Answer:
The first one is missing (d - 9) so it would be 5(d -9) or when you factor it out 5d - 45
In the second one (d + 7) is missing so it will be 8d(d + 7) so if you factor that out you will receive 8d^2 + 56
Step-by-step explanation:
3d^2 + 18d -21 =(3d -3)( d + 7)
3d^2 -30d +27 =(3d -3)(d - 9)
 
        
             
        
        
        
let's firstly convert the mixed fraction to improper fraction and then take it from there, keeping in mind that the whole is "x".
![\stackrel{mixed}{5\frac{5}{6}}\implies \cfrac{5\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{35}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{3}x~~ = ~~5\frac{5}{6}\implies \cfrac{7}{3}x~~ = ~~\cfrac{35}{6}\implies 42x=105\implies x=\cfrac{105}{42} \\\\\\ x=\cfrac{21\cdot 5}{21\cdot 2}\implies x=\cfrac{21}{21}\cdot \cfrac{5}{2}\implies x=1\cdot \cfrac{5}{2}\implies x=2\frac{1}{2}](https://tex.z-dn.net/?f=%5Cstackrel%7Bmixed%7D%7B5%5Cfrac%7B5%7D%7B6%7D%7D%5Cimplies%20%5Ccfrac%7B5%5Ccdot%206%2B5%7D%7B6%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B35%7D%7B6%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B7%7D%7B3%7Dx~~%20%3D%20~~5%5Cfrac%7B5%7D%7B6%7D%5Cimplies%20%5Ccfrac%7B7%7D%7B3%7Dx~~%20%3D%20~~%5Ccfrac%7B35%7D%7B6%7D%5Cimplies%2042x%3D105%5Cimplies%20x%3D%5Ccfrac%7B105%7D%7B42%7D%20%5C%5C%5C%5C%5C%5C%20x%3D%5Ccfrac%7B21%5Ccdot%205%7D%7B21%5Ccdot%202%7D%5Cimplies%20x%3D%5Ccfrac%7B21%7D%7B21%7D%5Ccdot%20%5Ccfrac%7B5%7D%7B2%7D%5Cimplies%20x%3D1%5Ccdot%20%5Ccfrac%7B5%7D%7B2%7D%5Cimplies%20x%3D2%5Cfrac%7B1%7D%7B2%7D)
 
        
             
        
        
        
Answer:

Step-by-step explanation:
The dimensions must be the same
10 yards = 10 × 3 feet = 30 feet
ratio =  =
 = 
 
        
             
        
        
        
The first option is correct
        
             
        
        
        
Answer:
Step-by-step explanation:
Dilation of a line about a point not on the line shifts the line but leaves the slope intact .
New line slope will be -2
As both A and C lie on a horizontal line y = 2, C' will also lie on the same line
The distance between A and C is 0 - 2 = -2
a scale factor of 3 means C' is -2(3) = -6 units left of A
C' = (2 - 6, 2) = (-4. 2)