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3 years ago

14

Factor the expression 8x3y − 8x2y − 30xy. 8x3y − 8x2y − 30xy

1 answer:

Lelu [443]3 years ago

6 0

Answer:

2xy(2x +3)(2x -5)

Step-by-step explanation:

The greatest common factor of the coefficients 8 and 30 is 2. All of the variable expressions have a common factor of xy. We can factor those out to get ...

= (2xy)(4x^2 -4x -15)

Now, we want to find factors of the product (4)(-15) that have a sum of -4 (the x coefficient). Those factors are 6 and -10. Then we can rewrite the quadratic factor as ...

4x^2 +6x -10x -15

and factor by pairs:

= 2x(2x +3) -5(2x +3) = (2x -5)(2x +3)

The complete factorization is then ...

= 2xy(2x +3)(2x -5)

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3 years ago

∆ABC is similar to ∆DEF. The ratio of the perimeter of ∆ABC to the perimeter of ∆DEF is 1 : 10. The longest side of ∆DEF measure

exis [7]

Answer:

Part 1) The length of the longest side of ∆ABC is 4 units

Part 2) The ratio of the area of ∆ABC to the area of ∆DEF is $\frac{1}{100}$

Step-by-step explanation:

Part 1) Find the length of the longest side of ∆ABC

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

The ratio of its perimeters is equal to the scale factor

Let

z ----> the scale factor

x ----> the length of the longest side of ∆ABC

y ----> the length of the longest side of ∆DEF

so

$z=\frac{x}{y}$

we have

$z=\frac{1}{10}$

$y=40\ units$

substitute

$\frac{1}{10}=\frac{x}{40}$

solve for x

$x=(40)\frac{1}{10}$

$x=4\ units$

therefore

The length of the longest side of ∆ABC is 4 units

Part 2) Find the ratio of the area of ∆ABC to the area of ∆DEF

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x ----> the area of ∆ABC

y ----> the area of ∆DEF

$z^{2}=\frac{x}{y}$

we have

$z=\frac{1}{10}$

so

$z^2=(\frac{1}{10})^2$

$z^2=\frac{1}{100}$

therefore

The ratio of the area of ∆ABC to the area of ∆DEF is $\frac{1}{100}$

3 0

2 years ago

X+y=3 x=6-4y using substitution

kenny6666 [7]

Givens

x + y = 3

x =6 - 4y

Solution

Use the top equation to substitute for x in the second equation.

x = 3 - y

Put this result into the second given equation and solve for y

3 - y = 6 - 4y Add 4y to both sides.

3 - y + 4y = 6 Combine on the left

3 + 3y = 6 Subtract 3 from both sides

3 - 3 + 3y = 6 - 3 Combine

3y = 3 Divide by 3

3y/3 = 3/3 Combine

y = 1

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

x + y = 3 but y = 1

x + 1 = 3 Subtract 1 from both sides.

x + 1 - 1 =3 - 1

x = 2

Answer

x = 2

y = 1

4 0

3 years ago

Read 2 more answers

What number would this be?

kobusy [5.1K]

Answer:

Approximately 775,000.

Step-by-step explanation:

The number is almost in between 750,000 and 800,000. The number in the middle of these two is 775,000.

4 0

3 years ago

Read 2 more answers