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nirvana33 [79]
3 years ago
6

9. A plumber charges $25 to come to your house. He also charges $60 for each hour that he works. The

Mathematics
1 answer:
Leviafan [203]3 years ago
7 0

Answer:

The formula would be h = \frac{C - 25}{60}\\\\ (where "h" is the number of hours and C is the total amount of money given to the plumber). And if we use this formula we will know that In this case, the plumber was working for 2 hours

Step-by-step explanation:

From the question itself, we know if we let "h" represent the numbers of hours the plumber works and "C" represents the total amount of money paid to the plumber, then we can write the following equation...

C = 60h + 25

From here we can rearange the formula and get the following...

h = \frac{C - 25}{60}\\\\

h= \frac{145-25}{60}

h = \frac{120}{60}

h = 2

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43.5 centimeters by 934 millimeters. Hello many centimeters are wood framing will she need
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3 years ago
For the composite function, identify an inside function and an outside function and write the derivative with respect to x of th
alexira [117]

Answer:

The inner function is h(x)=4x^2 + 8 and the outer function is g(x)=3x^5.

The derivative of the function is \frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4.

Step-by-step explanation:

A composite function can be written as g(h(x)), where h and g are basic functions.

For the function f(x)=3(4x^2+8)^5.

The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.

Here, we have 4x^2+8 inside parentheses. So h(x)=4x^2 + 8 is the inner function and the outer function is g(x)=3x^5.

The chain rule says:

\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)

It tells us how to differentiate composite functions.

The function f(x)=3(4x^2+8)^5 is the composition, g(h(x)), of

     outside function: g(x)=3x^5

     inside function: h(x)=4x^2 + 8

The derivative of this is computed as

\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4

The derivative of the function is \frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4.

3 0
3 years ago
8(7 + 23) = 8(7) + 8(?)
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When using multiplication with brackets, you multiply the number by all the numbers within the bracket before adding them together.

Therefore when it is 8(7 + 23) it basically means: 8(7) + 8(23)
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