The solutions for each case are listed below:
- x = 65
- x = 35
- (x, y) = (48, 21)
- (x, y) = (15, 8)
<h3>How to solve on systems of linear equation by taking advantage of angle relationships</h3>
In this problem we must solve algebraic equations by taking advantage of angle properties. Now we proceed to solve the variables for each case:
Case 1 - Opposite angles
2 · x - 10 = 120
2 · x = 130
x = 65
Case 2 - Opposite angles
2 · x + 25 = 3 · x - 10
25 + 10 = 3 · x - 2 · x
35 = x
x = 35
Case 3 - Opposite angles generated by two perpendicular lines
2 · y + 50 = x + 44 (1)
5 · y - 17 = 7 · x - 248 (2)
- x + 2 · y = - 6
7 · x - 5 · y = 231
x = 48, y = 21
Case 4 - Opposited angles generated by two perpendicular angles
6 · x = 90 (3)
9 · y + 18 = 90 (4)
The solution to this system of linear equations is (x, y) = (15, 8).
To learn more on systems of linear equations: brainly.com/question/21292369
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Answer:
the requirements are missing:
- express the height of the rectangle in terms of w
- express the area of the rectangle in terms of w
1) the height of the rectangle is:
w + h + h + w = 500 + w
2w + 2h = 500 + w
2h = 500 + w - 2w = 500 - w
h = (500 - w) / 2 = 250 - 0.5w
2) the are of the rectangle is:
w x h = w x (250 - 0.5w) = 250w - 0.5w²
-5.55 - 8.55c + 4.35c
-8.55c + 4.35c = -4.2c
-5.55 - 4.2c is the answer.
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