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Oksi-84 [34.3K]
3 years ago
10

A 45-inch string is cut into 2 pieces. If the ratio of the longer piece to the shorter piece is 3:2, what is the length of the s

horter piece?
a. 9
b. 12
c. 18
d. 27
e. 36
Mathematics
1 answer:
Amiraneli [1.4K]3 years ago
8 0
The answer is 30 inches. All the answers above are incorrect.
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Find the x-intercepts of the parabola with vertex (-5,80) and y-intercept (0,-45). Write your answer in this form (x of 1 , y of
Ivan
A parabola is a quadratic function, and a quadratic can be expressed in vertex form, which is:

y=a(x-h)^2+k, where (h,k) is the vertex (absolute maximum or minimum point of the quadratic)

In this case we are given that (h,k) is (-5,80) so we have so far:

y=a(x--5)^2+80

y=a(x+5)^2+80, we are also told that it passes through the point (0,-45) so:

-45=a(0+5)^2+80

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-125=25a  divide both sides by 25

-5=a, so now we know the complete vertex form is:

y=-5(x+5)^2+80

The x-intercepts occur when y=0 so:

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5(x+5)^2=80  divide both sides by 5

(x+5)^2=16  take the square root of both sides

x+5=±√16  which is

x+5=±4  subtract 5 from both sides

x=-5±4 so the x-intercepts are:

x=-1 and -9


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Kahn academy question:
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