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## Question Explanations For

##
*Practice Test 3 (Math No-Calculator)*

## 1.

*x*+ 4

*y*, all you need to do is multiply both 3

*x*and 2

*y*by 2, and then add them to get (3

*x*)(2) + (2

*y*)(2) = (15)(2) + (10)(2) = 50.

## 2.

*i*are different, so you can find the answer just by finding the coefficient of

*i*. By using FOIL to expand the binomials, you can find that the coefficient of

*i*is equal to (2

*i*)(4) + (

*i*)(3) = 11

*i*. Since none of the other answer choices include the term 11

*i*, you have found the answer.

## 3.

## 4.

Next, multiply this by the number of hours to get:

## 5.

## 6.

*y*, so multiply the second equation by 2, and subtract the first equation from the second equation:

## 7.

If you got (C), you may have missed the last step, which was to flip the equation so that 1/A becomes A.

## 8.

*y*= 0, so first substitute that into the equation. Now you are solving 3

*x*

^{2}+ 10

*x*– 8 = 0. The fastest way to find the answer, however, is just to look at your possibilities. You know that (B) is not possible, because this would result in the equation 0 = –8, which is not correct. Next, you know that the square will always be positive. Since you need 3

*x*

^{2}+ 10

*x*to equal 8, you know that 4 is not possible, and therefore neither is 8 — both of these would give you a large positive number greater than 8, just in the first term alone; you can therefore also eliminate (C) and (D). You can check the remaining answer by plugging it in, but you know that it has to be correct.

## 9.

*a*is the number of additional gigabytes over 100 used each month, and each time

*a*increases by 1,

*C*increases by 5 (since a has a coefficient of 5). Therefore, each additional gigabyte over 100 gigabytes per month costs $5, so (B) is correct.

## 10.

*y*-axis, so the absolute value function must be for

*x*-values; you can eliminate (D). Next, when

*x*is zero,

*y*is –1. Plugging in values, you can see that only equation that gives you this result is

## 11.

*x*is equal to 0. Plugging this into (A) gives you 6, (B) gives you 7, (C) gives you 6, and (D) gives you 4. Since 6 is the value in the table, either (A) or (C) is correct. When

*x*= 1, (A) gives you 7 and (C) gives you 8, meaning that (A) is correct. You can check the other values in the table to verify that (A) matches the values of all of them.

## 12.

*x*- 5 =

*y*

^{2}+ 1. Next, isolate for a variable — in this case

*x*is easier to isolate:

*x*and

*y*and see which one satisfies this equation. (A) gives -1 = 7/5, so it is incorrect. (B) gives 1 = 2, so it is incorrect. (D) gives 4 = 7/5, so it is incorrect. However, (C) gives 3 = 3, so it is correct.

## 13.

*ax*+ 3)(

*x*– 4) =

*ax*

^{2}+ (3 – 4

*a*)

*x*– 12. By comparing this to the equation given in the question, you know that 3 – 4

*a*= –5, or

*a*= 2.

## 14.

## 15.

*x*+ 4)(

*x*– 1) – 6, and so you can rewrite the expression as

## 16.

## 17.

*x*–

*y*)(

*x*+

*y*) = 20. You know that

*x*–

*y*= 4, so

*x*+

*y*must equal 20/4 = 5. Substituting

*a*for

*x*and

*b*for

*y*gives you

*a*+

*b*= 5.

## 18.

*x*= 2(–2

*x*– 3) + 6. Simplifying gives 5

*x*= 0, so

*x*=0. Since

*x*= 0,

*xy*= 0 no matter what

*y*is.

## 19.

*d*

^{2}and the new value of 1/

*d*

^{2}, and the original force and the new force — since distance is the only factor that changes.

Since you know that the original force and the new force must be in the ratio 4:1 = 64:16, the new force must be 16 exanewtons.

## 20.

*x*-intercept since you can determine that the

*y*-intercept is (0,16) from the equation. Substituting 0 in for

*y*, you get . Solving for

*x*gives you:

Now that you have the triangle’s two intercepts, (12,0) and (0,16), you can solve for its perimeter since you know that the two lines *x* = 0 and *y* = 0 constitute two of its sides. The base of the triangle is 12, and the height of the triangle is 16. Using the Pythagorean Theorem, you can find that the third side (the hypotenuse) of the triangle has length . Therefore, the perimeter of the triangle is 12 + 16 + 20 = 48.