers. what is 3 less than the sum of those integers ?

Answers

The consecutive integers are i, i+1, i+2, i+3.

3 less than sum of the integers

= i + i +1 + i + 2 + i + 3 - 3 = 4i + 3

Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113. Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours. (4 points)

Part B: Write the equation obtained in Part A using function notation. (2 points)

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

Answers

Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113. Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours. (4 points)

time      rent
hours          $

3                 43
8               113

Assume a linear relation, this is r(t)= Ax + C

=> [r - 43] / [ x - 3] = [113 - 43] / 8 - 3]

=> [r - 43] / [x - 3] = 70 / 5

=> [r - 43] / [x - 3] = 14

=> r - 43 = 14 [x - 3]

=> r - 43 = 14x - 14*3

=> r - 43 = 14x - 42

=> r - 14x - 1 = 0   <----- standard form

Part B: Write the equation obtained in Part A using function notation. (2 points)

r - 14x - 1 = 0 => r(x) = 14x + 1 <------------- function notation, r(x)

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

1) Horizontal axis = x

2) Vertical axis = y

3) Domain x > 0 = [0, ∞)

4) Range r > 0 = [0, ∞)

5) r-intercept=> x = 0 => r = 14(0) + 1 = 1 => (0,1)

6) slope: 14

7) x-intercept => r = 0 => 0 = 14x + 1 => x = -1/14 => (-1/14, 0)

Remember that angle measures in degrees and radians are based on the proportion of the angle to a complete circle, meaning a fraction of either 360° or 2π. Given that 360° = 2π, we can convert between degrees and radians. With this information in mind, set up a proportion and use it to convert an angle of 225° into radians.

Answers

Given that 360 degrees = 2pi

And you want to compute 225 degrees in to radians, let's assume the final answer is x

Then, 360 / 2pi = 225 / x

Solve for it, you will get x= 5pi/4

4(8x-8)=-192 what's that mean and can someone help me asap

Answers

This is algebra. 4 times whatever is in the parentheses (8x-8) has to be equal to -192. If you do the math, x= -7

You're setting sales goals for next month. You base your goals on previous average sales. The actual sales for the same month for the last four years have been 24 units, 30 units, 23 units, and 27 units. What is the average number of units you can expect to sell next month?

A. 26
B. 28
C. 30
D. 104

Answers

To find the average, you need to add up all the values and dived by 4

24+30+23+27 = 104
104/4 = 26
A is correct

The correct answer will be A

24 + 30 + 23 + 27 = 104

104/4 = 26

In square QRST, points U and V are midpoints. If the square has a side length of 18 mm, what is the probability that a point chosen at random in the square lies in the shaded triangle region? Round the answer to the nearest thousandth. A. 0.028 B. 0.056 C. 0.125 D. 0.222

Answers

Calculate first the area of the shaded triangle region and the area of the square then you could get the probability of the point
The formula for the area of triangle is b h / 2
Where:b = h = half of side length of square = 9 mm
Area of triangle = 9 mm * 9 mm / 2
Area of triangle = 40.5 mm^2

Area of square = s^2
Area of square = (18 mm)^2
Area of square = 324 mm^2

Probability that a point is in the shaded region
= Area of triangle / Area of square
= 40.5 / 324
= 0.125

The answer is letter C. 0.125

Answer:

Step-by-step explanation:

A video game club charges a fixed annual membership fee of $20 and $2 per video game rented. Let f(n) represent the total annual cost of renting n video games. Which of the following functions best represents the relationship between f(n) and n if the membership was increased by $15 the next year?
f(n) = 2n + 35
f(n) = 20n + 2
f(n) = 10n + 35
f(n) = 2n + 10

Answers

fixed annual membership fee of $20
$2 per video game rented.
Let f(n) represent the total annual cost of renting n video games
so
f(n) = 20 + 2n

if increased by $15 the next year
then
f(n) = 20 + 2n + 15
f(n) = 2n + 35

answer
f(n) = 2n + 35 (first choice)

Answer:

The correct answer is A, "f(n) = 2n + 35."

Step-by-step explanation:

I got it correct on the test. I hope this helps!

Factor the trinomial below.

x^2-5x-14

A. (x-2)(x-7)
B. (x+2)(x-7)
C. (x+2)(x+7)
D. (x-2)(x+7)

Answers

The answer is B.
Proof:
-7+2=-5
-7*2=-14

Also, when you FOIL it becomes
x^2-7x+2x-14
That simplifies to
x^2-5x-14

Answer:

The factored form is

[tex]x^2-7x+2x-14=(x+2)(x-7)[/tex]

Step-by-step explanation:

Given the trinomial

[tex]x^2-5x-14[/tex]

we have to factor the above trinomial.

[tex]x^2-5x-14[/tex]

By middle term splitting method

[tex]x^2-7x+2x-14[/tex]

Taking x common from first two terms and 2 from last two terms

[tex]x(x-7)+2(x-7)[/tex]

[tex](x+2)(x-7)[/tex]

which are required factors.

Hence, option B is correct.

If it takes 4 people 4 days to dig a hole, how long does it take 2 people to dig a half-hole

Answers

the answer is 4 days. because if 2 people were digging a whole hole, it would take twice as long, being 8 days. digging half a hole, you would just cut the 8 in half, leaving 4 days for 2 people to dig half a hole.

Do all rational equations have a single solution? why? is there a time when a rational equation doesn't have a solution?

Answers

Answer: All rational equations don’t necessary have a single solution however they do have solutions that can’t fulfill the answer. Any solution where the denominator is equal to zero results in an undefined equation.

A new parking lot is being built for a medical office. the expression representing the number of parking spots in the new lot is 15x/4 -9 , where x represents the number of parking spots in the first row . how many spots are in the parking lot if there are 32 parking spots in the first row

Answers

did you ever get the awnzer

its 69---------------------------------

Can someone help me please? I don't know how to do this problem, could someone explain step by step? It would be greatly appreciated. I've also included 15 points to whoever answers this.

Answers

see picture for answer

Root 12 can still be simplified because its prime factors are 2, 2, and 3.
Take the 2's out to get 6(2)root 3.
6*2=12 so that simplifies to 12 root 3
Now just subtract 12 root 3 and root 3
This leaves you with eleven root 3
Final answer: C

What is the value of X in the isosceles trapezoid below?
A. 81 B. 15 C. 11 D. 41

Answers

The correct answer is: [C]: " x = 11 " .
______________________________________
9x + (4x + 37) = 180 ;

9x + 4x + 37 = 180 ;

13x + 37 = 180 ;

Subtract "37" from each side of the equation;

13x + 37 - 37 = 180 - 37 ;

to get:

   13x = 143 ;

Divide each side of the equation by "13" ;
to isolate "x" on one side of the equation ; and to solve for "x" ;
______________________________________________________
    13x / 13 = 143 / 13 ;

          x = 11 ; which is: Answer choice: [C] .
______________________________________________________

Final answer:

Without additional details, this question can't be answered accurately. Typically, one uses properties of an isosceles trapezoid, such as base angles or diagonal lengths, to find unknown variables. More information would allow a more precise answer.

Explanation:

Without a visual or additional information about the isosceles trapezoid, it would be challenging to accurately identify the value of X. However, typically in a problem like this, you would use the properties of an isosceles trapezoid, such as its base angles or the lengths of its diagonals, to find the value of an unknown variable. If given the measures of the other sides, it might be possible to calculate the remaining length. An example would be a problem like this: If the bases of an isosceles trapezoid are 10 and 20 units long, respectively, and the non-parallel sides (legs) are equal and represented by X, then based on specific conditions, X could potentially be calculated.

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A rectangle is graphed on the coordinate grid.

Which represents the equation of the side that is parallel to side s?

Answers

With two points you can define a line.

So, the line parallel to s is q, which has these two points: (3,6) and (6,3)

There are different ways to get the line. For instance, this one:

y = a*x+b,

a = slope = difference_y/difference_x = (3-6)/(6-3) = -1,

y = -x + b,

Now use any point, say (3,6) to get b:

6 = -3+b-> b = 9,

line is y = -x + 9,

It checks out in the other point: (6,3) --> 3 = -6+9 = 3. Good.

Other method could be:

y-y2 = a*(x-x2), where (x2,y2) is one of the two points and a is the slope as defined before.

Hope it helps!

The side that is parallel to side s is side q. The equation of side q is: y = -x + 9.

What is the Equation of a Line?

We can represent the equation of a line as, y = mx + b, where m is the slope of the line and b is the y-intercept.

The side that is parallel to side s is q.

Slope (m) of q = change in y / change in x = (6 - 3) / (3 - 6) = 3/-3 = -1.

Substitute m = -1 and (3, 6) = (a, b) into y - b = m(x - a):

y - 6 = -1(x - 3)

y - 6 = -x + 3

y = -x + 3 + 6

y = -x + 9

Equation of the side that is parallel to side s is: y = -x + 9.

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write a conditional statement that correctly describes each venn diagram
I REALLY NEED HELP WITH THIS!!!!!!!!!!!!

Answers

if m < A = 40, then it is an acute angle

if 2x = 4, then x = 2

A conditional statement that correctly describes each Venn diagram include the following;

I. If m∠A = 40, then it represent acute angles.

II. If 2x = 4, then x is equal to 2.

What is a conditional statement?

In Mathematics, a conditional statement is a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, a conditional statement typically has the form "if P then Q."

Where:

P and Q represent sentences or statements.

Part I.

Based on the Venn diagram shown in the image above, we can logically deduce the following conditional statement;

"If m∠A = 40, then it represent acute angles."

All acute angles are less than 90 degrees.

Part I.

Based on the Venn diagram shown in the image above, a conditional statement that correctly describes it can be written as follows;

"If 2x = 4, then x is equal to 2."

Proof:

2x = 4

x = 4/2

x = 2

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help
The coordinate grid shows the graph of four equations:

A coordinate grid is shown from negative 12 to positive 12 on the x axis and also on the y axis. Line A passes through the ordered pairs negative 3, 4 and 9, negative 2. Line B passes through the ordered pairs 2, 8 and 8, negative 8. Line C passes through the ordered pairs negative 3, negative 4 and 4, 6. Line D passes through the points 2, negative 2 and 5 and 6.

Which set of equations has (5, 0) as its solution?

A and B
C and D
B and D
A and D

Answers

When you graph the following lines, the set of equations that has (5, 0) as its solution are lines A and B. You can see that both lines passes though the coordinate (5,0). Another way of determining if the given coordinate is a solution to the equation to to establish an equation using these points. In here, i will use the point - slope form.
for line A, we have (-3,4) and (9, -2)
y - y1 = m(x - x1)
y - 4 = (-2 - 4/9 -(-3))(x - (-3))
y - 4 = -(1/2)(x+3)
2y - 8 = -x - 3
2y = -x + 5

substitute (5,0)
2(0) = -5 + 5
0 = 0

A monomial term has the form ax^n where the coefficient is a and the degree is

Answers

The degree is the little number above the x so in this case it would be n.

The answer is "n" ; which is the "exponent value" in the term, "axⁿ " .
________________________________________________________

Which expression is equivalent to (a^8)^4

Answers

[tex](a^8)^4=a^{8*4}=a^{32}[/tex]

The expression [tex](a^8)^4[/tex] is equivalent to [tex]a^{32}[/tex].

The correct option is [tex]a^{32}[/tex].

To simplify the expression [tex](a^8)^4[/tex], we need to apply the exponent rule for raising a power to a power. According to this rule, when we have an exponent raised to another exponent, we multiply the exponents together.

In this case, [tex](a^8)^4[/tex] can be simplified as [tex](a^8)^4[/tex], which equals [tex]a^{32}[/tex]. Therefore, the expression [tex](a^8)^4[/tex] is equivalent to [tex]a^{32}[/tex].

To understand why we multiply the exponents, think of it this way: [tex](a^8)^4[/tex] means we have the base a raised to the 8th power, and that whole expression is raised to the 4th power. When we multiply the exponents, 8 x 4, we get 32. This tells us that we have a multiplied by itself 32 times, which is represented by [tex]a^{32}[/tex].

Therefore, the correct answer is [tex]a^{32}[/tex].

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Solve the triangle. A = 54°, b = 11, c = 8
options:

No triangles possible
a ≈ 13.4, C ≈ 49.6, B ≈ 76.4
a ≈ 13.4, C ≈ 45.6, B ≈ 80.4
a ≈ 9, C ≈ 45.6, B ≈ 80.4

Answers

In this problem, you apply principles in trigonometry. Since it is not mentioned, you will not assume that the triangle is a special triangle such as the right triangle. Hence, you cannot use Pythagorean formulas. The only equations you can use is the Law of Sines and Law of Cosines.

For finding side a, you can answer this easily by the Law of Cosines. The equation is

a2=b2 +c2 -2bccosA
a2 = 11^2 + 8^2 -2(11)(8)(cos54)
a2 = 81.55
a = √81.55
a = 9

Then, we use the Law of Sines to find angles B and C. The formula would be

a/sinA = b/sinB = c/sinC
9/sin54° = 11/sinB
B = 80.4°

9/sin54° = 8/sinC
C = 45.6°

The answer would be: a ≈ 9, C ≈ 45.6, B ≈ 80.4

HELP If f(x)=2x-12, then f^-1(x)=?

Answers

The inverse of f(x) is f^-1(x) is (x+12)/2

which of the following is equal to the rational expression when x does not equal -6

x^2-36 / x+6

A.) x^2-6
B.) x+6
C.) 1/x-6
D.) x-6

Answers

when x does not equal -6

x^2-36 / x+6

(x + 6)(x - 6)
= ------------------ = x - 6
x + 6

answer
D.) x - 6

Final answer:

The rational equation [tex]x^2 - 36 / (x+6)[/tex], when x is not -6, simplifies to x - 6. The correct answer is D.) x - 6.

Explanation:

This is a Mathematics problem related to algebraic expressions and rational expressions. Given the equation [tex]x^2 - 36 / (x+6)[/tex], when x is not equal to -6, we can simplify this equation by factoring. Note that x^2 - 36 is a difference of two squares, which factors into (x-6)(x+6). So we now have [tex](x-6)(x+6) / (x+6).[/tex]

Since x is not -6, we can cancel out the (x+6)s, leaving us with x-6. Therefore, the answer is D.) x - 6. It's important to be careful with the conditions given in the problem, as they can affect the result.

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find the point that splits segment cd in half if point c is located at (-2,4) and point d is located at (3,7)

Answers

the anwser is
x1+x2/2
so
-2+3/2
=1/2
=0.5

Answer: The required co-ordinates of the point are (0.5, 5.5).

Step-by-step explanation: We are given to find the co-ordinates of the point that splits CD in half if point C is located at (-2,4) and point D is located at (3,7).

The point that splits the line segment CD in half will be the mid-point of the segment CD.

We know that

the co-ordinates of the mid-point of a line segment with endpoints (a, b) and (c, d) are given by

[tex]\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]

Therefore, the co-ordinates of the given point that splits CD in half are given by

[tex]\left(\dfrac{-2+3}{2},\dfrac{4+7}{2}\right)=\left(\dfrac{1}{2},\dfrac{11}{2}\right)=(0.5,5.5).[/tex]

Thus, the required co-ordinates of the point are(0.5, 5.5).

Find the measurement of arc AB

45°
60°
90°
180°

Answers

the triangle shown in the middle is a 45-90-45 degree triangle ( the orange lines on the legs mean legs are equal)

so if you were to mirror it there would be 90 degrees between A & B

answer is 90 degrees

Find the length and width of the rectangle if the length is 12 units more then the width and the perimeter is 7 times the width

Answers

L = W + 12
P = 7W = 2L + 2W
7W = 2W + 24 + 2W
3W = 24
W = 8
L = 20

PLEASE HELP!! I WILL GIVE 50 POINTS AND BRAINLIEST ANSWER IF YOU PLEASE JUST HELP ME!!! ITS ONLY 8TH GRADE SO IT SHOULDNT BE THAT HARD!!! PLEASE!!!!! HELP!!!!!!!!
Task 5—Polynomial Division and the Remainder Theorem
Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).
Part 1. Show all work using long division to divide your polynomial by the binomial.
Part 2. Show all work to evaluate f(a) using the function you created.
Part 3. Use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function

Answers

Suppose the quadratic equation is x²+2x+1 and the binomial is x+1.

Part 1. In executing the long division method, you merely use the form like what were taught to in elementary:

Quotient
-------------------------
divisor| DIvidend

But in this case, we deal with polynomials instead of only numbers. The complete solution is

x + 1
-----------------------------
x+1 | x²+2x+1
-x²+x
------------------
0 + x+1
- x+1
-----------------
0
So, the answer is x+1.

Part 2. The quadratic equation is f(a) = x²+2x+1, where a is the constant in the binomial x-1. Thus, a=1. Substituting a to the x values, f(1) = (1)²+2(1)+1=0. The zero means that there is no remainder. Thus, (x+1) is a factor.

Part 3. The remainder theorem works similar to Part 2. If you substitute f(a) and the answer is a non-zero number, then that is the remainder when you divide the quadratic equation with the binomial. Only when the answer is zero that you can confirm that the linear binomial is a factor.

A hybrid car can travel 45 miles on 1 gallon of gas. Determine the amount of gas needed for a 500 mile trip

Answers

they can drive 45 miles on 1 gallon, so divide 500 by 45

500/45 = 11.11

they would need 11.11 gallons of gas

What is the volume of a hemisphere with a diameter of 6 feet to the nearest hundredth of a cubic foot?

Answers

a hemisphere is 1/2 the volume of a sphere

volume of a sphere is 4/3pir^3

so 1/2 of that would be 2/3pir^3

d/2=r
6/2=r=3

v=2/3pi3^3
v=2/3pi27
v=2pi9
v=18pi
aprox
v=56.548667764616278292327580899031 cubic feet
round
v=56.55 cubic feet

The volume the hemisphere is 56. 55 cubic feet

what is the volume of the hemisphere ?

The volume of a hemisphere is the space occupied by the hemisphere.

Formula used to find volume of the hemisphere is :

V = 2/3 × π × r ^3

Given : diameter = 6 feet

r = d/2 = 3 feet

V = 2/3 × π × 3 ^3

⇒ 2/3 × 22/7 × 27

V = 56.5486 cubic feet

round off to nearest hundredth is :

V = 56. 55 cubic feet

Hence , the volume of hemisphere is 56. 55 cubic feet .

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Which graph represents y = |x2| − 3x − 4?

Answers

y = |x²| - 3x - 4. Since the absolute vale of x² is always positive, y will behave the same way as y = x² - 3x - 4.

It's a parabola open upward (a>0) with a axis of symmetry (-b/2a) = 3/2 and y intercept = 4 ( for x=0, y=4).
Moreover x intercepts (roots of the quadratic) → x₁ = 4 and x₂ = -1
All the above correspond to the last graph
Then it's the last graph

The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches. What is the volume of a pyramid with a base area of 15 square inches and a height of 7 inches?

Answers

Answer:

Step-by-step explanation:

The volume of a pyramid with a base area of 15 square inches and a height of 7 inches is 35 cubic inches.

What is Three dimensional shape?

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Suppose the base of the pyramid has length = L units and width = W units, slant height = K units, and the height of the pyramid is of H units.

Then the volume of the pyramid will be

V = (L × B × H) / 3

V = (Base area x H) / 3

The volume of a pyramid varies jointly with the base area of the pyramid and its height.

The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches.

Then the volume of a pyramid with a base area of 15 square inches and a height of 7 inches will be

V = (15 x 7) / 3

V = 35 cubic inches

Hence, the volume of a pyramid with a base area of 15 square inches and a height of 7 inches is 35 cubic inches.

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Two points in the xy plane have cartesian coordinates (2.00, 24.00) m and (23.00, 3.00) m. determine (a) the distance between these points and (b) their polar coordinates

Answers

Final answer:

The distance between the two points is approximately 29.70 m. The polar coordinates of the points are approximately (24.20 m, 1.46 radians).

Explanation:

To find the distance between two points in the Cartesian coordinate plane, we can use the distance formula.

The distance between the points (2.00, 24.00) m and (23.00, 3.00) m is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values, we get:

d = sqrt((23.00 - 2.00)^2 + (3.00 - 24.00)^2)

d = sqrt(441 + 441)

d = sqrt(882)

d ≈ 29.70 m

The polar coordinates of a point (x, y) can be found using the formulas:

r = sqrt(x^2 + y^2)

p = atan2(y, x)

Plugging in the values, we get:

r = sqrt(2.00^2 + 24.00^2)

p = atan2(24.00, 2.00)

r ≈ 24.20 m

p ≈ 1.46 radians

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