# Act 5-in-5 #6-10 Recap

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• 1.

### What value of a in the equation 3x + a – 7 = 5x – a causes the solution for x to be 4?

• A.

- 7.5

• B.

- 0.5

• C.

5

• D.

7.5

• E.

19.5

D. 7.5
Explanation
To find the value of a that causes the solution for x to be 4, we need to solve the equation. We start by combining like terms: 3x + a - 7 = 5x - a. Next, we can simplify by adding a to both sides: 3x + 2a - 7 = 5x. Then, we subtract 3x from both sides: 2a - 7 = 2x. Finally, we add 7 to both sides and divide by 2: 2a = 2x + 7. Since we want the solution for x to be 4, we substitute x = 4 into the equation: 2a = 2(4) + 7. Solving this, we get a = 7.5. Therefore, the value of a that causes the solution for x to be 4 is 7.5.

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• 2.
• A.

• B.

• C.

• D.

• E.

B.
• 3.

### A recipe calls for cooking a turkey 1 hour for every 3 pounds it weighs.  How long should a 25 pound turkey cook?

• A.

8 hours, 15 minutes

• B.

8 hours, 20 minutes

• C.

8 hours, 30 minutes

• D.

8 hours, 33 minutes

• E.

8 hours, 40 minutes

B. 8 hours, 20 minutes
Explanation
The recipe states that a turkey should be cooked for 1 hour for every 3 pounds it weighs. Therefore, to determine how long a 25 pound turkey should cook, we divide 25 by 3, which equals 8 with a remainder of 1. This means that the turkey should be cooked for 8 hours, and since there is a remainder of 1, we add an additional 20 minutes to the cooking time. Thus, the correct answer is 8 hours, 20 minutes.

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• 4.
• A.

• B.

• C.

• D.

• E.

D.
• 5.
• A.

2.5 and -3

• B.

0.4 and -3

• C.

1.5 and -5

• D.

-1.5 and 5

• E.

-2.5 and 3

A. 2.5 and -3
• 6.
• A.

120 degrees

• B.

90 degrees

• C.

60 degrees

• D.

30 degrees

• E.

15 degrees

D. 30 degrees
Explanation
The given answer, 30 degrees, is the correct answer because it is the angle measure of an equilateral triangle. In an equilateral triangle, all three sides are equal in length and all three angles are equal to 60 degrees. Therefore, each angle of the equilateral triangle is 60 degrees divided by 2, which equals 30 degrees.

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• 7.

### Both S and T are positive integers, and the smallest positive integer that is divisible by both S and T is 144.  The greatest common factor of S and T is 2.  If S = 16, then T = ?

• A.

9

• B.

18

• C.

24

• D.

36

• E.

48

B. 18
Explanation
If the smallest positive integer that is divisible by both S and T is 144, and the greatest common factor of S and T is 2, then both S and T must be divisible by 2. Since S = 16, which is divisible by 2, T must also be divisible by 2. Therefore, the possible values for T are 18, 36, and 48. However, since we are looking for the smallest positive integer, the correct answer is 18.

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• 8.

### A map is laid out in the standard (x, y) coordinate plane.  How long, in units, is an airplane’s path on the map as the airplane flies along a straight line from City A located at (20, 14) to City B located at (5, 10)?

• A.

• B.

• C.

• D.

7

• E.

B.
Explanation
The length of the airplane's path can be calculated using the distance formula in the coordinate plane. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, the coordinates of City A are (20, 14) and the coordinates of City B are (5, 10). Plugging these values into the distance formula, we get:

d = sqrt((5 - 20)^2 + (10 - 14)^2)
= sqrt((-15)^2 + (-4)^2)
= sqrt(225 + 16)
= sqrt(241)

Therefore, the length of the airplane's path on the map is sqrt(241) units.

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• 9.
• A.

• B.

• C.

• D.

• E.

B.
• 10.

### Ticket sales for full attendance in a 500-seat theater were \$14,250.  If tickets in the 2 sections of the theater sold for \$30 and \$25, respectively, how many of the more expensive type of ticket were sold?

• A.

330

• B.

348

• C.

350

• D.

352

• E.

360

C. 350
Explanation
Let's assume that x represents the number of tickets sold for \$30 and y represents the number of tickets sold for \$25. The total number of tickets sold can be represented by the equation x + y = 500. The total revenue from ticket sales can be represented by the equation 30x + 25y = 14,250. By solving these two equations simultaneously, we can find that x = 350 and y = 150. Therefore, 350 tickets of the more expensive type were sold.

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• 11.

### How many units long is the circumference of a circle with diameter of 8 units?

• A.

• B.

• C.

• D.

• E.

B.
Explanation
The circumference of a circle is calculated using the formula C = πd, where d is the diameter of the circle. In this case, the diameter is given as 8 units. Therefore, the circumference of the circle would be 8π units long.

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• 12.

### What is the slope of a line perpendicular to the following 2 parallel lines? 6x + 3y = 88x + 4y = 5

• A.

- 2

• B.

-1/6

• C.

1/2

• D.

6

• E.

8

C. 1/2
Explanation
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. The given lines are 6x + 3y = 8 and 8x + 4y = 5. To find the slope of the first line, we rearrange the equation to y = (-2x + 8)/3, which has a slope of -2/3. The negative reciprocal of -2/3 is 3/2, which is equal to 1/2. Therefore, the slope of a line perpendicular to the given parallel lines is 1/2.

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• Mar 21, 2023
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• Dec 15, 2015
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