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3 years ago

Factor 256x^3 - 500y^3

1 answer:

5 0

(256 • (x3) - ( 2^2• 5^3 y^3)
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 2^8 x^3 - ( 2^2 • 5^3 y^3)

256x^3 - 500y^3 = 4 • (64x^3 - 125y^3)

64x^3 - 125y^3
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final factoization:

(4x - 5y) • (16x^2 + 20xy + 25y^2)

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Complete square to solve 3x^2 + 12x – 9 = 0

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Step-by-step explanation: Have a brilliant day mate- Lily ^_^

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3 years ago

In the image, shape ABCD is similar to shape WXYZ. Find the measure of side ZW.

vladimir2022 [97]

Solution:

we are given that

In the image, shape ABCD is similar to shape WXYZ.

we have been asked to find the measure of side ZW.

As we know that when two shapes are similar then the ratios of their corresponding sides are equal.

So we can write

$\frac{zw}{6}= \frac{18}{24}\\
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ZW=6*\frac{18}{24}\\
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ZW=\frac{18}{4}\\
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3 years ago

a square garden has a diagonal of 12 m. What is the perimeter of the garden? Express in simplest radical form

lianna [129]

Answer:

The perimeter of the garden, in meters, is $24\sqrt{2}$

Step-by-step explanation:

Diagonal of a square:

The diagonal of a square is found applying the Pythagorean Theorem.

The diagonal of the square is the hypothenuse, while we have two sides.

Diagonal of 12m:

This means that $d = 12$ , side s. So

$s^2 + s^2 = 12^2$

$2s^2 = 144$

$s^2 = \frac{144}{2}$

$s^2 = 72$

$s = \sqrt{72}$

Factoring 72:

Factoring 72 into prime factors, we have that:

72|2

36|2

18|2

9|3

3|3

$72 = 2^{3}*3^{2}$

So, in simplest radical form:

$s = \sqrt{72} = \sqrt{2^{3}*3^{2}} = \sqrt{2^3}*\sqrt{3^2} = 2\sqrt{2}*3 = 6\sqrt{2}$

Perimeter of the garden:

The perimeter of a square with side of s units is given by:

$P = 4s$

In this question, since $s = 6\sqrt{2}$

$P = 4s = 4*6\sqrt{2} = 24\sqrt{2}$

The perimeter of the garden, in meters, is $24\sqrt{2}$

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2 years ago

Ms.Groves has trays of paint for students in her art class.each tray has 5 colors.one of the colors is purple.what fraction of t

seropon [69]

So we need to find the fraction of many times does purple show up in 20 trays in which every tray has 5 colors. To find the answer we need to find the overall number of all colors and that is 20 trays * 5 colors and that equals to 100 colors. So purple shows 20 times and 20/100 is 1/5 when we simplify the fraction.

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3 years ago

Read 2 more answers

An arts academy requires there to be 5 teachers for every 125 students and 4 tutors for every 88 students. How many students doe

nikitadnepr [17]

Answer:

25 students peer teacher, 22 students per tutor, 4 tutors for 81 students

Step-by-step explanation:

You need to find the unit rate,

for the teachers, to find the unit rate would be 125 divided by 5. For tutors it would be 88 divided by 4.

Then to find how many tutors you need for 81 students you would need 4 tutors because you want to divide 81 by the unit rate we got (22), and since the answer would be a decimal (3.68.....) you would need to round the whole number up to four because you cant have a decimal of a person.

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3 years ago