For this case we must indicate an expression equivalent to:
![(x ^ {\frac {1} {4}} * y ^ {16}) ^ {\frac {1} {2}}](https://tex.z-dn.net/?f=%28x%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B4%7D%7D%20%2A%20y%20%5E%20%7B16%7D%29%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B2%7D%7D)
By definition of power properties we have:
![(a ^ m) ^ n = a ^ {m * n}](https://tex.z-dn.net/?f=%28a%20%5E%20m%29%20%5E%20n%20%3D%20a%20%5E%20%7Bm%20%2A%20n%7D)
We can rewrite the expression as:
![((x ^ {\frac {1} {4}}) ^ {\frac {1} {2}}) * ((y ^ {16}) ^ {\frac {1} {2}}) =\\x ^ {\frac {1} {8}} * y ^ 8](https://tex.z-dn.net/?f=%28%28x%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B4%7D%7D%29%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B2%7D%7D%29%20%2A%20%28%28y%20%5E%20%7B16%7D%29%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B2%7D%7D%29%20%3D%5C%5Cx%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B8%7D%7D%20%2A%20y%20%5E%208)
Answer:
![x ^ {\frac {1} {8}} * y ^ 8](https://tex.z-dn.net/?f=x%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B8%7D%7D%20%2A%20y%20%5E%208)
Answer:
5n+p>40
n+p<20
Step-by-step explanation:
Since pennies are worth 1 cent and nickels 5, using n as the number of nickels and p as the number of pennies, we can say that 5*n+1*p>40. Then, n+p is less than 20, so n+p<20. Our answer is then
5n+p>40
n+p<20
Answer:
![\frac{2x^2-3x}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%5E2-3x%7D%7B7%7D)
Step-by-step explanation:
÷ ![\frac{7}{x^2}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7Bx%5E2%7D)
=>
× ![\frac{x^2}{7}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B7%7D)
=>
× ![\frac{x^2}{x}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7Bx%7D)
=>![\frac{x(2x-3)}{7}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%282x-3%29%7D%7B7%7D)
=> ![\frac{2x^2-3x}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%5E2-3x%7D%7B7%7D)
Check the picture below
so... it looks more or less like so
now, notice the "p" distance, bear in mind that, if the parabola opens downwards, "p" is a negative unit, so, in this case -4
thus
![\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}})} \\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bparabola%20vertex%20form%20with%20focus%20point%20distance%7D%5C%5C%5C%5C%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%28y-%7B%7B%20k%7D%7D%29%5E2%3D4%7B%7B%20p%7D%7D%28x-%7B%7B%20h%7D%7D%29%20%5C%5C%5C%5C%0A%5Cboxed%7B%28x-%7B%7B%20h%7D%7D%29%5E2%3D4%7B%7B%20p%7D%7D%28y-%7B%7B%20k%7D%7D%29%7D%20%5C%5C%0A%5Cend%7Barray%7D%0A%5Cqquad%20%0A%5Cbegin%7Barray%7D%7Bllll%7D%0Avertex%5C%20%28%7B%7B%20h%7D%7D%2C%7B%7B%20k%7D%7D%29%5C%5C%5C%5C%0A%7B%7B%20p%7D%7D%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%0A%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%0A%5Cend%7Barray%7D)
Answer:
D.$79.89
Step-by-step explanation:
Cost of one yard of fabric = $6.99
Length of fabric bought = 8 yards
Cost of one bag of polyester filling = $7.99
Number of bags of polyester filling bought = 3
Total cost of fabric = ![6.99\times 8=\$55.92](https://tex.z-dn.net/?f=6.99%5Ctimes%208%3D%5C%2455.92)
Total cost of polyester filling = ![7.99\times 3=\$23.97](https://tex.z-dn.net/?f=7.99%5Ctimes%203%3D%5C%2423.97)
Total cost of materials bought = Total cost of fabric + Total cost of polyester filling
![=55.92+23.97=\$79.89](https://tex.z-dn.net/?f=%3D55.92%2B23.97%3D%5C%2479.89)
Total cost of materials bought is
.