Question 14 of 40
Which function is the inverse of y=2/3 x-6?
A. y=3/2x-1/6
B. y=2/3x+6
C. y=2/3x+4
D. y=3/2x+9

The average rate of change of the function is: 0

You should know that average rate of change is also referred to as the slope of the function

At point where x = -8, the value of f(-8) = -10 and

At x = -1, the value of f(-1) = -10

We have to determine the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -1.

When x₁ = -8, f(x₁) = f(-8) = -10 also

when x₂ = -1, f(x₂) = f(-1) = -10

This implies that

Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]  

                     = [f(-1) - f(-8) ] / [-1-(-8)]

                     = [-10 - (-10)] / [-1+8]

                     = [-10 + 10] / 7

                     = 0 / 7

                     = 0

In conclusion, 0 is the average rate of change which is also the slope of the function

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Answer:

49 ft tall

Step-by-step explanation:

Using a ratio

7 is to 3 as      height is to    21 ft

7/3 = height / 21

height = 21 * 7/3 = 49 ft tall

Answer:

70

Step-by-step explanation:

On Tuesday, the balance in your bank account is $40.

Since from Wednesday to Friday you withdraw $10 a day, keep adding $10 to each day.

On Wednesday the balance is $40 + $10 = $50

On Thursday the balance is $50 + $10 = $60

On Friday the balance is $60 + $10 = $70

The balance in your bank account at the end of the day on Friday is $70

Answer:

18.78

Step-by-step explanation:

100_60÷100×46.95=18.78

Answer:

Step-by-step explanation:

First, I will convert the decimal as a fraction or decimal, whichever one you prefer. I did fraction. So, -3.5 is the same as -7/2.

Second, for fraction multiplication, you will multiply the numerator and then the denominator.

[tex]\frac{-7 times -7}{8 times 2} = \frac{49}{10}[/tex]

Third, we will convert the improper fraction to a mixed fraction by using long division 49 divided by 16 = 3R1.

3 WILL BE YOUR WHOLE NUMBER. 1 IS YOUR NUMERATOR AND 16 IS YOUR DENOMINATOR.

The Answer is 3 [tex]\frac{1}{16}[/tex]. Letter D

4.8 fl oz is the amount of water that is used by Sofia to make the slime

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Given that:

Sofia is making a bath of slime using a recipe that includes glue, water, and a salt solution. She uses 7.5 fl oz of glue.

The amount of glue is 12.5 times the amount of salt solution.

There are 4.2 less fluid ounces of salt solution than water.

We can set up equations using the three statements:

Let G,  S and W represent glue, salt solution and water respectively

G = 7.5

G = 12.5S

S = W - 4.2

Since G = 7.5, we can write:

7.5 = 12.5S

S = 7.5/12.5 = 0.6

S = W - 4.2

0.6 = W - 4.2

W = 0.6 + 4.2

W = 4.8

Thus, the amount of water that is used by Sofia to make the slime is 4.8 fl oz.

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Complete Question

Sofia is making a batch of slime using a recipe that includes glue, water, and salt solution. She uses 7.5 fl. oz of glue. The amount of glue is 12.5 times the amount of salt solution. There are 4.2 less fluid oz of salt solution in the water. How many fluid ounces of water does Sofia use to make a batch of slime?

The equation of the line of best fit for this data-set is given as follows:

y = 10x + 60.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the coefficients are given as follows:

The function goes through point (0,60), hence the intercept b of the line of fit is given as follows:

b = 60.

When x increases by 2, from 0 to 2, y increases by 20, from 60 to 80, hence the slope m is obtained as follows:

m = 20/2 = 10.

Hence the line of fit is given as follows:

y = 10x + 60.

Meaning that the third option is correct.

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Answer:

y = 10x + 60.

Step-by-step explanation:

Answer:

When two lines intersect each other at a single point, linear pairs of angles are formed. If the angles so formed are adjacent to each other after the intersection of the two lines, the angles are said to be linear. If two angles form a linear pair, the angles are supplementary, whose measures add up to 180°.

Answer:

2nd choice

Step-by-step explanation:

m/54.2 = 82.5/271

Cross multiply:

m(271) = (82.5)(54.2)

m = 4471.5/271 = 16.5

The total number of different ways in which the ribbons can be awarded is 24,024 ways, so the third option is the correct one.

There is a competition with 14 dogs, and there are 4 prizes for the dogs.

To find the number of ways in which the ribbons (prizes) can be awarded, we need to take the product between the numbers of options for each.

For example for the blue ribbon (first prize) there are 14 dogs to select, so there are 14 options.

For the red one there are 13 options (because one dog is already selected for the blue ribbon).

For the yellow one there are 12 options.

For the white there are 11 options.

Then the total number of different combinations is:

C = 14*13*12*11 = 24,024

Thus, the third option is the correct one.

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Answer:

------------------------------------------

Initial volume of gas was 4 gallons.

The volume of gas pumped into tank after s seconds was:

The total volume of gas become:

The slope of the equation y = 4x + 8 is 4 and the y-intercept is 8.

The slope of a line is the change in the dependent variable with respect to the change in the independent variable.

The slope is rise over run.

Therefore, the equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Hence,

y = 4x + 8

Therefore, the slope is 4 and the y-intercept is 8

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For exponential equation a^1/n = r option D is true i.e. r^n=a.

What are exponential equations?

Exponents are used in exponential equations, as the name implies. We already know that the exponent of a number (base) specifies how many times the number (base) has been multiplied. But what happens if a number is variable? When the power is a variable in an equation, it is referred to as an exponential equation.

For example, 3^x = 81, 5^x - 3 = 625, 62^y - 7 = 121, etc are some examples of exponential equations.

Exponential equations are classified into three categories. These are :

As given,

                 a^1/n=r

Now we take 1/n from left side of exponential equation to right side i.e.

      a=r^n   (As a^1/2 = 4 ---> a=4^2)

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Answer:

V = 157 in³

Step-by-step explanation:

the volume (V) of a cone is calculated as

V = [tex]\frac{1}{3}[/tex] πr²h ( r is the radius and h the height )

here diameter = 10 , then r = 10 ÷ 2 = 5 , then

V = [tex]\frac{1}{3}[/tex] × 3.14 × 5² × 6 ( cancel 3 and 6 by 3 )

  = 3.14 × 25 × 2

 = 3.14 × 50

= 157 in³

The ratio of the shapes' perimeters and areas are 2/3 and 4/9 respectively

In order for two shapes to be similar, the corresponding angles of the shapes must be congruent and the ratios of corresponding sides must be equal.

If the two shapes are similar, then the ratio of their perimeters will be equal to the ratio of the corresponding side lengths, and the ratio of their areas will be equal to the square of the ratio of the corresponding side lengths.

Thus, in this case, we have:

Ratio of perimeter = 12/18 = 2/3

Ratio of area = 12²/18² = 4/9

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5. If  Jackson bought an ultra-slim Television. The size of this screen is 17.69.

6.  If the ramp has a 550 incline and the height of the ramp is 15m. The height of the ramp is -68.24.

5. Size of the screen

Pythagorean theorem

c²= a² + b²

c² = 12² + 13²

c²= 144+169

c = √313

c = 17.69

6. Height

Using SOH CAH TOA

sin550= 15/x

x= 15/sin550

x= 15/-0.2195

x= -68.24

Therefore the size is 17.69  and the height is -68.24.

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The expression of the numbers as negative or positive is as follows;

6. ¹/₄

7. -15 yards

8. +6 pounds

9. +535 pounds

10. -9 degrees.

11. -²/₃ of the crowd

12. +$20

13. -10 points

14. -570

15. - ½

11. -350 feet

12. -500 miles

13. +10 feet

14. -13 degrees

15. + 20 miles

We can express numbers in this regards as either positive or negative with a positive number indicating a gain while a negative number indicates a loss.

Thus;

6. One-fourth of the students brought their hunch to school is expressed as; ¹/₄

7. After the penalty, there was a loss of 15 yards on the play is expressed as; -15 yards

8. He gained 6 pounds of muscle is expressed as; +6 pounds

9. He made a 535 deposit into a bank account is expressed as; +535 pounds

10. The temperature was 9 degrees below zero is expressed as; -9 degrees.

11. Two-thirds of the crewed left the stadium is expressed as; -²/₃ of the crowd

12. She received $20 on her birthday is a gain and expressed as; +$20

13. The student lost 10 points on the final exam is a loss and expressed as; -10 points

14. He made a 570 withdrawal from a bank account is a loss and is expressed as; -570

15. One-half of the gallon of milk is gone is a loss and is expressed as; - ½

Write the number that represents the given scenario. (DOK 1)

11. A submarine is 350 feet below sea level is negative and is expressed as; -350 feet

12. The family traveled 500 miles south on a road trip is in the negative y-axis and is; -500 miles

13. A rabbit hops 10 feet forward is positive movement and is; +10 feet

14. The temperature dropped 13 degrees is a loss and is expressed as -13 degrees

15. A hot air balloon traveled 20 miles north is in the positive direction and is expressed as; + 20 miles

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Answer:

≈ 113.16

Step-by-step explanation:

The circumference of a circle (the distance around) is equal to [tex]\pi[/tex] * diameter

[tex]\pi * diameter = 37.7[/tex]

[tex]\frac{\pi }{\pi } *diameter = \frac{37.7}{\pi }[/tex]

diameter = 12.006

radius = diameter / 2

radius = 6.003

The area of a circle is [tex]\pi r^{2}[/tex]

[tex]\pi 6.003^{2}[/tex]

= 113.16

Answer: The solution for k is -3/4.

To solve the equation, you can follow these steps:

Add 10k to both sides of the equation: -6k - 10 = 10 - 10k becomes -6k = 20

Divide both sides by -6: -6k/-6 = 20/-6 becomes k = -3/4

Step-by-step explanation:

Answer: 7 and 6

Step-by-step explanation: 7 x 6 = 42

The answers are given below.

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given:

1) 2Sin(9θ).Cos(5θ)=1/2(Sin14θ+Sin4θ)

2) Sin(3θ)Sin(5θ)Cos(3θ)Cos(5θ)=1/2(Sin8θ+Sin2θ)

3)Cos6θ+Cos4θ=2Cos5θCosθ

4)Sin(13θ/2)+Sin9θ=2Sin(11θ/2)Sinθ

5)Cosθ=2√5/5

6)Cos2θ=23/2

7)Tan(π/12)=2-√3

8)Sin(165°)=√6-√2 /4

9)Cos(5π/18)Cos(2π/9)-Sin(5π/18)Sin(2π/9)=Cos(π/2)

                                                                      =0

Hence, these are the answers .

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The volume of the cylinder is 169.7. (Option C)

Based on the provided information, let the radius of the cylinder be r and diameter of the cylinder be 2r. The diameter and height of the circular cylinder is the same. When examining the cross section of the cone and cylinder, there are two similar triangles. Hence,

(15 – 2r)/15 = r/5

5(15 – 2r)= 15r

75 – 10r = 15r

r = 3

Volume of the cylinder = πr^2h where r is the radius of the cylinder and h is the height of cylinder. As h = 2r, Hence,

V = πr^2(2r) = (22/7)(3^2)(6) = 169.7

Note: The question is incomplete as the options are incorrect. The correct options are A) 127.5 B) 151.6 C) 169.7 D) 168.5

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As per the given dimensions of cone in the figure, the Lateral area for the given cone is 123.15 [tex]in^2[/tex] and the surface area is 173.41[tex]in^2[/tex].

A cone is a characteristic three-dimensional geometric shape with a smooth and curving surface that is directed upward ,in mathematics.

What is the lateral surface area of a cone?

The area that the cone's curved surface covers is known as the lateral area of the cone. It is also known as the cone's curved surface area (CSA) or lateral surface area (LSA).

To solve the given question, we first need to use the pythagorus theorem in triangle made by the lateral slant height, actual height and the radius of the given cone,

Hence the pythagorus theorem gives,

[tex]9.8=\sqrt{h^2+4^2}[/tex]where h is the height of the cone.

Now Using the formula for Lateral surface area of the cone,

LSA = [tex]\pi *r=\sqrt{h^2+4^2}[/tex] where , h is height and r =4 in

Hence LSA = 123.15  [tex]in^2[/tex]

Again, Using the formula for Surface area of a cone,

SA = [tex]\pi *r(r+\sqrt{r^2+h^2}[/tex] , where h is height of cone and r = 4in

Hence , SA =  173.41 [tex]in^2[/tex].

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Answer:

Step-by-step explanation:

We will have to convert this to vertex form.

First we add y to both sides.

y = 3x^2 + 9x - 3

The vertex form is y = a(x – h)^2 + k

y = 3(x^2 + 3x) - 3

We need to complete the square now, and half if 3 is 1.5, and 1.5^2 is 2.25, so we add 2.25 inside the parentheses but we have to be careful, because if we subtract 2.25 from outside the parentheses it wouldn't work because the 2.25 inside the parentheses is being multiplied by 3, so we have to subtract 2.25*3=6.75 from the outside.

y=3(x^2 + 3x + 2.25) - 9.75

we can simplify this now to

y=3(x + 1.5)^2 - 9.75

and now this is vertex form. From here it is incredibly easy to get the vertex. Just take the x value required to make the total in the parentheses zero, so in this problem it would be -1.5 (Because (-1.5+1.5)^2 is zero) and then you have your x coordinate. From there we just take k, which in this problem is -9.75, and it is the y value of our vertex.

In conclusion, the vertex is (-1.5. -9.75)

Answer:

We use decimals every day while dealing with money, weight, length, etc. Decimal numbers are used in situations where more precision is required than whole numbers can provide. For example, when we calculate our weight on the weighing machine, we do not always find the weight equal to a whole number on the scale.

Step-by-step explanation:

Hope this helps!

Answer:

Line ZL and line LZ.

Step-by-step explanation:

Since it is a line (because a line needs to have two or more points to be able to graph), it can be represented in two ways. The first being ZL, and the second being LZ.

Brainliest please.

Answer:

Step-by-step explanation

Oh

Answer:

48% of students picked a vanilla cupcake

Step-by-step explanation:

We can get 48% from this question by turning this data into a fraction

27 students picked vanilla out of a total amount of 50

= 27/50

= 48%

This equals a percentage of 48% of students picking a vanilla cupcake

Answer:

48%

Step-by-step explanation:

The missing side in the triangle is 13 units which is the hypotenuse. The values of sine, cosine, and tangent of the referenced angle are 5/13, 12/13, and 5/12 respectively.

Trigonometry is the branch of mathematics that deals with particular functions of angles and how to apply them in calculations. There are six widely used angles-related trigonometric functions. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant(csc) are their respective names and acronyms.

In the given triangle the reference angle is θ.

So, the adjacent side (P) has a length of 12 units. The opposite (B) is the side having a length of 5 units. So, the hypotenuse will be

Then, acc to Pythagoras theorem, the hypotenuse (H) will be

H² = P² + B²

H² = 5² + 12²

H² = 25 + 144

H² = 169

H = √169

H = 13 units

This is the missing side of the given triangle.

The sine is

sinθ = opposite/ hypotenuse

= 5/13

cosθ = adjacent/ hypotenuse

= 12/13

tanθ = opposite/ adjacent

= 5/12

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Answer:0.39685026299

Step-by-step explanation:

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