Answer: Jen’s 83
Step by step;
Answer and Explanation:
If the rectangle is dilated by a scale factor of 2, that means that all of its sides are doubled.
(a) Originally, AB = CD = 15
So, we just multiply 15 by 2: 15 * 2 = 30. Now, A'B' = C'D' = 30 cm
Originally, AC = BD = 8
We just multiply 8 by 2: 8 * 2 = 16. Now, A'C' = B'D' = 16 cm
(b) Basically, the drawing will be of a new rectangle with dimensions of 30 cm by 16 cm.
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Answer: D) 5</h3>
Work Shown:
a = 3 and b = 4 are the two legs
c = x is the unknown hypotenuse
Use the pythagorean theorem to solve for c
a^2 + b^2 = c^2
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
c^2 = 25
c = sqrt(25)
c = 5
First, we'd need to find the feasible region which is bounded by the constraints 2 ≤ x ≤ 6, 1 ≤ y ≤ 5 and x + y ≤ 8. Let's graph all of them and we'll get the feasible region as unshaded in the attached image. To find the maximum for p = 3x + 2y, we'll plug the coordinates of the vertices in and compare them.
p(6,1) = 3(6) + 2(1) = 20
p(2,1) = 3(2) + 2(1) = 8
p(2,5) = 3(2) + 2(5) = 16
p(3,5) = 3(3) + 2(5) = 19
p(6,2) = 3(6) + 2(2) = 22
So the maximum value of p is 22 as x = 6 and y = 2.