The answer is 1700 because 1679 rounded to the nearest hundred is 1700
The volume of the box is length * width * height
x^3 + 9x^2 + 6x - 16 = (x + 2) * width * (x + 8) = (x^2 + 10x + 16) * width
using synthetic division
-2 1 9 6 -16
-2 -14 16
-8 1 7 -8 0
-8 8
1 -1 0
Therefore, x^3 + 9x^2 + 6x - 16 = (x + 2)(x + 8)(x - 1)
Therefore, the width of the prism is x - 1
Answer:
![-\frac{16}{17}\\-0.94117](https://tex.z-dn.net/?f=-%5Cfrac%7B16%7D%7B17%7D%5C%5C-0.94117)
Step-by-step explanation:
![\frac{-\frac{1}{2}}{\frac{2\left(9+3\right)-4-3}{4\left(8\right)}}\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=\frac{-\frac{1}{2}}{\frac{2\left(9+3\right)-4-3}{4\cdot \:8}}\\\frac{2\left(9+3\right)-4-3}{4\cdot \:8}=\frac{17}{32}\\\frac{2\left(9+3\right)-4-3}{4\cdot \:8}\\2\left(9+3\right)-4-3=17\\2\left(9+3\right)-4-3\\2\left(9+3\right)=24\\2\left(9+3\right)\\\mathrm{Add\:the\:numbers:}\:9+3=12\\=2\cdot \:12\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:12=24\\=24-4-3](https://tex.z-dn.net/?f=%5Cfrac%7B-%5Cfrac%7B1%7D%7B2%7D%7D%7B%5Cfrac%7B2%5Cleft%289%2B3%5Cright%29-4-3%7D%7B4%5Cleft%288%5Cright%29%7D%7D%5C%5C%5Cmathrm%7BRemove%5C%3Aparentheses%7D%3A%5Cquad%20%5Cleft%28a%5Cright%29%3Da%5C%5C%3D%5Cfrac%7B-%5Cfrac%7B1%7D%7B2%7D%7D%7B%5Cfrac%7B2%5Cleft%289%2B3%5Cright%29-4-3%7D%7B4%5Ccdot%20%5C%3A8%7D%7D%5C%5C%5Cfrac%7B2%5Cleft%289%2B3%5Cright%29-4-3%7D%7B4%5Ccdot%20%5C%3A8%7D%3D%5Cfrac%7B17%7D%7B32%7D%5C%5C%5Cfrac%7B2%5Cleft%289%2B3%5Cright%29-4-3%7D%7B4%5Ccdot%20%5C%3A8%7D%5C%5C2%5Cleft%289%2B3%5Cright%29-4-3%3D17%5C%5C2%5Cleft%289%2B3%5Cright%29-4-3%5C%5C2%5Cleft%289%2B3%5Cright%29%3D24%5C%5C2%5Cleft%289%2B3%5Cright%29%5C%5C%5Cmathrm%7BAdd%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A9%2B3%3D12%5C%5C%3D2%5Ccdot%20%5C%3A12%5C%5C%5Cmathrm%7BMultiply%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A2%5Ccdot%20%5C%3A12%3D24%5C%5C%3D24-4-3)
![\mathrm{Subtract\:the\:numbers:}\:24-4-3=17\\=\frac{17}{4\cdot \:8}\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:8=32\\=\frac{17}{32}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}\\=-\frac{\frac{1}{2}}{\frac{17}{32}}\\\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}\\=-\frac{1\cdot \:32}{2\cdot \:17}\\Refine\\=-\frac{32}{2\cdot \:17}\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:17=34\\=-\frac{32}{34}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubtract%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A24-4-3%3D17%5C%5C%3D%5Cfrac%7B17%7D%7B4%5Ccdot%20%5C%3A8%7D%5C%5C%5Cmathrm%7BMultiply%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A4%5Ccdot%20%5C%3A8%3D32%5C%5C%3D%5Cfrac%7B17%7D%7B32%7D%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3Afraction%5C%3Arule%7D%3A%5Cquad%20%5Cfrac%7B-a%7D%7Bb%7D%3D-%5Cfrac%7Ba%7D%7Bb%7D%5C%5C%3D-%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%7D%7B%5Cfrac%7B17%7D%7B32%7D%7D%5C%5C%5Cmathrm%7BDivide%5C%3Afractions%7D%3A%5Cquad%20%5Cfrac%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%7B%5Cfrac%7Bc%7D%7Bd%7D%7D%3D%5Cfrac%7Ba%5Ccdot%20%5C%3Ad%7D%7Bb%5Ccdot%20%5C%3Ac%7D%5C%5C%3D-%5Cfrac%7B1%5Ccdot%20%5C%3A32%7D%7B2%5Ccdot%20%5C%3A17%7D%5C%5CRefine%5C%5C%3D-%5Cfrac%7B32%7D%7B2%5Ccdot%20%5C%3A17%7D%5C%5C%5Cmathrm%7BMultiply%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A2%5Ccdot%20%5C%3A17%3D34%5C%5C%3D-%5Cfrac%7B32%7D%7B34%7D)
![\mathrm{Cancel\:the\:common\:factor:}\:2\\=-\frac{16}{17}\\\mathrm{Decimal:\quad }\:-0.94117](https://tex.z-dn.net/?f=%5Cmathrm%7BCancel%5C%3Athe%5C%3Acommon%5C%3Afactor%3A%7D%5C%3A2%5C%5C%3D-%5Cfrac%7B16%7D%7B17%7D%5C%5C%5Cmathrm%7BDecimal%3A%5Cquad%20%7D%5C%3A-0.94117)
Answer:
gcf, hcf, gcd (65; 169) = 13: greatest (highest) common factor (divisor), calculated. The numbers have common prime factors.
Answer:
t=2x-2/-2x-5
Step-by-step explanation:
y=-2x-5
ty= 2x-2
add the y value in
t-2x-5=2x-2
combine like terms
t=4x+3
hope this helps :)