Which function represents the inverse of function f?

Answer:

m = -3

b = 9

y = -3x + 9

Step-by-step explanation:

Let us solve the question

∵ The line passes through points (4, -3) and (3, 0)

∵ The rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex]

∵ (x1, y1) and (x2, y2) are 2 points on the line

∴ x1 = 4 and y1 = -3

∴ x2 = 3 and y2 = 0

→ Substitute them in the rule of the slope to find it

∵ m = [tex]\frac{0--3}{3-4}[/tex] = [tex]\frac{0+3}{-1}[/tex] = -3

∴ m = -3

∵ The form of the equation of the line is y = m x + b

→ Substitute the value of m in the form of the equation.

∴ y = -3x + b

→ To find b substitute x and y by the coordinates of the point (3, 0) or (4, -3)

∵ x = 3 and y = 0

∴ 0 = -3(3) + b

∴ 0 = -9 + b

→ Add 9 to both sides

∴ 9 = b

∴ b = 9

→ Substitute the value of b in the equation

∵ y = -3x + 9

∴ The equation of the line is y = 3x + 9

Answer:

200

Step-by-step explanation:

Answer: Since flipping a coin and rolling a 6-sided die are independent events ,thus the probability of getting head and an even number is just the product of the individual probability of events.

Let A be the event of getting a head ,and B be the event of getting an even number on die.

therefore, P(A and B)=P(A) P(B)=(1/2)*(3/6)=1/4=0.25.

Answer:

She draw 40 flowers

Step-by-step explanation:

Given

[tex]Length = \frac{1}{5}m[/tex]

[tex]Flower = \frac{1}{200}m[/tex]

Required

Determine the number of flowers

To do this, we simply divide the length of the border by the length of the flower.

[tex]Number = \frac{1}{5}/ \frac{1}{200}[/tex]

Convert to multiplication

[tex]Number = \frac{1}{5}* \frac{200}{1}[/tex]

[tex]Number = \frac{200}{5}[/tex]

[tex]Number = 40[/tex]

Hence, she draw 40 flowers

Answer:

6 1/2

Step-by-step explanation:

Answer:

6.5 quarts.

Step-by-step explanation:

This is rather simple math because 2 pints equal 1 quart. You divide 13 by 2, which is an uneven number so you are guaranteed a half, and you get 6.5

                                               Question 1)

Given the points

Finding the slope between (3, 5) and (3, -6)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [-6 - 5] / [3 - 3]

               = -11 / 0

               = undefined or ∞

Thus, the slope of the line = m = undefined.

Note: The undefined slope means the line is vertical.

                                            Question 2)

Given the points

Finding the slope between (-6, 2) and (8, 2)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [2 - 2] / [8 - (-6)]

               = 0 / 14

               = 0

Thus, the slope of the line = m = 0.

Note: The zero slope means the line is horizontal.

Answer:

Equation of line best fits the scatter plot is y = [tex]-\frac{30}{7} x + 108[/tex]

Step-by-step explanation:

Let the equation of line be y = mx + c

where m = slope of line and c is the intercept on y -axis

from the graph intercept on y-axis is 108

and the slope of line is given by m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] where ([tex]x_2,y_2[/tex]) and ([tex]x_1,y_1[/tex]) is the points on line

let, points be (4,96) and (18,36)

on calculating this m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = [tex]-\frac{30}{7}[/tex]

Therefore equation of line best fits the scatter plot is y = [tex]-\frac{30}{7} x + 108[/tex]

Answer: a. Each term in Bill's pattern is twice the value of the corresponding item in Jan's pattern.

Step-by-step explanation:

Jan created a pattern by adding 3 and Bill created a pattern by adding 6.

6 is twice the value of 3 so Bill's terms will be twice the value of Jan's corresponding terms as well.

To prove it:

12 is twice the value of 6

18 is twice the value of 9

24 is twice the value of 12

Answer:

a+b = 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

3(a + b)^2 = 81

(a + b)^2 = 27

a + b = sq rt 27

a + b = [tex]\sqrt{9}[/tex]· [tex]\sqrt{3}[/tex]

a + b = 3[tex]\sqrt{3}[/tex]

Answer:

10) The first 2 on the left are functions and the one on the top right is a function, but the bottom right is not.

11) Domain = (2, 8, -1, 0) Range = (5, -2, 4, 5)

Answer:

14.3%

Step-by-step explanation:

6400-5600=800

800/6400×100=14.3

Answer:

14.3

Step-by-step explanation:

Answer:

it's 7 divided by 10

transfer the 0 up and make it 0.7

Answer:

A

Step-by-step explanation:

180⁰= a+b+81⁰

a=180⁰-117⁰=63⁰

b=180⁰-63⁰-81⁰=36⁰

y=4

Step-by-step explanation:

cube root 64

Answer:

37.7m

Step-by-step explanation:

Triangle ABC is shown. DE is a straight line with D on AC and E on BC AB = 46m, EC = 18m, CD = 29m and ED = 20m. Calculate the length AD.

We solve using Similarity Theorem

BA/AC =BD/DC

46/AD+29 = 20/29

Cross Multiply

46 × 29 =20 (AD + 29)

1334 = 20AD + 580

20AD = 1334 - 580

20AD = 754

AD = 754/20

AD = 37.7m

Answer:

32 cubes

Step-by-step explanation:

I would first determine the volume in inches of the rectangular prism.

V = 1/3 x 2/3 x 2/3 = 4/27 cubic inches.

Then I would calculate the volume of the cube with 1/6 inch sides

V = 1/6 x 1/6 x 1/6 = 1/216 cubic inches.

Then I would divide the V of the large prism by the V of the small cube

(4/27) / (1/216) = (4/27) * (216/1) = 32 cubes

Answer:

x = 66.5

x + 1 = 67.5

x + 2 = 68.5

x + 3 = 69.5

x + 4 = 70.5

x + 5 = 71.5

x + 6 = 72. 5

x + 7 = 73.5

x + 8 = 74.5

x + 9 = 84.5

Step-by-step explanation:

Given that :

Age of 10 friends are consecutive integers :

Let the ages be :

x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, x+9

The sum of their ages = 710

Hence,

x + x+1 + x+2 + x+3 + x+4 + x+5 + x+6 + x+7 + x+8 + x+9 = 710

10x + 45 = 710

10x = 710 - 45

10x = 665

x = 665 / 10

x = 66.5

x + 1 = 67.5

x + 2 = 68.5

x + 3 = 69.5

x + 4 = 70.5

x + 5 = 71.5

x + 6 = 72. 5

x + 7 = 73.5

x + 8 = 74.5

x + 9 = 84.5

Answer:

I think

y=1/3x-10/3

Step-by-step explanation:

Perpendicular Lines mean they have the negative reciprocal slope. This line has slope m = -1/3 so the perpendicular line has slope m = + 1/3

Our point is (3, 5)

Now use point slope form to find the equation: (y - y1) = m(x - x1)

(y - 5) = m(x - 3)

(y - 5) = 1/3(x - 3)

y -5=1/3x-10/3

9514 1404 393

Answer:

  p = 192

Step-by-step explanation:

p/8 +12 = 36 . . . . . given

p/8 = 24 . . . . . . . . .subtract 12

p = 8·24 . . . . . . . . .multiply by 8

p = 192

9514 1404 393

Answer:

Step-by-step explanation:

The linear pair at G totals 180°, so we have ...

  x + 2x = 180

  3x = 180 . . . . . collect terms

  x = 180/3 . . . divide by 3

  x = 60

__

The total of angles in the triangle is 180°, so ...

  x + y + 70 = 180

  60 + y + 70 = 180 . . . . substitute for x

  y = 180 -130 . . . . . . . . . subtract 130

  y = 50

Answer:

Isosceles and right triangle

Answer:

5/64 of a cup.

Step-by-step explanation:

Is there two columns of data and two data points? Like this:

Strawberries          Water

384                         30

320                         25

If so, then there are two ways to do it.

1) You can set up a ratio like this

384/30 = 1/x

Where x is the number of cups of water for 1 strawberry.

So,

x = 30/384 of a cup

x = 5/64 of a cup.

2) Look at the increase from one to the other.

64 strawberries requires 5 cups of water

Divide by 5 by 64 to get the water for one strawberry

5/64 of a cup.

Answer:

You can't find the area or perimeter with the information given. If this is a calculus level problem then it is possible.

Answer:

1) 63

2) 49

3) 87

4) 44

Step-by-step explanation:

Answer: 1,71572875

Step-by-step explanation: (4+2rad2)/3+2rad2

Answer:

6

Step-by-step explanation:

1/p = 1/(3 + 2sqrt2)

Multiplying by the conjugate (which you should pretty much always do to simplify), we get

(3-2sqrt2)/((3+2srqt)(3-2sqrt2))

which is

(3-2sqrt2)/(9-8) = 3-2sqrt2.

Therefore p + 1/p = 3+2sqrt2 + 3 - 2sqrt2 = 6