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ratelena [41]
3 years ago
8

If 3x +4y = 7 and 2y = 6x + 6, then what is xy

Mathematics
1 answer:
Jet001 [13]3 years ago
4 0
3x + 12x + 12 = 7
15x + 12 = 7
15x = -5
x = 1/3

3 (1/3) + 4y = 7
1 + 4y = 7
4y = 6
y = 1.5

3 (1/3) + 4 (1.5) = 7
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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
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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

-45=25a+80  subtract 80 from both sides

-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:

0=-5(x+5)^2+80  add 5(x+5)^2 to both sides

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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