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3 years ago

Factor 64a^3 -8b^3 Explain all steps.

Mathematics

1 answer:

grandymaker [24]3 years ago

8 0

Answer:

$8(2a- b)(4a^2+ 2ab+ b^2)$

Step-by-step explanation:

factor out the 8

then you have the sum/difference of cubes..

look that up SOAP: same opposite, always a plus

$64a^3 -8b^3\\8(8a^3 -b^3)$

$8(2a- b)(4a^2+ 2ab+ b^2)$

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3 years ago

At a restaurant the cost for one breakfast taco and one glass of milk is $3.94. The cost for 2 tacos and 3 glasses of milk is $8

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3 years ago

A 20-ft by the 40-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway i

Jlenok [28]

<h3>Answer: 2 feet</h3>

========================================================

Explanation:

x = width of the walkway in feet

This is some positive real number.

The dimension of 20 feet bumps up to 20+2x when adding on x from both directions. Similarly, the 40 ft dimension becomes 40+2x

Refer to the diagram below.

The 20 ft by 40 ft pool is surrounded by a larger rectangle that is 20+2x ft by 40+2x ft

The pool itself is 20*40 = 800 sq ft. Add on the walkway area to get 800+256 = 1056 sq ft.

-----------

Area = length*width

1056 = (20+2x)*(40+2x)

1056 = 20*40 + 20*2x + 2x*40 + 2x*2x ... FOIL rule

1056 = 800 + 40x + 80x + 4x^2

0 = 4x^2 + 40x + 80x + 800 - 1056

0 = 4x^2 + 120x - 256

4x^2 + 120x - 256 = 0

4(x^2 + 30x - 64) = 0

x^2 + 30x - 64 = 0

Let's use the quadratic formula to finish solving for x.

Plug in a = 1, b = 30, c = -64

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-30\pm\sqrt{(30)^2-4(1)(-64)}}{2(1)}\\\\x = \frac{-30\pm\sqrt{1156}}{2}\\\\x = \frac{-30\pm34}{2}\\\\x = \frac{-30+34}{2} \ \text{ or } \ x = \frac{-30-34}{2}\\\\x = \frac{4}{2} \ \text{ or } \ x = \frac{-64}{2}\\\\x = 2 \ \text{ or } \ x = -32\\\\$

Recall we made x be positive. This is because a negative walkway width does not make sense. This means we'll ignore x = -32.

The only practical solution is x = 2

Therefore, the walkway is <u>2 feet wide</u>

4 0

2 years ago

Please someone answer this.

klio [65]

The triangle ABC may be rotated along a fixed point, translated to a different position and reflected across a mirror line.

<h3>Types of transformation</h3>

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Translating a shape means moving it entirely to a different position, without changing it in any way.

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Thus, the triangle ABC may be rotated along a fixed point, translated to a different position and reflected across a mirror line.

Learn more about transformation here:

brainly.com/question/4289712

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2 years ago

A scientist begins an experiment with a culture of 5 bacteria cells. Every hour, the number of bacteria cells triples. Which equ

olga2289 [7]

Answer:

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Every hour, the number of bacteria cells triples.

Which equation can be used to represent the number of bacteria cells, y, as it relates to time in hours, x?

I think it would be y = 5 * (3^x)

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3 years ago