Answer:
- 8x^3+1 ⇒ (2x+1)(4x^2−2x+1)
- 2x^4+16x ⇒ 2x(x+2)(x^2−2x+4)
- x^3+8 ⇒ (x+2)(x^2−2x+4)
Step-by-step explanation:
The factoring of the sum of cubes is ...
a³ +b³ = (a +b)(a² -ab +b²)
1. a=2x, b=1
= (2x)³ + 1³
__
2. There is an overall factor of 2x. Once that is factored out, a=x, b=2.
= (2x)(x³ +2³)
__
3. a=x, b=2
= x³ +2³
Answer:
Step-by-step explanation:
hol sinaoteentnedbieinlrpeagntaaau
First off, I think the equation should have a negative 9 in it originally and then you move it to the other side and it becomes positive.
You'll basically complete the square for two equations at the same time. Set it up like this:
(16x^2 + 96x) + (9y^2 - 18y) = 9
Divide everything by 16 to get the x^2 by itself, then divide everything by 9 to get y^2 by itself. You should end up with this.
(x^2 + 6x) + (y^2 - 2y) = 9/144
then complete the square by taking the second term of each polynomial, dividing by two, and squaring it.
For instance the first one will be 6/2 = 3^2 = 9
The next one will be 2/2 =1^2 = 1
Add these to numbers to the polynomials as well as to the other side of the equation to keep it equal. You should end up with this.
(x^2 + 6x+9) + (y^2 - 2y+1) = (9/144)+9+1
Then find a common denominator on the right side of the equals sign and add them all together to get:
(x^2 + 6x+9) + (y^2 - 2y+1) = 1449/144
Factor out the two polynomials
(x+3)^2 + (y-1)^2 = 1449/144
the center of the circle is (-3,1) according to the factored out polynomials and the radius will be the square root of the number on the right side of the equals sign = sqrt(1449/144) = 3.17
9 simplified is radical 3 then 2 on the outside make the answer 3
You need to find 6% of 250. To do that, change 6% to a decimal (0.06) and multiply that by 250. That answer is how many tickets you have.
6%=0.06
250
x0.06
______
15.00. move the decimal point in 2 spaces
15
Final Answer: 15 tickets are yours.
