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2 years ago

Factor the polynomial 64x^3-125

1 answer:

7 0

$64 x^{3} -125$

= $(4x)^{3} - 5^{3}$ ------> because, $(4x)^{3}$ is same as 64x³ and
$5^{3}$ is same as 125

Using the formula: $a^{3}- b^{3} =(a-b)(a ^{2} +ab+b ^{2} )$ , we get,

= $(4x -5)((4x)^{2} +4x*5+ 5^{2} )$

= $(4x -5)(16 x^{2} +20x+25)$ ------>that's your answer!!

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Function f(x)=|x| is transformed to create function g(x)=|x+4|+3. What transformations are performed to function f to get functi

Ahat [919]

Answer:

Step-by-step explanation:

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Function f is translated 4 units down.

(this one is correct) Function f is translated 3 units up.

Function f is translated 4 units up.

(this one is correct) Function f is translated 4 units to the left.

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3 0

2 years ago

The age of a boy is twice that of his sister. five years ago the boy was 3 times the age of his sister. How old is the boy

joja [24]

Answer:

<h2>20 years old.</h2>

Solution,

Let the age of sister be X

Let the age of boy be 2x

Now,

Five years ago,

 $3(x - 5) = 2x - 5 \\ or \: 3x - 15 = 2x - 5 \\ or \: 3x - 2x = - 5 + 15 \\ x = 10$ 

Again,

Replacing value,

 $age \: of \: boy = 2x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 10 \\ \: \: \: \: \: \: \: \: \: \: \: = 20$ 

hope this helps..

Good luck on your assignment..

7 0

3 years ago

Can someone please help and explain its due in a littleee

larisa [96]

Answer:

Step-by-step explanation:

6 0

2 years ago

The Frill family and the Smith family go to the movies.

Sati [7]

Step-by-step explanation:

Let a be the price of 1 adult ticket.

Let c be the price of 1 child ticket.

given,

$6a + 2c = 124$

as equation 1,

and

$3a + 5c = 100$

as equation 2.

Now we will solve for a and c using elimination method of simultaneous equations.

Now we multiply equation 2 by 2 to eliminate a and solve for c.

$3a \times 2 + 5c \times 2 = 100 \times 2 \\ 6a + 10c = 200$

This new equation will be equation 3.

Now we will use equation 1 - equation 3 to eliminate a and solve for c.

$(6a - 6a) + (2c - 10c) = 124 - 200 \\ 0 + ( - 8c) = - 76 \\ - 8c = - 76 \\ c = - 76 \div - 8 \\ = 9.5$

Now substitute c into equation 2.

$3a + 5(9.5) = 100 \\ 3a + 47.5 = 100 \\ 3a = 100 - 47.5 \\ 3a = 52.5 \\ a = 52.5 \div 3 \\ = 17.5$

Therefore one adult ticket will cost $17.50 and one child ticket will cost $9.50.

7 0

2 years ago

What is the equation for the points (-3,1) and (9,7)

Scorpion4ik [409]

Answer:

The equation of line with given points is 2Y - X - 5 = 0

Step-by-step explanation:

Given points are ( - 3 , 1) and (9 , 7)

Equation of line is y = mx +c

where m is the slop of line

Now m = $\frac{y2 - y1}{x2 - x1}$

Or, m = $\frac{7 - 1}{9 + 3}$

so, slop = $\frac{6}{12}$

∴ slop = $\frac{1}{2}$

Now the equation of line with points ( -3 , 1) and slop m is :

Y - y1 = m ( X - x1)

Or, Y - 1 = $\frac{1}{2}$ (X + 3)

Or, 2Y - X - 5 = 0

Hence The equation of line with given points is 2Y - X - 5 = 0 Answer

6 0

3 years ago