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Elenna [48]
3 years ago
8

Find the inverse function

Mathematics
1 answer:
Alex3 years ago
3 0

The inverse of this function is f(x) = \frac{3x + 15}{4}


To find the inverse of any function, start by switching the x and f(x) term. Then solve for the new f(x). The result will be the inverse function. The step-by-step process is below for you.


f(x) = \frac{-15 + 4x}{3} ----> Switch the x and f(x)


x = \frac{-15 + 4f(x)}{3} ----> Muliply both sides by 3


3x = -15 + 4f(x) ----> Add 15 to both sides


3x + 15 = 4f(x) ----> Divide both sides by 4.


f(x) = \frac{3x + 15}{4}

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Answer:

The answer is B.

Step-by-step explanation:

You have to use Pythogorean Theorem, c² = a² + b² where c is the hypotenuse and a,b is the side lengths :

{c}^{2}  =  {a}^{2}  +  {b}^{2}

Let a = 40,

Let b = 9,

{c}^{2}  =  {40}^{2}  +  {9}^{2}

{c}^{2}  = 1600 + 81

{c}^{2}  = 1681

c =  \sqrt{1681}

c = 41 \: units

*Take note, hypotenuse will <u>a</u><u>l</u><u>w</u><u>a</u><u>y</u><u>s</u><u> </u><u>b</u><u>e</u><u> </u><u>t</u><u>h</u><u>e</u><u> </u><u>l</u><u>o</u><u>n</u><u>g</u><u>e</u><u>s</u><u>t</u><u> </u><u>l</u><u>e</u><u>n</u><u>g</u><u>t</u><u>h</u> among the 3 lengths.

*Pythogorean Theorem can only applied in a right-angle triangle.

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Five plus three equals
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5

+

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Step-by-step explanation:

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3 years ago
Pyramid A is a square pyramid with a base side length of 12 inches and a height of 8 inches. Pyramid B is a square pyramid with
yan [13]

Answer:

<em>The volume of pyramid B is 64 times the volume of pyramid A.</em>

<em></em>

Step-by-step explanation:

Given:

Two square pyramids A and B.

Side Length of A, s_A = 12 inches

Height of A, h_A = 8 inches

Side Length of B, s_B = 48 inches

Height of B, h_B = 32 inches

To find:

How many times bigger is the volume of pyramid B than pyramid A?

OR

V_B is how many times bigger than V_A ?

Solution:

First of all, let us have a look at the formula for volume of a pyramid:

V=\dfrac{1}{3} \times \text{Area of Base} \times \text{Height}

Here, base is square, so:

V=\dfrac{1}{3} \times s^2 \times h

Volume of pyramid A:

V_A=\dfrac{1}{3} \times s_A^2 \times h_A

\Rightarrow V_A=\dfrac{1}{3} \times 12^2 \times 8 = 384\ inch^3

Volume of pyramid B:

V_B=\dfrac{1}{3} \times s_B^2 \times h_B

\Rightarrow V_B=\dfrac{1}{3} \times 48^2 \times 32 \\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 4^2 \times 4\\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 64\\\Rightarrow V_B= 24576\ inch^3 = 384\times 64\ inch^3\\\Rightarrow V_B = V_A\times 64\ inch^3

<em>The volume of pyramid B is 64 times the volume of pyramid A.</em>

3 0
3 years ago
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