Answer:
1. 2^9 = 512
2. 2^3 = 8
3. 7^3 = 343
4. 6^3 = 216
5. 3^6 = 729
Step-by-step explanation:
To start we have to express the number as a multiplication of prime numbers, from there we can take the expression as a power
1.
2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512
2^9 = 512
2.
2 x 2 x 2 = 8
2^3 = 8
3.
7 x 7 x 7 = 343
7^3 = 343
4.
6 x 6 x 6 = 216
6^3 = 216
5.
3 x 3 x 3 x 3 x 3 x 3 = 729
3^6 = 729
Answer:
x = -
, x = 
Step-by-step explanation:
to find the points of intersection equate the 2 equations , that is
7x - 15 = 10 + 12x - 6x² ( subtract 10 + 12x - 6x² from both sides )
6x² - 5x - 25 = 0 ← factor the quadratic on left side
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 6 × - 25 = - 150 and sum = - 5
the factors are - 15 and + 10
use these factors to split the x- term
6x² - 15x + 10x - 25 = 0 ( factor the first/second and third/fourth terms )
3x(2x - 5) + 5(2x - 5) = 0 ← factor out (2x - 5) from each term
(2x - 5)(3x + 5) = 0
equate each factor to zero and solve for x
3x + 5 = 0 ⇒ 3x = - 5 ⇒ x = - 
2x - 5 = 0 ⇒ 2x = 5 ⇒ x = 
Answer: They would be Parrellel
Step-by-step explanation:
![\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} 729=27^2\\ \qquad (3^3)^2\\ 1000=10^3 \end{cases}\implies 729^{15}+1000\implies ((3^3)^2)^{15}+10^3 \\\\\\ ((3^2)^{15})^3+10^3\implies (3^{30})^3+10^3\implies (3^{30}+10)~~[(3^{30})^2-(3^{30})(10)+10^2] \\\\\\ (3^{30})^3+10^3\implies (3^{30}+10)~~~~[(3^{60})-(3^{30})(10)+10^2]](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bdifference%20and%20sum%20of%20cubes%7D%20%5C%5C%5C%5C%20a%5E3%2Bb%5E3%20%3D%20%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29%20%5C%5C%5C%5C%20a%5E3-b%5E3%20%3D%20%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20729%3D27%5E2%5C%5C%20%5Cqquad%20%283%5E3%29%5E2%5C%5C%201000%3D10%5E3%20%5Cend%7Bcases%7D%5Cimplies%20729%5E%7B15%7D%2B1000%5Cimplies%20%28%283%5E3%29%5E2%29%5E%7B15%7D%2B10%5E3%20%5C%5C%5C%5C%5C%5C%20%28%283%5E2%29%5E%7B15%7D%29%5E3%2B10%5E3%5Cimplies%20%283%5E%7B30%7D%29%5E3%2B10%5E3%5Cimplies%20%283%5E%7B30%7D%2B10%29~~%5B%283%5E%7B30%7D%29%5E2-%283%5E%7B30%7D%29%2810%29%2B10%5E2%5D%20%5C%5C%5C%5C%5C%5C%20%283%5E%7B30%7D%29%5E3%2B10%5E3%5Cimplies%20%283%5E%7B30%7D%2B10%29~~~~%5B%283%5E%7B60%7D%29-%283%5E%7B30%7D%29%2810%29%2B10%5E2%5D)
now, we could expand them, but there's no need, since it's just factoring.
Answer:
C
Step-by-step explanation:
bc i’m right