The rule for expressing a radical as a rational exponent is as follows:
![\sqrt[n]{x^y} = x^ \frac{y}{n}](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bx%5Ey%7D%20%3D%20x%5E%20%5Cfrac%7By%7D%7Bn%7D%20)
So, to find
![\sqrt[3]{27x^2y^3z^4}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B27x%5E2y%5E3z%5E4%7D%20%20)
use that rule.
The cube root of 27 is 3, so the equation will start with 3.
Hope that helps!
Answer:
c. d = 5
Step-by-step explanation:
The difference in coordinates B and C is (14, 17) -(2, 1) = (12, 16). When the figure is scaled by 0.25, that difference becomes ...
0.25(12, 16) = (3, 4)
The length of a line segment with those coordinate differences is ...
d = √(3² +4²) = √25 = 5 . . . . matches selection c.
Answer:
The price of the homes in the Pittsburgh sample typically vary by about $267,210 from the mean home price of $500,000.
Step-by-step explanation:
The dotplots reveal that the variability of home prices in the Pittsburgh sample is greater than the variability of home prices in the Philadelphia sample. Therefore, the standard deviation of the home prices for the Pittsburgh sample is $267,210 rather than $100,740. The correct interpretation of this statistic is that the price of homes in Pittsburgh typically vary by about $267,210 from the mean home price of $500,000.
Answer:
Step-by-step explanation:
![\sf 3(t+3)+5(3+2t)-76 = 0\\\\Expanding \ Parenthesis\\\\3t + 9 + 15 + 10t -76 = 0\\\\13t + 24 -76 = 0\\\\13t - 52 = 0\\\\Add \ 52 \ to \ both \ sides\\\\13t = 52\\\\Dividing\ both\ sides\ by\ 13\\\\t = 52/13\\\\t = 4\\\\\rule[225]{225}{2}](https://tex.z-dn.net/?f=%5Csf%203%28t%2B3%29%2B5%283%2B2t%29-76%20%3D%200%5C%5C%5C%5CExpanding%20%5C%20Parenthesis%5C%5C%5C%5C3t%20%2B%209%20%2B%2015%20%2B%2010t%20-76%20%3D%200%5C%5C%5C%5C13t%20%2B%2024%20-76%20%3D%200%5C%5C%5C%5C13t%20-%2052%20%3D%200%5C%5C%5C%5CAdd%20%5C%2052%20%5C%20to%20%5C%20both%20%5C%20sides%5C%5C%5C%5C13t%20%3D%2052%5C%5C%5C%5CDividing%5C%20both%5C%20sides%5C%20by%5C%2013%5C%5C%5C%5Ct%20%3D%2052%2F13%5C%5C%5C%5Ct%20%3D%204%5C%5C%5C%5C%5Crule%5B225%5D%7B225%7D%7B2%7D)
Hope this helped!
<h3>~AH1807</h3>
Step-by-step explanation:
(a): 5x^2 + 25 = 5 * x^2 + 5 * 5 = 5(x^2 + 5).
(b): 2x^2 - 3x - 2 = 2x^2 - 4x + x - 2
= 2x(x - 2) + 1(x - 2) = (2x + 1)(x - 2).
