# 2015 MTAP Reviewer for Grade 9 Solutions(6-10)

Previously, we solved the first 5 problems in 2015 Eliminations of MMC for grade 9. This time, let’s move on to the other 5 problems. You may utilize this site if you are not a grade 9 student. We have a search button at the top menu to take you to the right page. All reviewers for grade 9 can be checked here.

Problem:

If and , what is x?

Solution:

We solve for y for the second equation,

Now, we substitute this y to the first equation,

we equate this to 0,

Observe that this is a quadratic equation in x/9, thus by factoring we have

Solving for x’s:

Solving for another x:

Since x>0 is the given restriction in the problem, the only solution is x=9.

Problem 7:

If , what is f(x-3)?

Solution:

We can rewrite f(x) in factor form as follows,

To find f(x-3), we let x=x-3,

Problem 8:

If and , for all real number x. For what real number does

Solution:

Solving for g(-a) and f(-a),

For f(-a),

Going back to the desired equation,

Solving for a:

Solving for another value of a:

Therefore, the answers are 0 and -1.

Problem 9:

Solve for x:

Solution:

First step is to square both sides of equation to remove the outermost radical.

Squaring both sides again,

Problem 10:

Solve for x:

Solution:

By cross multiplying the left side of equation we have,

let A=2x, B=x+2,

Simplifying,

By factoring,

Plugging in the real values of A and B we have,

Solving for x:

### Dan

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