She was looking to pay 220 dollars. Since 10% of 220 is 22, 220+22=242.
<u>Answer:</u>
If Matthew knows the volume of a rectangular prism then the height of the prism is 6 meters.
<u>Solution:</u>
Given, Matthew knows the volume of a rectangular prism is 132
And the area of the base is 22
We have to find what is the height?
Now, we know that,
volume of the rectangular prism = area of the base of the prism
height of the prism.
So, substitute the given information in the above formula.
132 = 22
height of the prism.
Height of the prism = ![\frac{132}{22} = \frac{12}{2} = 6m](https://tex.z-dn.net/?f=%5Cfrac%7B132%7D%7B22%7D%20%3D%20%5Cfrac%7B12%7D%7B2%7D%20%3D%206m)
Hence height of the prism is 6 meters.
Answer:
Step-by-step explanation:
![\frac{6 {x}^{ - 1} {y}^{ \frac{7}{2} } }{ \sqrt{16 {x}^{2} } {y}^{2} } \\ \\ = \frac{6 {x}^{ - 1} {y}^{ \frac{7}{2} } }{ \sqrt{(4 {x} {y})^{2} }}\\ \\ = \frac{6 {x}^{ - 1} {y}^{ \frac{7}{2} } }{ {4 {x} {y}}}\\ \\ = \frac{6}{4} {x }^{ - 1 - 1} {y}^{ \frac{7}{2} - 1 } \\ \\ = \frac{3}{2} {x }^{ - 2} {y}^{ \frac{5}{2} } \\ \\ equating \: it \: with \: \\ a {x}^{b} {y}^{c} \\ \\ \implies \\ a = \frac{3}{2} \\ \\ b = - 2 \\ \\ c = \frac{5}{2} \\ \\ abc = \frac{3}{2} \times ( - 2) \times \frac{5}{2} \\ \\ = - \frac{15}{2} \\ \\ =- 7 \frac{1}{2} \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B6%20%7Bx%7D%5E%7B%20-%201%7D%20%20%7By%7D%5E%7B%20%5Cfrac%7B7%7D%7B2%7D%20%7D%20%7D%7B%20%5Csqrt%7B16%20%7Bx%7D%5E%7B2%7D%20%7D%20%20%7By%7D%5E%7B2%7D%20%7D%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%20%5Cfrac%7B6%20%7Bx%7D%5E%7B%20-%201%7D%20%20%7By%7D%5E%7B%20%5Cfrac%7B7%7D%7B2%7D%20%7D%20%7D%7B%20%5Csqrt%7B%284%20%7Bx%7D%20%7By%7D%29%5E%7B2%7D%20%7D%7D%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B6%20%7Bx%7D%5E%7B%20-%201%7D%20%20%7By%7D%5E%7B%20%5Cfrac%7B7%7D%7B2%7D%20%7D%20%7D%7B%20%7B4%20%7Bx%7D%20%7By%7D%7D%7D%5C%5C%20%20%5C%5C%20%20%3D%20%20%20%5Cfrac%7B6%7D%7B4%7D%20%20%7Bx%20%7D%5E%7B%20-%201%20-%201%7D%20%20%7By%7D%5E%7B%20%5Cfrac%7B7%7D%7B2%7D%20-%201%20%7D%20%20%5C%5C%20%20%5C%5C%20%20%20%3D%20%20%20%5Cfrac%7B3%7D%7B2%7D%20%20%7Bx%20%7D%5E%7B%20-%202%7D%20%20%7By%7D%5E%7B%20%5Cfrac%7B5%7D%7B2%7D%20%7D%20%20%5C%5C%20%20%5C%5C%20equating%20%5C%3A%20it%20%5C%3A%20with%20%5C%3A%20%20%5C%5C%20a%20%7Bx%7D%5E%7Bb%7D%20%20%7By%7D%5E%7Bc%7D%20%20%5C%5C%20%20%5C%5C%20%20%5Cimplies%20%5C%5C%20a%20%3D%20%20%5Cfrac%7B3%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20b%20%3D%20%20-%202%20%5C%5C%20%20%5C%5C%20c%20%3D%20%20%5Cfrac%7B5%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20abc%20%3D%20%20%5Cfrac%7B3%7D%7B2%7D%20%20%5Ctimes%20%28%20-%202%29%20%5Ctimes%20%20%5Cfrac%7B5%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20-%20%20%5Cfrac%7B15%7D%7B2%7D%20%20%20%5C%5C%20%20%5C%5C%20%20%3D-%207%20%5Cfrac%7B1%7D%7B2%7D%20%20%5C%5C%20)
The first term is, x2 its coefficient is 1 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is -40
Step-1 : Multiply the coefficient of the first term by the constant 1 • -40 = -40
Step-2 : Find two factors of -40 whose sum equals the coefficient of the middle term, which is -3 .
-40 + 1 = -39
-20 + 2 = -18
-10 + 4 = -6
-8 + 5 = -3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 5
x2 - 8x + 5x - 40
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-8)
Add up the last 2 terms, pulling out common factors :
5 • (x-8)
Step-5 : Add up the four terms of step 4 :
(x+5) • (x-8)
Which is the desired factorization
Answer: 6 • ( x + 5 ) • ( x - 8 )