The correct answer is option A. Erica is correct in saying that the two lines are not necessarily the same and we should also look at the y-intercepts before determining how many solutions there were. <span>Two lines with equal slopes could be the same line, but only if they have the same y-intercept.</span>
Let point C be (x, 0), then
AC = sqrt((x - 0)^2 + (0 - 2)^2) = sqrt(x^2 + 4) and
BC = sqrt((x - 9)^2 + (0 - 4)^2) = sqrt(x^2 - 18x + 81 + 16) = sqrt(x^2 - 18x + 97)
AC + BC = sqrt(x^2 + 4) + sqrt(x^2 - 18x + 97)
For minimum AC + BC, d(AC + BC)/dx = 0
d(AC + BC)/dx = x/sqrt(x^2 + 4) + (2x - 18)/sqrt(x^2 - 18x + 97) = 0
x(x^2 - 18x + 97) = -(2x - 18)(x^2 + 4)
x^3 - 18x^2 + 97x = -(2x^3 + 8x - 18x^2 - 72) = -2x^3 + 18x^2 - 8x + 72
3x^3 - 36x^2 + 105x - 72 = 0
x^3 - 12x^2 + 35x - 24 = 0
x = 8, 3, 1
Therefore, point C = (8, 0) or (3, 0) or (1, 0)
Answer:
a
Step-by-step explanation:
Answer:
Step-by-step explanation:
From the first receipt:
2 pounds of grapes + 4 pounds of oranges = 10.70 which, in an algebraic equation, looks like this:
2g + 4o = 10.70
From the second receipt:
3 pounds of grapes + 2 pounds of oranges = 9.65 which, in an algebraic equation, looks like this:
3g + 2o = 9.65
Putting those together into a system and solving using the elimination method:
2g + 4o = 10.7
3g + 2o = 9.65
I am going to eliminate the oranges first since it's easier to do that. I will multiply the second equation by -2 to get a new system:
2g + 4o = 10.7
-6g - 4o = -19.3
As you can see, the oranges are eliminated because 4o - 4o = 0o. That leaves us with only the grapes:
-4g = -8.6 so
g = 2.15
Grapes cost $2.15 per pound. Now sub that into either one of the original equations to solve for the cost per pound of oranges:
2(2.15) + 4o = 10.7 and
4.3 + 4o = 10.7 and
4o = 6.4 so
o = 1.60
Oranges cost $1.60 per pound. That is choice D from your list.
Answer:
108 cubic cm
Step-by-step explanation:
Multiply 3, 3, and 12. Just multiply the dimensions of the cubes.