All categories

3 years ago

What is the factored form of x^3-1

Mathematics

2 answers:

Shkiper50 [21]3 years ago

8 0

Answer:

Step-by-step explanation:

egde

Lena [83]3 years ago

5 0

X^3-1 rewrite as x^3-1^3
differences of cubes formula: a^3-b^3=(a-b)(a^2+ab+b^2)
a=x, b=1
(x-1)(x^2+x*1+1^2)
(x-1)(x^2+x+1)

You might be interested in

Which point is on the line that passes through point Z and is perpendicular to line AB?

tankabanditka [31]

Step 1

Find the slope of the line AB

we know that

the formula to find the slope between two points is equal to

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

we have

$A(-2,4)\\B(0,-4)$

substitute in the formula

$m=\frac{(-4-4)}{(0+2)}$

$m=\frac{(-8)}{(0+2)}$

$m1=-4$

Step 2

Find the slope of the line that passes through point Z and is perpendicular to line AB

we know that

If two lines are perpendicular, then the product of their slopes is equal to minus one

$m1*m2=-1$

$m2=-\frac{1}{m1}$

we have

$m1=-4$

substitute

$m2=\frac{1}{4}$

Step 3

Find the equation of the line that passes through point Z and is perpendicular to line AB

we have

$Z(0,2)\\m2=\frac{1}{4}$

we know that

the equation of the line into point -slope form is equal to

$y-y1=m*(x-x1)$

substitute

$y-2=\frac{1}{4}*(x-0)$

$y=\frac{1}{4}x+2$

Verify which point is on the line that passes through point Z and is perpendicular to line AB

we know that

If a point is on the line, then the coordinates of the point must be satisfy the equation of the line

we are going to proceed to verify each point to determine the solution

Substitute the values of x and y of the point in the equation of the line. If the equation is true, then the point is on the line

Step 4

point $A(-4,1)$

$1=\frac{1}{4}*(-4)+2$

$1=1$ --------> the equation is true

therefore

the point $A(-4,1)$ is on the line

Step 5

point $B(1,-2)$

$-2=\frac{1}{4}*(1)+2$

$-2=\frac{9}{4}$ --------> the equation is not true

therefore

the point $B(1,-2)$ is not on the line

Step 6

point $C(2,0)$

$0=\frac{1}{4}*(2)+2$

$0=\frac{5}{2}$ --------> the equation is not true

therefore

the point $C(2,0)$ is not on the line

Step 7

point $D(4,4)$

$4=\frac{1}{4}*(4)+2$

$4=3$ --------> the equation is not true

therefore

the point $D(4,4)$ is not on the line

the answer is the option

$A(-4,1)$

4 0

3 years ago

Read 2 more answers

For the function below, give the ordered pair if x = 2 f(x)=-3(x+2)2+9

Kay [80]

Answer:

(2, -39)

Step-by-step explanation:

f(x)=-3(x+2)^2+9

f(2)=-3(2+2)^2+9

f(2)=-3(4)^2+9

f(2)=-3(4)(4)+9

f(2)=-3(16)+9

f(2)=-48+9

f(2)=-39

8 0

2 years ago

an air conditioning system can circulate 360, cubic feet of air per minute. how many cubic yards of air can it circulate per min

ahrayia [7]

Alright, lets get started.

3 feet = 1 yard

If we cube both sides of the equation, we will get the conversion into cubic yards

So,

$3*3*3 cubic feet = 1 * 1*1 cubic yards$

27 cubic feet = 1 cubic yards

So, 1 cubic feet = $\frac{1}{27}$ cubic yards

So, 360 cubic feet = $360 *\frac{1}{27}$ cubic yards

So, 360 cubic feet = 13.33 cubic yards

13.33 cubic yards of air can it circulate per minute. : Answer

Hope it will help :)

3 0

3 years ago

Read 2 more answers

A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced.

zzz [600]

Answer:

$CI=(66.54,78.46)$

Step-by-step explanation:

Given : A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed.

To find : A 99% confidence interval for the mean yield when the new catalyst is used ?

Solution :

Let X be the yield of the batches.

We have given, n=10 , $\bar{X}=72.5\%$ , s=5.8%