Answer:
30 years old
Step-by-step explanation:
Let the two ages be A and C.
Then C = (1/2)A, and A = C + 15.
Substitute C + 15 for A in C = (1/2)A:
C = (1/2)(C + 15), or 2C = C + 15.
Then C = 15, and A = C + 15 becomes A = 15 + 15, or A = 30.
1*10<span>- 3 is the standard form of 0.001</span>
Answer:
$9327
Step-by-step explanation:
Apparently, the cost function is supposed to be ...
C(x) = 0.4x^2 -112x +17167
This can be rewritten to vertex form as ...
C(x) = 0.4(x^2 -280) +17167
C(x) = 0.4(x -140)^2 +17167 -0.4(19600)
C(x) = 0.4(x -140)^2 +9327
The vertex of the cost function is ...
(x, C(x)) = (140, 9327)
The minimum unit cost is $9327.
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<em>Comment on the question</em>
You found the number of units that result in minimum cost (140 units), but you have to evaluate C(140) to find the minimum unit cost.
1. the answer is 24. think of x as the original amount, and y as the new amount. y times 1.5 is x, and y+12 is x. reverse that to figure out y, which is what we need, and you have x/1.5 = y as well as x-12 = y. Use the equal values method and make an equation x/1.5=x-12. solve this equation to get x, which is 36. to figure out the new amount, y, you need to subtract 12, which would help you get 24 as your final answer.
2. once again, create an equation. let's call team 1 x and team 2 y. team one has 1/4th as many as team 2, so that would be x=1/4y. An easier way to write that is 4x=y. after 6 people quit team two, that would be y-6. after the transfer, that would be y-6-12, and x+12 for the teams. they are equal after these, so y-6-12=x+12. solve this equation to get y-18= x+12. if you recall earlier, y was 4 times x, so substitute that into y to get 4x-18=x+12. Solve the equation to get 10 people on team one originally. your final answer is 10 people.
