5x - 2y = -6 ⇒ 10x - 4y = -12
2x - 1y = 1 ⇒ <u>10x - 5y = 5</u>
y = -17
5x - 2(-17) = -6
5x + 34 = -6
<u> - 34 - 34</u>
<u>5x</u> = <u>-40</u>
5 5
x = -8
(x, y) = (-8, -17)
2x + 3y = 432 ⇒ 10x + 15y = 2160
5x + 2y = 16 ⇒ <u>10x + 4y = 32</u>
<u>11y</u> = <u>2128</u>
11 11
y = 193.4545455
2x + 3(193.4545455) = 432
2x + 580.3636364 = 432
<u> - 580.3636364 - 580.3636364</u>
<u>2x</u> = <u>-148.3636364</u>
2 2
x = -74.1818182
(x, y) = (-74.1818184, 193.4545455)
Answer:
512
Step-by-step explanation:
Suppose we ask how many subsets of {1,2,3,4,5} add up to a number ≥8. The crucial idea is that we partition the set into two parts; these two parts are called complements of each other. Obviously, the sum of the two parts must add up to 15. Exactly one of those parts is therefore ≥8. There must be at least one such part, because of the pigeonhole principle (specifically, two 7's are sufficient only to add up to 14). And if one part has sum ≥8, the other part—its complement—must have sum ≤15−8=7
.
For instance, if I divide the set into parts {1,2,4}
and {3,5}, the first part adds up to 7, and its complement adds up to 8
.
Once one makes that observation, the rest of the proof is straightforward. There are 25=32
different subsets of this set (including itself and the empty set). For each one, either its sum, or its complement's sum (but not both), must be ≥8. Since exactly half of the subsets have sum ≥8, the number of such subsets is 32/2, or 16.
Answer:
$42 more.
Step-by-step explanation:
Baseball: 8(3) = $24
Basketball: 6(11) = $66
66 - 24 = $42
Answer:
Step-by-step explanation:
We can form a right triangle where the distance between the ranger's current position and fire is the hypotenuse of the triangle. In a right triangle, the tangent of an angle is equal to its opposite side divided by the hypotenuse.
Therefore, we have:
, where 
is the distance between the base of the tower and the fire.
Solving, we get:
