Y=-2x+2 and y=x^2-3x.
If there are solutions the x and y values are equal so we can say y=y:
x^2-3x=-2x+2 add 2x to both sides
x^2-x=2 subtract 2 from both sides
x^2-x-2=0 now factor...
x^2+x-2x-2=0
x(x+1)-2(x+1)=0
(x-2)(x+1)=0
So there are two solutions, when x=-1 and 2
Using y=-2x+2 we can find the corresponding y values for the solutions...
y(-1)=-2(-1)+2=2+2=4, y(2)=-2(2)+2=-4+2=-2 so the two solutions are the points:
(-1,4) and (2,-2)
7.04 = 704/100 = 176/25
7.04 = 704%
There are a total of 32 problems.
Assumed all 32 problems are 3 points questions ⇒ 32 x 3 = 96 points.
The test is worth 111 points, so there is an extra of 111-96 points = 15 points.
The difference in points in the 2 type of questions is 4 - 3 = 1 points.
Number of 4 points questions = 15 ÷ 1 = 15.
Number of 3 points questions = 32 - 15 = 17.
Answer: There are 17 3-points questions and 15 4-points questions.
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