This system has one solution. {y=5x−9y=x2−3x+7 What is the y-coordinate of the solution?

1 answer:

3 0

The y-coordinate of the solution is 11.

Both equations have y isolated. We will use substitution for this system:

5x-9=x²-3x+7

We want to gather all of the variables on one side, so we will subtract 5x from each side:

5x-9-5x=x²-3x+7-5x
-9=x²-8x+7

We want the equation to be equal to 0 to solve it, so we will add 9 to both sides:

-9+9=x²-8x+7+9
0=x²-8x+16

This is easy to factor; factors of 16 that sum to -8 are -4 and -4:
0=(x-4)(x-4)

Since these are the same factor, we solve it to get our answer:
x-4=0
x-4+4=0+4
x=4

Substitute this into the first, linear, equation:
y=5(4)-9=20-9=11

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Step-by-step explanation:

I beleive those options corresponds to another question, i will ignore them. We want to know an interval in which the probability that a height falls there is 0.8.

In such interval, the probability that a value is higher than the right end of the interval is (1-0.8)/2 = 0.1

If X is the distribuition of heights, then we want z such that P(X > z) = 0.1. We will take W, the standarization of X, wth distribution N(0,1)

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The values of the cumulative distribution function of W, denoted by $\phi$ , can be found in the attached file. Lets call $y = \frac{z-70}{4}$ . We have