Answer:
87.97 or 88
Step-by-step explanation:
The minimum happens at x = -b/2a
x = -30 / 2(3) = -30/6 = -5
Now replace x in the equation with -5 and solve:
3(-5)^2 + 30(-5) +27 = 75 - 150 + 27 = -48
The minimum is at (-5,-48)
let's firstly convert the mixed fractions to improper fractions, and then add.
![\bf \stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}}~\hfill \stackrel{mixed}{2\frac{5}{6}}\implies \cfrac{2\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{17}{6}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{13}{4}+\cfrac{17}{6}\implies \stackrel{\textit{we'll use the LCD of 12}}{\cfrac{(3)13~~+~~(2)17}{12}}\implies \cfrac{39+34}{12}\implies \cfrac{73}{12}\implies 6\frac{1}{12}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B1%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%204%2B1%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B13%7D%7B4%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B2%5Cfrac%7B5%7D%7B6%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Ccdot%206%2B5%7D%7B6%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B17%7D%7B6%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Ccfrac%7B13%7D%7B4%7D%2B%5Ccfrac%7B17%7D%7B6%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bwe%27ll%20use%20the%20LCD%20of%2012%7D%7D%7B%5Ccfrac%7B%283%2913~~%2B~~%282%2917%7D%7B12%7D%7D%5Cimplies%20%5Ccfrac%7B39%2B34%7D%7B12%7D%5Cimplies%20%5Ccfrac%7B73%7D%7B12%7D%5Cimplies%206%5Cfrac%7B1%7D%7B12%7D)
Answer:
y = 2x + 8
Step-by-step explanation:
Recall that two parallel lines have the same slope.
Thus, if we begin with y = 2x - 4, we know that this new line through (-1, 6) will also have slope 2.
Starting from the slope-intercept form y = mx + b, we substitute 2 for m, -1 for x and 6 for y:
6 = 2(-1) + b
and solve for the new y-intercept, b:
6 = -2 + b, or
b = 8
Then the new line has the equation y = 2x + 8
