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## Question Explanations For

##
*Practice Test 2 (Math No-Calculator)*

## 1.

*x*+ 6 = 5

*x*. You can subtract 3

*x*from each side of the equation to get 6 = 2

*x*, so

*x*= 3.

## 2.

*a*

^{2}–

*a*+ 6.

## 3.

*x*– 2|. Since the function is drawn with a solid line and the shaded values are above it, you know the

*y*values are greater than or equal to the function, so

*y*≥ |

*x*– 2|.

## 4.

*m*represent the amount of money that Sophia and Jazmin had originally. Then 2(

*m*– 15,000) =

*m*+ 15,000 after Sophie gives Jazmin $15,000. Rearranging gives 2

*m*=

*m*+ 45,000, so

*m*= 45,000.

## 5.

*x*in the equation for this function. Therefore, (B) is correct.

## 6.

*x*. However, the $0.10 he pays for electricity does vary according to how many kilowatt-hours he uses, so that value must be multiplied by

*x*. Adding the two together gives you 1,195 + 0.1

*x*dollars.

If you chose (C), you may have forgotten that the electricity cost was ten cents, not dollars, per kWh.

## 7.

*y*= –

*ax*+ 5 and

*y*= -3

*x*+ 5/2. It is now clear that

*a*= 3.

If you chose (D), you may have forgotten to divide the second equation by 2.

## 8.

*y*must be 90° since it forms a triangle with

*F*and

*D*. Similarly, we know that angle ABD is 60° because it is equal to angle BDF, and because

*BD*is parallel to

*CE*, angle BCE is also 60°. This means that angle

*x*is 180° – 60° = 120°, so

*x*–

*y*= 120° – 90° = 30°.

If you chose (C) or (D), you may have found either the value of *y* or *x* and stopped there.

## 9.

Plugging this into the other given equation gives you:

You know that *y* = 4*x* = 4(3) = 12. Finally, *x* + *y* = 3 + 12 = 15.

If you got (A) or (C), you found the value of *x* or *y* and stopped there.

## 10.

*h*increases by 1,

*C*decreases by 2. This means that after an hour, Niki has two fewer cars remaining to test drive, meaning that he test drives cars at a rate of 2 per hour.

## 11.

*x*

^{2}– 1) = (

*x*+ 1)(

*x*– 1), and then cancel out the (

*x*+ 1) from the numerator and denominator (since you know that

*x*is positive, this expression cannot equal zero). You are then left with (

*x*– 1)(

*x*– 1) = (

*x*– 1)

^{2}.

## 12.

*x*)=

*cx*

^{2}– 9

*c*. From here, you can see that the equation is now in the quadratic standard form f(

*x*)=

*ax*

^{2}+

*bx*+

*c*. When considering the graph of a parabola, the constant

*a*affects its width, the constant

*b*affects its horizontal shift, and the constant

*c*shows its

*y*-intercept. In this case, the equation is missing its middle term, so

*b*=0. This means that the graph has no horizontal shift. So, the axis of symmetry is the

*y*-axis. The vertex lies on this line of symmetry, so its

*x*-value is 0. This means that the vertex of the parabola is (0, -18), and plugging that point into the given equation and solving for

*c*gives you

*c*

*=2.*

The Correct Answer is (D) —
You can rewrite the left side of the equation as:
The Correct Answer is (A) —
Rewrite the sentence as 5
The Correct Answer is (B) —
Since each circle has an area of π, you know that each circle has a radius of 1. If you draw a square connecting the centers of the circles, that square will have an area of 4, since each side has length 1 + 1 = 2. That square covers the shaded area, but the shaded area does not include the four quarter-circles also covered by the square. Subtracting those four quarter-circles leaves you with an area of 4 – 4(π/4) = 4 – π.
The Correct Answer is (63) —
Rearranging the first equation gives you
The Correct Answer is ($$ \frac 15 \le x \le 1 $$) —
The correct answers is anything in the range ⅕ ≤
The Correct Answer is (7) —
The slope of the line that passes through these points is equal to the difference in
The Correct Answer is (3) —
You know that the width of the rectangle is 6, so to have an area of 24 it must have a height of 24/6 = 4. Since you are given one
The Correct Answer is (18) —
Notice that you can square both sides of the first equation to get:
## 13.

By comparing this with the right side of the equation, you can see that *a* = –4.

## 14.

*x*=

*x*

^{2}– 14. This can be rearranged to give 0 =

*x*

^{2}– 5

*x*– 14, which factors as (

*x*+ 2)(

*x*– 7). Of the solutions, –2 and 7, only –2 is negative.

## 15.

## 16.

*y*= 16 –

*x*. Plugging this in for

*y*in the second equation:

Substitute this value of *x* into the first equation to get *y* = 16 – 7 = 9. Therefore, the value of *xy* is (7)(9) = 63.

## 17.

*x*≤ 1. First, substitute

*y*= 2

*x*into the first inequality to get |3

*x*- 1| ≤ 2

*x*. Split this absolute value expression into two cases and solve the first case:

Next, solve the second case:

You can see that *x* ≤ 1 and *x* ≥ ⅕. Combining these conditions tells you that a possible value for *x* is anything in the range ⅕ ≤ *x* ≤ 1.

## 18.

*y*-values divided by the difference in

*x*-values: . You can cross-multiply and simplify to find that

*a*= 7.

## 19.

*y*-value, –1, the other

*y*-value must be 3 for the rectangle to have a height of 4.

## 20.