Answer:
The two solutions of the equation is (0,-4)(6,0).
Now the width is w.
It's twice as long as wide, so now the length is 2w.
If the length is increased by 4 cm, the length will be 2w + 4.
The width is decreased by 3 cm, so the width will be w - 3.
The are of the new rectangle is 100 cm^2.
area = length * width
area = (2w + 4)(w - 3)
The area of the new rectangle is 100, so we get
(2w + 4)((w - 3) = 100
2w^2 - 6w + 4w - 12 = 100
2w^2 - 2w - 112 = 0
w^2 - w - 56 = 0
(w - 8)(w + 7) = 0
w - 8 = 0 or w + 7 = 0
w = 8 or w = -7
A width cannot be negative, so discard w = -7.
w = 8
The width is 8 cm.
The length is twice the width, so the length is 16 cm.
Answer:
x=17, y=9. (17, 9).
Step-by-step explanation:
x+y=26
3x+8y=123
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x=26-y
3(26-y)+8y=123
78-3y+8y=123
78+5y=123
5y=123-78
5y=45
y=45/5
y=9
x=26-9=17
Answer:
D.) (14, 0); the time it takes for the bird to reach the ground
Step-by-step explanation:
The attached graph shows a plot of the table values and the two offered solution options.
The dependent variable in this scenario is the bird's height above the ground. When that is zero, the bird is on the ground. This fact makes choices B and C seem ridiculous.
We note from the table and graph that the bird is on a path that decreases in height by 3 feet every 2 seconds. If the bird continues that rate of descent, it will reach the ground after 14 seconds.
That is, its (time, height) pair will be (14, 0), matching choice D.
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Choosing any answer to this question requires making assumptions that are inconsistent with real-world bird behavior. At least, the problem statement should say what assumptions are applicable.