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Romashka-Z-Leto [24]
3 years ago
6

The area of the rectangle is 54 units squared. Write and solve an equation to find x.

Mathematics
1 answer:
lord [1]3 years ago
6 0

Answer: x=5

Step-by-step explanation:

The area of a rectangle can be found with the following formula:

A=lw

Where "l" is the length and "w" is the width.

In this case you can identify in the figure given in the exercise that:

l=4x-2\\\\w=3

You know that the area of that rectangle is the following:

A=54

Therefore, knowing those values, you can substitute them into the formula and then you must solve for "x" in order to find its value. You get that this is:

54=(4x-2)(3)\\\\54=12x-6\\\\54+6=12x\\\\\frac{60}{12}=x\\\\x=5

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Please answer this multiple choice question CORRECTLY for 30 points and brainliest!!
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Solve the inequality for x:

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Subtract 7x from each side:

-2x -3 ≤ 7

Add 3 to each side:

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Divide both sides by -2, also when dividing  both sides of an inequality you flip the direction of the inequality sign:

x ≥ -5

The dot will be on -5, because the inequality includes equal to, the dot is solid and is greater than, the arrow will point to the right.

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4 years ago
6v(2v + 3) 2) 7(−5v − 8)
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Answer:

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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.

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Step-by-step explanation:

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