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2 years ago

3 + 12(3p + 2) = 9(p - 3)

Mathematics

1 answer:

VikaD [51]2 years ago

8 0

Answer:

$3 + 12(3p + 2) = 9(p - 3) \\ 3 + 36p + 24 = 9p - 27 \\ 27p = - 54 \\ p = - \frac{54}{27} \\ \boxed{p = - 2}$

<h3>p=-2 is the right answer.</h3>

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Solve (2/3)-(1/x)=5/6

Keith_Richards [23]

$\frac{2}{3} - \frac{1}{x} = \frac{5}{6}$ Multiply both sides by 3
$2 - \frac{1(3)}{x} = \frac{5(3)}{6}$ Simplify the numerators
$2 - \frac{3}{x} = \frac{15}{6}$ Multiply both sides by 6
$12 - \frac{3(6)}{x} = 15$ Simplify the numerator
$12 - \frac{18}{x} = 15$ Multiply both sides by x
12x - 18 = 15x Subtract 12x from both sides
-18 = 3x Divide both sides by 3
-6 = x Switch the sides to make it easier to read
x = -6

Check your answer by plugging -6 in for the x in the original problem:

$\frac{2}{3} - \frac{1}{x} = \frac{5}{6}$ Plug in -6 for x
$\frac{2}{3} - \frac{1}{-6} = \frac{5}{6}$ Change $\frac{2}{3}$ to $\frac{4}{6}$ so all denominators are the same
$\frac{4}{6} - \frac{1}{-6} = \frac{5}{6}$ Change $\frac{1}{-6}$ to $\frac{-1}{6}$ for easier work
$\frac{4}{6} - \frac{-1}{6} = \frac{5}{6}$ Subtract the numerators (4 - (-1) )
$\frac{5}{6}$ = $\frac{5}{6}$

So, x = -6 .

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2 years ago

What is the volume of a cylinder, in cubic centimeters, with a height of 8 centimeters

Arisa [49]

Answer:

1608.5 cm³

Step-by-step explanation:

Use the cylinder volume formula, V = $\pi$ r²h

If the diameter is 16 cm, then the radius is 8 cm.

Plug in the radius and height into the formula, and solve:

V = $\pi$ r²h

V = $\pi$ (8)²(8)

V = $\pi$ (64)(8)

V = 1608.5

So, to the nearest tenth, the volume of the cylinder is 1608.5 cm³

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2 years ago

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