Mr. Cutler should make 2 bricks and 7 tiles to maximize his profit.
<u>Step-by-step explanation:</u>
Let the no. of bricks be 'b'
Let the no. of tiles be 't'
Time taken for 1 brick = 10 mins
Time taken for 1 tile = 20 mins
Clay used for 1 bick = 3 pounds
Clay used for 1 tile = 2 pounds
Profit on each brick = $2
Profit on each tile = $3
Total time available= 160 mins
Total clay available = 20 pounds
10b + 20t = 160
b + 2t = 16
b = 16 - 2t
3b + 2t = 20
3(16 - 2t) +2t = 20
48 - 6t + 2t = 20
48 - 4t = 20
-4t = 20-48
4t = 28
t = 7
b = 16 - 2t
b = 16 - 14
b = 2
Mr. Cutler should make 2 bricks and 7 tiles to maximize his profit.
So it went from the 16th term to the 17th term, and went from 21 to -1... what would the "common difference"
d be then?
le'ts see
![\bf a_{16}=21\quad and\quad a_{17}=-1 \\\\\\ a_{16}+d=-1\implies 21+d=-1\implies d=-1-21\implies \boxed{d=-22}](https://tex.z-dn.net/?f=%5Cbf%20a_%7B16%7D%3D21%5Cquad%20and%5Cquad%20a_%7B17%7D%3D-1%0A%5C%5C%5C%5C%5C%5C%0Aa_%7B16%7D%2Bd%3D-1%5Cimplies%2021%2Bd%3D-1%5Cimplies%20d%3D-1-21%5Cimplies%20%5Cboxed%7Bd%3D-22%7D)
alrite.. so d = -22.. hmm what would the first term be then?
![\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ n=16\\ d=-22\\ a_{16}=21 \end{cases} \\\\\\ a_{16}=a_1+(16-1)\boxed{-22}\implies 21=a_1+(16-1)(-22) \\\\\\ 21=a_1+(15)(-22)\implies 21=a_1-330\implies \boxed{351=a_1}\\\\ -------------------------------\\\\ a_n=a_1+(n-1)d\implies \boxed{a_n=351+(n-1)(-22)}](https://tex.z-dn.net/?f=%5Cbf%20n%5E%7Bth%7D%5Ctextit%7B%20term%20of%20an%20arithmetic%20sequence%7D%5C%5C%5C%5C%0Aa_n%3Da_1%2B%28n-1%29d%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0An%3Dn%5E%7Bth%7D%5C%20term%5C%5C%0Aa_1%3D%5Ctextit%7Bfirst%20term%27s%20value%7D%5C%5C%0Ad%3D%5Ctextit%7Bcommon%20difference%7D%5C%5C%0A----------%5C%5C%0An%3D16%5C%5C%0Ad%3D-22%5C%5C%0Aa_%7B16%7D%3D21%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0Aa_%7B16%7D%3Da_1%2B%2816-1%29%5Cboxed%7B-22%7D%5Cimplies%2021%3Da_1%2B%2816-1%29%28-22%29%0A%5C%5C%5C%5C%5C%5C%0A21%3Da_1%2B%2815%29%28-22%29%5Cimplies%2021%3Da_1-330%5Cimplies%20%5Cboxed%7B351%3Da_1%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0Aa_n%3Da_1%2B%28n-1%29d%5Cimplies%20%5Cboxed%7Ba_n%3D351%2B%28n-1%29%28-22%29%7D)
which of course, you can rewrite as
which are all the same.
Answer:
Slope: 1.5
Step-by-step explanation:
We first have to find what y is equal to. That means we take 3x - 5 and divide it by 2. We get 1.5x - 2.5. Since the lines are parallel and they have the same slope and different y - intercepts, we know that the slope will be equal.
Start by factoring -24
6* -4 = -24
7*-3 = -24
you are looking for factors that add to give the middle coefficient +5
7 and -3 add to give 5 and multiply to give -24
( x + 7)(x - 3) = 0
this gives the solution for x, because one or both (x + 7) and/or (x - 3) would have to be zero for them to multiply and be zero.
x = -7
x = 3
Answer:
8
Step-by-step explanation:
3 ounces is 4:80
5 ounces is X
x= <u>5 x 4.80</u>
3
x=8