Answer:
Step-by-step explanation:
The equation of a line in slope-intercept form is
y = mx + b
We need to find the slope, m, and the y-intercept, b.
The line we need is perpendicular to the line 2x + y = 8.
<em>The slopes of perpendicular lines are negative reciprocals.</em>
We solve the given equation for y to find the slope of the given line.
2x + y = 8
y = -2x + 8
The given line has slope -2.
The negative reciprocal of -2 is 1/2.
Our line has slope, m = 1/2.
Now we have
y = 1/2 x + b
Now we use the given point, (-2, 3), for x and y, using x = -2, and y = 3, and we solve for b.
y = 1/2 x + b
3 = 1/2 * (-2) + b
3 = -1 + b
4 = b
b = 4
Now we have
y = 1/2 x + 4
Answer:
say we're going to add "x" gallons of water, now how many gallons of alcohol is in pure water? well 0%, and 0% of "x" is (0/100) * x = 0.
the 3 gallons we know are 100% alcohol, how many gallons of alcohol is in it? well (100/100) * 3 = 3.
the resulting mix will have x + 3 gallons total and it's going to be 15% alcohol, how many gallons of alcohol is that? (15/100) * (x+3).
now, the amount of alcohol never increased, so the original 3 gallons of only alcohol will remain even after the water has been added, so.
![\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{gallons of }}{amount}\\ \cline{2-4}&\\ \textit{pure water}&x&0.00&0\\ \textit{pure alcohol}&3&1.00&3\\ \cline{2-4}&\\ mixture&x+3&0.15&0.15(x+3) \end{array} \begin{array}{llll} \\[3em] \leftarrow \textit{this amount}\\\\ \leftarrow \textit{must be equal to this one} \end{array} \\\\\\ 3 = 0.15(x+3)\implies 3=0.15x+0.45\implies 2.55=0.15x \\\\\\ \cfrac{2.55}{0.15}=x\implies 17=x](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Blcccl%7D%20%26%5Cstackrel%7Bsolution%7D%7Bquantity%7D%26%5Cstackrel%7B%5Ctextit%7B%5C%25%20of%20%7D%7D%7Bamount%7D%26%5Cstackrel%7B%5Ctextit%7Bgallons%20of%20%7D%7D%7Bamount%7D%5C%5C%20%5Ccline%7B2-4%7D%26%5C%5C%20%5Ctextit%7Bpure%20water%7D%26x%260.00%260%5C%5C%20%5Ctextit%7Bpure%20alcohol%7D%263%261.00%263%5C%5C%20%5Ccline%7B2-4%7D%26%5C%5C%20mixture%26x%2B3%260.15%260.15%28x%2B3%29%20%5Cend%7Barray%7D%20%5Cbegin%7Barray%7D%7Bllll%7D%20%5C%5C%5B3em%5D%20%5Cleftarrow%20%5Ctextit%7Bthis%20amount%7D%5C%5C%5C%5C%20%5Cleftarrow%20%5Ctextit%7Bmust%20be%20equal%20to%20this%20one%7D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5C%5C%203%20%3D%200.15%28x%2B3%29%5Cimplies%203%3D0.15x%2B0.45%5Cimplies%202.55%3D0.15x%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B2.55%7D%7B0.15%7D%3Dx%5Cimplies%2017%3Dx)
Answer:
20t
Step-by-step explanation:
15 is where the boat started so 20t is how much the boat traveled from the origional position of 15
Answer:
width= 27 ft, length=78 ft
Step-by-step explanation:
P=2l+2w
210=2l+2w
Divide by 2
105=l+w
l=5w-57
Substitute for l
105=6w-57
6w=162
w=27
l=5(27)-57
=135-27
l=78
Answer:
3.75
hope thus helped
Step-by-step explanation:
2 + 1 + 1/2 + 1/4 = 3.75
