Question

I don't understand how to do this someone help me math!!

Answer 1

-8

Explanation:

ky^2 = -5y + 7y^2 +9y - 15y^2 -4y

ky^2 = -8 y^2

k = -8

Answer 2

8

Explanation:

We believe the problem here requires that all of the coefficients in the expression on the left be zero. That is, the equation will be true for any value of y.

We can work this a couple of ways. One of them is to simplify the given expression. Let 'a' represent our unknown coefficient.

`-ay^2-[-5y-y(-7y-9)]-[-y(15y+4)]=0\\\\-ay^2-[-5y+7y^2+9y]+[15y^2+4y]=0\\\\-ay^2-[7y^2+4y]+15y^2+4y=0\\\\(-a-7+15)y^2+(-4+4)y=0\\\\(-a+8)y^2=0`

In order for this to be zero for all values of y, we must have (-a+8) = 0.

a = 8

The missing coefficient is 8.

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Since this expression must be true for every value of y, another way to work this is to choose a value of y. This will tell us what the coefficient must be for the expression to be zero. Let y = 1.

-a·1² -[-5·1 -1(-7·1 -9)] -[-1(15·1 +4)] = 0

-a -[-5-(-16)] -[-19] = 0

-a -11 +19 = 0

-a +8 = 0

a = 8 . . . . . . same as above

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Additional comment

The many minus signs are intended to make sure you're comfortable with arithmetic with negative coefficients and negative numbers. The key, of course, is that -(-a) = +a. The opposite of the opposite is the original.

We have assumed that the dash at the beginning of the line (before the answer box) is intended to be a minus sign. If that is not the case, then your answer will be -8, instead of 8.