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3 years ago

Which expression is equivalent to 5(x + 7)?

2 answers:

5 0

You need to multiply both numbers inside the parentheses by 5:

5 times x = 5x
5 times 7 = 35

So your answer is B. 5x + 35

WARRIOR [948]3 years ago

5 0

Answer:

Step-by-step explanation:

5(x+7)

5x+35

Using the distributing

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At 10:00 a.m. the temperature is –3.4°F. The temperature increases 0.5°F each hour for the next 6 hours. If the temperature drop

Marat540 [252]

Answer:

-3.4+3=-0.4 -0.4-5.3=-5.7 (-5.7F)

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2 years ago

Identify the number that does not belong with the other three. Explain your reasoning. 50.1 repeating 1, negative 50 over 2, neg

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Square root 50 does not belong....all of the other numbers are rational numbers. square root 50 is irrational.

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3 years ago

Jamie is x years old. His friend Ana is the same age.

SSSSS [86.1K]

<h3>Answer: 2x</h3>

Explanation:

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1 year ago

1.) Find the length of the arc of the graph x^4 = y^6 from x = 1 to x = 8.

xxTIMURxx [149]

First, rewrite the equation so that <em>y</em> is a function of <em>x</em> :

$x^4 = y^6 \implies \left(x^4\right)^{1/6} = \left(y^6\right)^{1/6} \implies x^{4/6} = y^{6/6} \implies y = x^{2/3}$

(If you were to plot the actual curve, you would have both $y=x^{2/3}$ and $y=-x^{2/3}$ , but one curve is a reflection of the other, so the arc length for 1 ≤ <em>x</em> ≤ 8 would be the same on both curves. It doesn't matter which "half-curve" you choose to work with.)

The arc length is then given by the definite integral,

$\displaystyle \int_1^8 \sqrt{1 + \left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx$

We have

$y = x^{2/3} \implies \dfrac{\mathrm dy}{\mathrm dx} = \dfrac23x^{-1/3} \implies \left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2 = \dfrac49x^{-2/3}$

Then in the integral,

$\displaystyle \int_1^8 \sqrt{1 + \frac49x^{-2/3}}\,\mathrm dx = \int_1^8 \sqrt{\frac49x^{-2/3}}\sqrt{\frac94x^{2/3}+1}\,\mathrm dx = \int_1^8 \frac23x^{-1/3} \sqrt{\frac94x^{2/3}+1}\,\mathrm dx$

Substitute

$u = \dfrac94x^{2/3}+1 \text{ and } \mathrm du = \dfrac{18}{12}x^{-1/3}\,\mathrm dx = \dfrac32x^{-1/3}\,\mathrm dx$

This transforms the integral to

$\displaystyle \frac49 \int_{13/4}^{10} \sqrt{u}\,\mathrm du$

and computing it is trivial:

$\displaystyle \frac49 \int_{13/4}^{10} u^{1/2} \,\mathrm du = \frac49\cdot\frac23 u^{3/2}\bigg|_{13/4}^{10} = \frac8{27} \left(10^{3/2} - \left(\frac{13}4\right)^{3/2}\right)$