Wilbur spends 2/3 of his income, share 1/12, and saves the rest. What part of his income does he save? Give the answer in simple
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Answer:
(-4,-18) and (5,90)
Step-by-step explanation:
I'll assume the first equation is supposed to be y – 10 = 11x + x<u>^2</u>
This is a parabola. The second equation is a straight line:
y – 12x = 30
We want to find the points at which these lines intersect. They will intersect for any (x,y) that
Let's rearrange the second equation to isolate y:
y – 12x = 30
y = 30 + 12x
Now we can take the this value of y and substitute it into the first equation:
<u>y</u> – 10 = 11x + x^2
<u>(30 + 12x)</u> – 10 = 11x + x^2
20 + 12x = 11x + x^2
0 = x^2 -x -20
We can factor this into (x+4)(x-5)
That means x can be either -4 or 5.
Find the value of y using these values of x in both original equations:
<u>For x = -4</u>
y – 10 = 11x + x^2
y = 11x + x^2 + 10
y = 11(-4)+(-4)^2 +10
y = -44 + 16 + 10
y = -18 The point both lines meet is at (-4, -18) which was already given in the problem.
<u>For x = 5</u>
y – 10 = 11x + x^2
y = 11x + x^2 + 10
y = 11(5) + (5)^2 + 10
y = 55 + 25 + 10
y = 90
The second point both lines meet is (5,90).
We should use both solutions in the second equation to verify these values, but I'll graph them, instead. See the attached graph to prove these points are correct.
