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Hatshy [7]
3 years ago
9

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!! Factor. 64x^9 − 125y^6

Mathematics
1 answer:
shepuryov [24]3 years ago
7 0

Identity:  \\ \boxed{  {a}^{3}   -  {b}^{3}  = (a - b)( {a}^{2}  + ab +   {b}^{2}) } \\  \\ 64 {x}^{9}  - 125 {y}^{6}  \\    \\ =  {(4 {x}^{3} )}^{3}  -  {(5 {y}^{2} )}^{3}  \\ \\   = (4 {x}^{3}  - 5 {y}^{2} )( \:  {(4 {x}^{3} )}^{2}  + 4 {x}^{3}  \times 5 {y}^{2}  +  {(5 {y}^{2} )}^{2}  \: ) \\  \\  = (4 {x}^{3}  - 5 {y}^{2} )(16 {x}^{6}  + 20 {x}^{3}  {y}^{2}  + 25 {y}^{4} )
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What ratios are equivalent<br> to 3/5
barxatty [35]
The given ratios 3: 5 and 15: 25 are equal. Because when you divide the ratio 15: 25 by 5 on both numerator and denominator, the first ratio 3: 5 can be obtained. Similarly, when you multiply the first ratio 3: 5 by 5, the ratio 15: 25 can be obtained.
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3 years ago
Determine the solution to the system of equations graphed below and explain
lawyer [7]

If x - 4 ≥ 0, then |x - 4| = x - 4, so

G(x) = F(x)   ⇒   3x + 2 = (x - 4) + 2

⇒   3x + 2 = x - 2

⇒   2x = -4

⇒   x = -2

Otherwise, if x - 4 < 0, then |x - 4| = -(x - 4), so

G(x) = F(x)   ⇒   3x + 2 = -(x - 4) + 2

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⇒   x = 1

However,

• when x = -2, we have

G(-2) = 3(-2) + 2 = -4

F(-2) = |-2 - 4| + 2 = 8

• when x = 1, we have

G(1) = 3(1) + 2 = 5

F(1) = |1 - 4| + 2 = 5

so only x = 1 is a solution to G(x) = F(x).

7 0
2 years ago
Which equation represents the line that passes through the point (4, -5) and is perpendicular to the line x + 2y = 5?
Lerok [7]

Answer:

y = 2x - 13

Step-by-step explanation:

Equation of a line is y = mx + c, m is the gradient and c is the intercept

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-5 = 4m + c

When two lines are perpendicular, the products of their gradients are equal to -1, m1 * m2 = -1

x + 2y = 5

2y = -x + 5

y = (-1/2 * x) + 5

therefore m = -1/2

m1 * m2 = -1

m * -1/2 = -1

-m = -2 , therefore m = 2

-5 = 4 * 2 + c

c = -5 - 8, which is -13

Therefore the equation for the line is

y = 2x - 13

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3 years ago
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Answer:

4x - 8 = 9

Step-by-step explanation:

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