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KIM [24]
2 years ago
9

Simplify and maybe also state the restrictions on the variable:

Mathematics
1 answer:
Viefleur [7K]2 years ago
6 0

\frac{15a^2\left(a-1\right)}{8\left(2a+3\right)}\cdot \frac{10\left(2a+3\right)}{3a}

\mathrm{Apply\:the\:fraction\:rule}:

\frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}

=\frac{15a^2\left(a-1\right)\cdot \:10\left(2a+3\right)}{8\left(2a+3\right)\cdot \:3a}

\mathrm{Cancel\:the\:common\:factor:}\:2a+3

=\frac{15a^2\left(a-1\right)\cdot \:10}{8\cdot \:3a}

\mathrm{Factor\:the\:number:\:}\:15=3\cdot \:5

=\frac{3\cdot \:5a^2\left(a-1\right)\cdot \:10}{8\cdot \:3a}

\mathrm{Cancel\:the\:common\:factor:}\:3

=\frac{5a^2\left(a-1\right)\cdot \:10}{8a}

\mathrm{Factor\:the\:number:\:}\:10=2\cdot \:5

=\frac{5a^2\left(a-1\right)\cdot \:2\cdot \:5}{2\cdot \:4a}

\mathrm{Factor\:the\:number:\:}\:8=2\cdot \:4

=\frac{5a^2\left(a-1\right)\cdot \:2\cdot \:5}{2\cdot \:4a}

\mathrm{Cancel\:the\:common\:factor:}\:2

=\frac{5aa\left(a-1\right)\cdot \:5}{4a}

\mathrm{Apply\:exponent\:rule}:

a^{b+c}=a^b\cdot \:a^c

a^2=aa

\mathrm{Cancel\:the\:common\:factor:}\:a

=\frac{5a\left(a-1\right)\cdot \:5}{4}

\mathrm{Multiply\:the\:numbers:}\:5\cdot \:5=25

=\frac{25a\left(a-1\right)}{4}

\mathrm{I\:hope\:that\:I\:helped\:you\:!}

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Bill has a container that is shaped like a cube. He uses 125 cubes with a side length of 1 inch to fill the container completely
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Answer:

5 inches

Step-by-step explanation:

Given

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Volume = Length^3

This gives;

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Take cube root of both sides

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Slav-nsk [51]

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  y = -1/6x +2

Step-by-step explanation:

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The slope of the line is the ratio of "rise" (vertical change) to "run" (horizontal change).

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The vertical change between those two points is 1 -2 = -1.

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The slope is then -1/6.

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The slope-intercept form of the equation of a line is often written as ...

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77julia77 [94]

Answer:

d=\frac{2w(c-2)}{5}

Step-by-step explanation:

The given formula is:

c=5d+4w/2w

We need to find d.

Multiply 2w on both sides, we get

c x 2w= 5d+4w/2w x 2w

2cw=5d+4w

Adding -4w on both sides, we get

2cw-4w=5d+4w-4w.

2cw-4w=5d

2w(c-2)=5d

Dividing by 5, we get

2w(c-2)/5 = 5d/5

2w(c-2)/5 = d

Hence the required formula with subject d is

d=\frac{2w(c-2)}{5}

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