What is an area of a square with an apothem of 48 inches?

Please help im being timed <br><br> Inverse of f(x)=15x+4

rusak2 [61]

Answer:

$f^{-1}$ (x) =

Step-by-step explanation:

let y = f(x), then rearrange making x the subject

y = $\frac{1}{5}$ x + 4 ( subtract 4 from both sides )

y - 4 = $\frac{1}{5}$ x ( multiply both sides by 5 to clear the fraction )

5y - 20 = x

Change y back into terms of x with x = $f^{-1}$ (x) , then

$f^{-1}$ (x) = 5x - 20

3 0

2 years ago

In the diagram, JKLM∼EFGH. Find the scale factor of EFGH to JKLM

mote1985 [20]

The answer is k= 2.5

Explanation: Rotating the shape will show that one side is 20:8. Divide these together and you get 2.5.

Hope this helps

5 0

3 years ago

Calc help pretty please

Gre4nikov [31]

Answer:

A. 77.4

Step-by-step explanation:

<u>Linear approximation formula</u>

$L(x)=f(a)+f'(a)(x-a)$

Given function:

$f(x)=(x+1)^2$

$\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times \dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}$

$\boxed{\begin{minipage}{5 cm}\underline{Differentiating $x^n$}\\\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=xn^{n-1}$\\\end{minipage}}$

$\boxed{\begin{minipage}{4 cm}\underline{Differentiating $ax$}\\\\If $y=ax$, then $\dfrac{\text{d}y}{\text{d}x}=a$\\\end{minipage}}$

Use the chain rule to differentiate the function.

$\textsf{Let }\:y=u^2\:\textsf{ where }u=(x+1)$

Differentiate the two parts separately:

$y=u^2 \implies \dfrac{\text{d}y}{\text{d}u}=2u$

$u=x+1 \implies \dfrac{\text{d}u}{\text{d}x}=1$

Put everything back into the chain rule formula:

$\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =2u \times 1\\ & = 2u \\ & = 2(x+1)\\ & = 2x+2 \end{aligned}$

$\textsf{Therefore, }\:f'(x)=2x+2.$ .

The <u>linear approximation</u> at a = 8 is:

$\begin{aligned}L(x) & =f(a)+f'(a)(x-a)\\\\\implies L(x) & = f(8)+f'(8)(x-8)\\& = (8+1)^2+(2(8)+2)(x-8)\\& = 81+18(x-8)\\& = 18x-63\end{aligned}$

Finally, substitute x = 7.8 into the <u>linear approximation equation</u>:

$\begin{aligned}\implies L(7.8) & =18(7.8)-63\\& = 140.4-63\\& = 77.4\end{aligned}$

4 0

1 year ago

Read 2 more answers

Imelda planted vegetables in of her garden. She divided the other half of her garden into 3 equal sections. She planted rose bus

ziro4ka [17]

The sections of the garden is an illustration of fractions

The number sentence best shows whether Imelda is correct is 1/2 ÷ 3

<h3>How to determine the number sentence?</h3>

From the question, we understand that she plants in 1/2 of the garden

Then 1/2 of the garden is divided into 3 sections, one of which is used to plant tulips

So, the area in which tulips are planted is:

Tulip = 1/2 ÷ 3

Hence, the number sentence best shows whether Imelda is correct is 1/2 ÷ 3