Find the inverse function of f informally.
f(x) = x^3 + 8

7.
We are given:
abcissa(x-coordinate) of given point: -6
let's say the ordinate(y-coordinate) of the given point is y
distance of the given point from (1,3) = √74

we can rewrite the given information as:
the distance between the points (-6,y) and (1,3) is √74

finding y:
we know that in order to find the distance between any two points, we use the distance formula, which goes as follows:
distance = [tex]\sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}[/tex]

from the data we are given, let's say that:
(x₁, y₁) = (-6, y)
(x₂, y₂) = (1, 3)
(you can use them interchangably, there is no restriction on which point gets to be labelled as 1)

plugging this in the distance formula, we get:
distance  = [tex]\sqrt{(-6-1)^2 + (y - 3)^2}[/tex]
we are also given that the distance is √74,

√74 = [tex]\sqrt{(-7)^2 + (y - 3)^2}[/tex]

squaring both sides to get rid of the square root

74 = (-7)² + (y - 3)²
74 = 49 + y² + (3)² -2(y)(3)         (using the "square of sum" identity)
74 = 49 + y² + 9 - 6y
74 = 58 + y² - 6y
y² - 6y + 58 - 74 = 0                   (subtracting 74 from both sides)
y² - 6y - 16 = 0
y² - 8y + 2y - 16 = 0                   (splitting the middle term)
y(y - 8) + 2(y - 8) = 0
(y + 2)(y - 8) = 0
which means that:
y + 2 = 0    ,     y - 8 = 0
y = -2 , y = 8
These are the two possible values of y

8.
We are given:
points A and B
A: (3, y)
B: (6, 2)
distance between A and B = 5 units
finding possible values of y
here, we will use the distance formula again to find the value of y
distance formula: [tex]\sqrt{(x_a-x_b)^2 + (y_a - y_b)^2}[/tex]
plugging the given values, we get:
5 = [tex]\sqrt{(3-6)^2 + (y - 2)^2}[/tex]
25 = (3 - 6)² + (y - 2)²              (squaring both sides)
25 = (-3)² + (y - 2)²
25 = 9 + y² + (2)² - 2(y)(2)
25 = 9 + y² + 4 - 4y
y² - 4y + 9 + 4 - 25 = 0            (subtracting 25 from both sides)
y² - 4y - 12 = 0
y² - 6y + 2y - 12 = 0                 (splitting the middle term)
y(y - 6) + 2(y - 6) = 0
(y + 2)(y - 6) = 0

y + 2 = 0   ,    y - 6 = 0
y = - 2  ,   y = 6
These are the two possible values of y

Answer:

this is the first answer

Step-by-step explanation:

hope this helps

Answer:

6 km

Step-by-step explanation:

1 meter = 1/1000 km

(1 meter = 1/1000 km) x 1000

1000 meters = 1 km

6000 meters = ?

1 x 6000m = 1000 x ?

6000 = 1000 x 6

6000/1000 = 1000 x 6/1000

6 = 6

Both sides divided by 1000 are 6, so the answer is 6 km.

Step-by-step explanation:

take all numbers, and add all of the numbers under 25 first, then add the ones over 25, then add the sum of both:

1

17

14

= 32

29

33

= 62

32 + 62 = 94

Answer:

Mary bought 9 Golden Delicious apples

Step-by-step explanation:

This can be solved by setting up a system of equations. Based on the information given, the equations would be set up as follows.

[tex].75d+1.25g=21.00\\d+g=22[/tex]

I prefer to solve using substitution, but elimination can be used as well

[tex].75d+1.25g=21.00\\g=22-d[/tex]

We can now plug in this g value to the first equation

[tex].75d + 1.25 (22-d)=21.00\\.75d + 27.5-1.25d=21\\27.5-0.5d=21\\-.5d=-6.5\\d=13[/tex]

This means mary bought 13 delicious apples. She bought 22 apples in total,  so the total number minus the amount of delicious apples will give us the amount of golden delicious apples.

22 - 13 = g

9 = g

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

Let me know if you have any questions! Spread the love.

Answer:

[tex]3(7b - c)( {c}^{2} + 2)[/tex]

My solved. is on the picture hope it helps brainliest if correct.

Answer:

6. Which displays the properties of the selected object?

a) Timeline

b) Property Inspector Box

c) Tools Panel

d) Stage

7. What is the extension of the Animate CC file ?

a) .mp3

b) .fls

c) .xls

d) .fla

8. This is a list of clear instructions for solving a problem.

a) Algorithm

b) Abstraction

c) Decomposition

d) Analysis

9. This is a diagrammatic representation of steps to solve a problem.

a) Looping

b) Flowlines

c) Flowchart

d) Algorithm

10. The ____ tool is used to draw star shapes.

a) Rectangle

b) Oval

c) Square

d) Polygon

Answer:

$33

Step-by-step explanation:

75% profit = 44 x 75% = $33
So, he will need to raise it by $33 to make a 75% profit
New price : #77

Check : If he sell it for $77, he makes a $33 profit, which is 75% of $44.

Answer:

C. f(x)=sin(x)

Step-by-step explanation:

Graphed each equation on desmos to see which one matched your image.

Good luck with your work, edge is the worst xD

The principal investment required to get a total amount of $240,000.00 from compound interest at a rate of 4.6% per year compounded 12 times per year over 20 years is $95,812.95.

Given Data

Interest Rate r= 4.6%

Final Amount A =  $240,000

Time T = 20 years

Answer:

P = $95,812.95

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 4.6/100

r = 0.046 per year,

Then, solve the equation for P

P = A / (1 + r/n)^nt

P = 240,000.00 / (1 + 0.046/12)^(12)(20)

P = 240,000.00 / (1 + 0.003833333)^(240)

P = $95,812.95

Learn more about compound interest here:

https://brainly.com/question/24924853

Answer:

C) 500.83

Step-by-step explanation:

Surface area for a cylinder formula:

SA = 2πrh + 2πr²

Given:

d = 11

r = d/2 = 11/2 = 5.5

h = 9

Work:

SA = 2πrh + 2πr²

SA = 2(3.14)(5.5)(9) + 2(3.14)(5.5)²

SA = 310.86 + 2(3.14)(30.25)

SA = 310.86 + 189.97

SA = 500.83

Answer:

Step-by-step explanation:

2n + 7n + 8 = n + 8

9n + 8 = n + 8

9n = n

n = 0

Answer:

n = 0

Step-by-step explanation:

2n + (7n + 8) = n + 8

2n + 7n + 8 = n + 8

9n + 8 = n + 8

9n -n = 8 - 8

8n = 0

n = 0

Answer:

12 cups

Step-by-step explanation:

You multiply the the quarts amount by 4

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

[tex]m = \frac{rise}{run} = \frac{y2 - y1}{x2 - x1} [/tex]

please like

Answer:

  undefined

Step-by-step explanation:

Slope is a measure of the vertical change relative to the horizontal change. On an x-y graph, it will be the difference in y-coordinates divided by the corresponding difference in x-coordinates. It is often referred to using the letter m.

  m = (y2 -y1)/(x2 -x1) . . . . . slope of line between points (x1, y1) and (x2, y2)

It does not matter which points you call point 1 and point 2.

__

For the points given on the graph we can compute the slope to be ...

  m = (2 -(-3))/(-1 -(-1)) = 5/0

The zero in the denominator makes this value "undefined." So, we say the slope of any vertical line is "undefined."

The equation for the area in terms of x gives the function David should

use to maximize the area.

Response:

The equation that David should use to help him maximize the area is option A.

The given parameter are;

Length of fencing David has = 400 yards

Area to be enclosed = Rectangular area with pre-existing fence (on one side)

Required:

The equation David should use to maximize the area.

Solution:

Let x represent the width of the area (the sides perpendicular to the pre-

existing fence), and let y represent the length of pre-existing fence

We have;

Length of fencing available = Opposite side to pre-existing fence + 2 × Width of the area

Opposite side to pre-existing fence = Length of pre-existing fence

Which gives;

Length of fencing available = Length of pre-existing fence + 2 × Width of the area

400 = y + 2·x

y = 400 - 2·x

Area = Length × Width

Which gives;

Area = y × x

Area as a function of x is therefore;

Area, f(x)= (400 - 2·x) × x

Which gives;

The correct option is therefore;

Learn more about writing equations here:

https://brainly.com/question/1461621

Answer:

C. x=12

Step-by-step explanation:

Angles in a triangles add up to 180 degrees. We are given that one angle is a right angle which means it's 90 degrees so...

2x+1+5x+5+90=180

Add like terms

96+7x=180

Subtract 96 from both sides

7x=84

Divide both sides by 7

x=12

Answer:

12, -4, -8

Step-by-step explanation:

1) c=12

c+3=15 subtract 3 from each side. c=12

2) b= -4

-7+b=-11 add 7 to each side. b = -4

3) d= -8

-4d=32 divide each side by negative 4. d = -8

Answer:

6 m

Step-by-step explanation:

Side = x

Surface area = [tex]6x^2[/tex]

[tex]6x^2 = 216[/tex]

[tex]x^2 =36[/tex]

x = 6

The answer is 6m

Hope this helps :)

Have a nice day!

The side length of the cube is calculated as 6m

Data;

The surface area of a cube is given as

[tex]A = 6x^2[/tex]

This indicates all the six sides in the cube.

Let's substitute the values and solve for x

[tex]A = 6x^2\\216 = 6x^2\\\frac{216}{6} =\frac{6x^2}{6} \\x^2 = 36\\x= \sqrt{36} \\x = 6[/tex]

The side length of the cube is calculated as 6m

Learn more on surface area of a cube here;

https://brainly.com/question/9573057

Step-by-step explanation:

"find" ?

the equations are already there.

do you mean solve in the sense of finding the zero points of the equations ?

if so,

the general solution of a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

3(3x² + 1) = 12x

9x² + 3 = 12 x

9x² - 12x + 3 = 0

a = 9

b = -12

c = 3

x = (12 ± sqrt(144 - 4×9×3))/18 = (12 ± sqrt(144-108))/18 =

= (12 ± sqrt(36))/18 = (12 ± 6)/18

x1 = (12 + 6) / 18 = 18/18 = 1

x2 = (12 - 6) / 18 = 6/18 = 1/3 = 0.3333333...

9y² - 12y - 14 = 0

same thing, we just use y instead of x.

a = 9

b = -12

c = -14

y = (12 ± sqrt(144 - 4×9×-14))/18 = (12 ± sqrt(144+504)/18 =

= (12 ± sqrt(648))/18 = (12 ± sqrt(324×2))/18 =

= (12 ± 18×sqrt(2))/18

y1 = (12 + 18×sqrt(2))/18 = 12/18 + sqrt(2) = 2/3 + sqrt(2) =

= 0.942809042...

y2 = (12 - 18×sqrt(2))/18 = 12/18 - sqrt(2) = 2/3 - sqrt(2) =

= -0.747546896...

Answer:

Alright breakdown

Step-by-step explanation:

#7. Constant of Proportionality.

divide the 276 by the 184: 276 / 184

which will give you an answer: 1.5

now, multiply 208 by 1.5: 312

Answer: YES

#8 same context, 300 / 425: 0.70

680 x 0.70 : 476

Answer NO

Answer:

x = 10

Step-by-step explanation:

Isolate the variable and get x by itself

4x^2 -400 = 0      add 400 to both sides

4x^2 = 400     divide both sides by 4

x^2 = 100.      take the square root of both sides

x = 10

Answer:

800g

Step-by-step explanation:

10% of x = 80 g

x = 80 x 10

x = 800g

Answer:

Vertex: (0, -4)

Graph: I can't share a link so you can go to desmos and paste your equation

Step-by-step explanation:

the vertex is where the axis of symmetry meets with the parabola.

The axis of symmetry is (-b)/(2a) which equals 0 because there is no linear x value

therefore,

y=3(0)^2-4

=-4

so the vertex is (0, -4)

to find the other points, list two x values larger than 0 and substitute into the equation to find y

list two x values smaller than 0 and substitute to find the points on the left of the vertex.

Answer:

8g³

Step-by-step explanation:

(2g)³ = 2³·g³

Answer:

54 degrees
54 degrees
72 degrees

or

54 degrees
63 degrees
63 degrees

an isosceles triangle has 2 equal angles, and the angles of a triangle always add up to 180 degrees

Step-by-step explanation:

[tex]225 \times \frac{\pi}{180} = 3.927 \: radianes[/tex]

Answer:

If john as 5 apples and has 6 friends That what an apple. How many apples will everybody get.

Step-by-step explanation: