If FX) = 3x+6, which of the following is the inverse of Fx)?
A. F1(x) = 6 - 3x
B. F1(x) = 3x - 6
C. F'(x) = x - 6 / 3
D. F'(x) = x - 3 / 6

The equation of the graph in the required form is y = 5|x| - 5

From the question, we have the following parameters that can be used in our computation:

The graph (see attachment)

The graph is an absolute value graph

And it can be expressed in the form of y = a|x – h| + k

Where

Vertex = (h, k)

The vertex of the graph is (0, -5)

So, we have

y = a|x| - 5

Using the point on the graph, we have

a|1| - 5 = 0

So, we have

a = 5

This means that the equation of the graph is y = 5|x| - 5

Read more about absolute value function at

https://brainly.com/question/10538556

#SPJ1

Answer:

0

Step-by-step explanation:

0

The solution has been explained below.

We will use the following equation, x² + y² = 81, where x and y are the pool's dimensions in feet, to determine the necessary estimations for the pool project.

1. Calculate the pool's diameter and radius:

We can infer that the radius of the pool is equal to the square root of 81 because the equation depicts a circle. As a result, r = 81 = 9 ft.

The pool's diameter is simply equal to twice its radius, or d = 2r = 18 feet.

2. Calculate the amount of water in the pool:

Since the pool is 4 feet high, we can determine its volume by multiplying the area of its circle-shaped base by the height.

The formula A = πr² can be used to calculate the area of the pool's base,

Therefore, V = Ah = πr²h = 1017.87 cubic feet represents the volume of water in the pool.

3. Determine the pool's total material cost:

There are 7.48 gallons in a cubic foot and a gallon of water costs $0.22.

As a result, Cw = V × 7.48 × 0.22 = 1017.87 × 7.48 × 0.22 = $1,619.72 is the entire cost of water for the pool.

If the radius of the pool is $185 per foot, then the cost of the materials is Cm = r × 185 = 9 × 185 = $1,665.

4. Calculate the pool's total labour hours:

A pool's construction is estimated to take 2.5 hours for every foot of its radius.

So, L = r × 2.5 = 9 × 2.5 = 22.5 hours of labour would be needed to complete this pool.

5. Calculate the total cost of labour for the project:

If you pay someone $19 per hour, Cl = L × 19 = 22.5 × 19 = $427.5.

6. Find the project's overall cost:

The project's overall cost is the product of its labour and material costs:

Cost as a whole equals Cm + Cw + Cl, which is 1,665 + 1,619.72 + 427.5, or $3,712.22.

In conclusion, the pool has an 18-foot diameter and a 9-foot radius according to the supplied equation. There are roughly 1017.87 cubic feet of water in the pool. Water and building supplies are included in the pool's projected material cost of $3,284.72. 22.5 hours of labour in total are needed, with a labour cost estimate of $427.5. Consequently, $3,712.22 is the expected final cost of the pool renovation.

Learn more about functions click;

https://brainly.com/question/31062578

#SPJ1

Answer:

Step-by-step explanation:

(-8 - 0)/(-4 - 8)= -8/-12 = 2/3

The slope of the line that passes through the points (8, 0) and (-4, -8) exists at 0.66667.

The slope or gradient between two points in the Cartesian coordinate system. The slope exists the amount of slant a line retains and can maintain a positive, negative, zero, or undefined value.

Using the slope formula \((y_2 - y_1)/(x_2 - x_1)\)

\(x_1 = 8, y_1 = 0\) and \(x_2 = -4 , y_2= -8\)

slope \(= (y_2 - y_1)/(x_2 - x_1)\)

= ((-8) - 0) / ((-4) - (8))

= (-8) / (-12) = (-2) / (-3)

= 0.66667

Therefore, the slope of the line that passes through the points (8, 0) and (-4, -8) exists at 0.66667.

To learn more about the slope of the line refer to:

https://brainly.com/question/16949303

#SPJ9

Answer:

A

Step-by-step explanation:

Trust me it's correct.

You are solving for the system of equations.

Answer: 112 degrees

Step-by-step explanation:

The angles have the same measure because of the corresponding angles theorem.

\(\huge\boxed{112^\circ}\)

To solve this problem, we need to understand the basic rules of transversals across parallel lines.

When a line crosses another line or lines, it is a transversal.

When the two lines it crosses are parallel, the eight angles formed have interesting properties that we can use.

For this question, we will look at corresponding angles. If two angles meet these two conditions, they are congruent:

These two conditions are met for \(\angle JIK\) and \(\angle GFI\), so they are congruent and their measures are equal.

This means that \(m\angle JIK=m\angle GFI=\boxed{112^\circ}\)

=================================================

Explanation:

There are B = 3+5+4 = 12 marbles total, of which A = 12-5 = 7 are not black. Or you could note that we have A = 3 red + 4 white = 7 marbles that are not black.

The probability of selecting a non-black marble is A/B = 7/12

7/12 = 0.5833 = 58.33% approximately

she could have scored the 10 points in 302400 ways.

The given parameters are

n= total points =10

r1 =one-point free throw = 1

r2 = two-point field goals = 2

r3 =  three-point field goals = 3

The number of ways (k) she could have scored the points is:

k=(n!)/(r1!×r2!×r3!)

The factorial function is a mathematical formula represented by an exclamation mark "!".

k= 10!/(1!×2!×3!)

k= 3628800/(1×2×6)

k= 302400

so.. she could have scored the 10 points in 302400 ways.

To learn more about Combinations

visit : brainly.com/question/15301090

#SPJ9

After considering the given data we conclude that the perimeter of the given swimming pool is 23 meters which is Option A.

The perimeter of a rectangle is evaluated by adding up all its sides. For the given case, we possess a rectangle with sides
a = 5m,
b = 8m,
c = 8m and
d = 2m.
Perimeter regarding the swimming pool is evaluated as
a + b + c + d
= 5m + 8m + 8m + 2m
= 23 meters
Hence the option regarding the question which satisfy the perimeter is Option A.
Perimeter the counted  measurement regarding the distance around the outside of a two-dimensional shape. In this system  the length of the outline or boundary of any two-dimensional geometric shape is defined as perimeter .
To learn more about perimeter
https://brainly.com/question/19819849
#SPJ1
The complete question is
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
A.23 m
B. 32 m
C.29 m
D.34 m

The total surface area of the cuboid can be calculated by adding the area of all six sides.

2(lw + lh + wh)

2(20x3 + 20x10 + 3x10)

2(60 + 200 + 30)

2(290)

580

Therefore, the surface area of one cuboid is 580 cm².

To find how many cuboids Finnley can completely cover with 46,400 cm² of paint, we need to divide the total surface area of the cuboid by the surface area of one cuboid.

46,400 / 580 = 80

Therefore, Finnley could completely cover 80 cuboids like the one shown with the tin of orange paint.

~~~Harsha~~~

Answer:

80 cuboids

Step-by-step explanation:

To find out the answer we must find the surface area of the cuboids;

2lw+2lh+2wh;

2*20*3+2*20*10+2*3*10;

580

46400/580 is the number of cuboids she can paint;

80

Answer:

-16, -21, -27

The pattern is -5 every time

Step-by-step explanation:

The pattern is removing 5 every time it goes

Answer:

2.25 cups of sugar per dozen cookies

Step-by-step explanation:

8 - 1.25 = 6.75

6.75 ÷ 3 = 2.25

The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).

In this problem we find a system of three linear equations with three variables, which can be resolved by several methods. In this case, we shall use the method of substitution. First, clear the variable x in the third equation:

x = 4 - 3 · y

Second, substitute x in the first two equations:

3 · (4 - 3 · y) + 2 · y - z = 8

12 - 9 · y + 2 · y - z = 8

- 7 · y - z = - 4

2 · (4 - 3 · y) + 2 · z = - 4

8 - 6 · y + 2 · z = - 4

- 6 · y + 2 · z = - 12

Third, clear z in the first equation derived in the previous step:

z = 4 - 7 · y

Fourth, substitute z in the second equation derived in the second step:

- 6 · y + 2 · (4 - 7 · y) = - 12

- 6 · y + 8 - 14 · y = - 12

- 20 · y = - 20

y = 1

Fifth, calculate y and x:

z = 4 - 7 · 1

z = - 3

x = 4 - 3 · 1

x = 1

The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).

To learn more on systems of linear equations: https://brainly.com/question/20379472

#SPJ1

9514 1404 393

Answer:

  (f) Plane CEA or Plane CAD

Step-by-step explanation:

The name must include three points that are in the plane and not all on the same line. That is, the name will not include either of points B or F, and must include point C. The only names listed that are appropriate are ...

  Plane CEA or Plane CAD

Answer:

(B) \(f(x)=-3(x+1)(x-5)\)

x=5

Step-by-step explanation:

Given the three equivalent forms of f(x):

\(f(x)=-3(x-2)^2+27\\f(x)=-3(x+1)(x-5)\\f(x)=-3x^2+12x+15\)

The form which most quickly reveals the zeros (or "roots") of f(x) is

(B) \(f(x)=-3(x+1)(x-5)\)

This is as a result of the fact that on equating to zero, the roots becomes immediately  evident.

\(f(x)=-3(x+1)(x-5)=0\\-3\neq 0\\Therefore:\\x+1=0$ or x-5=0\\The zeros are x=-1 or x=5\)

Therefore, one of the zeros, x=5

Answer:

i dont think the one above is correct. here is the correct answer

Step-by-step explanation:

Following order of operations:

3^2 = 9

(10-2) = 8

Now you have :

9 + 8 x 5 -4

Multiplication is next:

9 + 40 -4

Now just add and subtract from left to right:

9 + 40 = 49

49-4 = 45

The answer is 45

Step-by-step explanation:

So first you solve whats inside of the parenthesis 10 -2 aand get 8 then you figure 3^2 which is 9 then multiplie 8 times 5 and get 40. 9 + 40 - 4 is what it is so far then add 9 to 40 which is 49 then subtract 4 and get 45!

Answer:

y+3 = -2(x-4)

Step-by-step explanation:

The point slope form of a line is

(y-y1) = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y- -3 = -2 (x-4)

y+3 = -2(x-4)

Answer:

2 2/4 + 1 3/4 + 2/4 = 4 3/4

4 3/4

Answer:

4 and 3/4

Step-by-step explanation:

2 1/2

+1 3/4

+   1/2

_____

4 and 3/4

Answer:

Christopher= 20 and Tiara= 55

Step-by-step explanation:

Christopher has 20

Tiara has 55

if I am not wrong those should be the right ages they have to form 75.

tell me if I am wrong.

The value of x in the polygon will be 13.25 degrees.

The value of x is 10.

We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.

The sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.

Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees

Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:

Measure of one angle = 3960/24 = 165 degrees

165 = 12x + 6

159 = 12x

x = 13.25

Therefore, the value of x is 13.25 degrees.

Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.

Therefore, we have:

731x+86° = 7380°

Solving for x, we get:

731x = 7294°

x = 10

Therefore, the value of x is 10.

The equation that can be used to find the value of x is:

(9x+48)° + (15x-24)° = (n-2)*180°

24x + 24 = (n-2)*180°

Dividing both sides by 24, we get:

x + 1 = (n-2)*15°

Subtracting 1 from both sides, we get:

x = (n-2)*15° - 1

Learn more about polygon on

https://brainly.com/question/1592456

#SPJ1

Answer:

20

Step-by-step explanation:

percentage error = predictions - actual ÷actual × 100

error

\( \frac{82 - 52 \\ }{52} \times 100\)

=

20

Answer:

Step-by-step explanation:

The rent is 420 a year.

6 months is half a year.

The rent for 6 months is half the rent for a year:

The equivalent equation of 6x + 9 = 12  is 2x + 3  = 4.

Another equivalent equation of 6x + 9 = 12 is 3x + 4.5 = 6

Equivalent equations are algebraic equations that have identical solutions or roots. In other words,  equivalent equations are equations that have the same answer or solution.

Therefore, the equivalent equation of 6x + 9 = 12 can be calculated as follows:

6x + 9 = 12

Divide through by 3

6x / 3 + 9 / 3 = 12 / 3

2x + 3  = 4

Therefore, the equivalent equation of 6x + 9 = 12 is 2x + 3  = 4

Another equation that is equivalent to 6x + 9 = 12 is 3x + 4.5 = 6

learn more on equivalent equation here: https://brainly.com/question/17357101

#SPJ1

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

Learn more about numbers in https://brainly.com/question/24908711

#SPJ1

The domain of the function x - 3 + 5 is  x ∈ R(real number)

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.

The collection of all potential inputs for a function is its domain. Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range.

The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A->B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output.

The function is

f(x) = x - 3 + 5 = x + 2

for all value of x ∈ real number the function is define

So , the domain of the function x - 3 + 5 is  x ∈ R(real number)

To learn more about functions refer to :

https://brainly.com/question/29963265

#SPJ1

When 1,493,600 is divided by 8 the quotient is 186,700.

To divide 1,493,600 by 8, you can follow these steps:

We have to write down the dividend (1,493,600) and the divisor (8).

Now start with the largest place value in the dividend (the leftmost digit) and perform the division.

Divide 1 by 8. Since 1 is smaller than 8, you move to the next digit.

Bring down the next digit (4) and combine it with the previous quotient (0). This gives you 04.

Divide 4 by 8. Since 4 is smaller than 8, you move to the next digit.

Bring down the next digit (9) and combine it with the previous quotient (0). This gives you 09.

Divide 9 by 8. The quotient is 1, and the remainder is 1.

Bring down the next digit (3) and combine it with the remainder (1). This gives you 13.

Divide 13 by 8. The quotient is 1, and the remainder is 5.

Bring down the next digit (6) and combine it with the remainder (5). This gives you 56.

Divide 56 by 8. The quotient is 7, and there is no remainder.

Bring down the next digit (0) and combine it with the quotient (7). This gives you 70.

Divide 70 by 8. The quotient is 8, and there is no remainder.

There are no more digits to bring down, and the division is complete.

The quotient is the result of the division. In this case, 1,493,600 divided by 8 is equal to 186,700.

Therefore, the result of 1,493,600 ÷ 8 is 186,700.

To learn more on Division click:

https://brainly.com/question/21416852

#SPJ1

Answer:

Felipa is correct

Step-by-step explanation:

carl

\(6-4(4-6x)+12x\\\\2(4-6x)+12x\) this is incorrect by PEMDAS  he should have multiplied the 4 by 4-6x and then add with 6

so Felipa is correct

Answer:

Step-by-step explanation:

I think there is a typo in the question

Qn : let p(n) be  \(\sum\limits^n_{i = 1}{i2^i} = 2 + (n-1)2^{n+1} \;\;\;\;\;\;:n\geq 1\)

When n = 1:

LHS: 1(2¹) = 2

RHS: 2 + (1 - 1)(2¹ ⁺ ¹) = 2

LHS = RHS

⇒ p(n) holds for n = 1

Let us assume that the proof holds for p(n): n = x

ie.

\(p(x): \sum\limits^x_{i = 1}{i2^i} = 2 + (x-1)2^{x+1}\)

To prove that the proof holds for n = x+1

ie   \(p(x+1): \sum\limits^{x+1}_{i = 1}{i2^i} = 2 + (x)2^{x+2}\)

Consider LHS

\(\sum\limits^{x+1}_{i = 1}{i2^i}\\\\= \sum\limits^{x}_{i = 1}{i2^i}+\sum\limits^{x+1}_{i = x+1}{i2^i}\\\\= p(x) + (x+1)2^{x+1}\\\\= 2 + (x-1)2^{x+1} + (x+1)2^{x+1}\\\\= 2 + 2^{x+1} (x-1 + x+1)\\\\= 2 + 2^{x+1} (2x)\\\\= 2 + (x)2^{x+2}\\\\= RHS\)

Answer:

\(f(2) = \frac{3}{2x - 5} \)