Question 1

Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-The sum of the measures of the angles in any triangle is 180 degrees. In triangle ABC, angles A and B have the same measure, while angle C is 114 degrees larger than each of the other two angles. Find the measure of angle C.
A) 22 degrees
B) 44 degrees
C) 136 degrees
D) 158 degrees

Accepted Answer

Since the sum of the angles in a triangle is 180 degrees and angle C is 114 degrees larger than each of the other two angles (which are equal), we can set up the equation: A + B + C = 180. Given A = B and C = A + 114, we can substitute to get 2A + (A + 114) = 180, simplifying to 3A + 114 = 180. Solving for A gives A = 22, so C = 22 + 114 = 136 degrees.

Question 2

Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-Pennies are packaged 50 in a roll. A mother gave her son 167 pennies for his bank and had 33 pennies left over. How many rolls of pennies did she use?
A) 7 rolls
B) 5 rolls
C) 6 rolls
D) 4 rolls

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 3

Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-Elaine had 65 buttons. Her grandmother donated 5 cards of buttons to the collection. Elaine sorted the buttons into 10 piles, putting 10 buttons in each pile. How many buttons were on each card from Elaine's grandmother?
A) 93 buttons
B) 96 buttons
C) 7 buttons
D) 63 buttons

Accepted Answer

Elaine initially had 65 buttons and sorted them into 10 piles with 10 buttons each, making 100 buttons in total. This means she added 35 buttons (100 - 65) from her grandmother's cards. Since there were 5 cards, each card had 7 buttons (35 buttons / 5 cards = 7 buttons per card).

Question 4

Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-Junior high classes of 25 students each met in the cafeteria to take achievement tests. If exactly 5 students sat at each table and 10 tables were used, how many classes took the tests?
A) 15 classes
B) 5 classes
C) 4 classes
D) 2 classes

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 5

Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-Find the measure of an angle whose supplement is 11 times the measure of its complement.
A) 16.4°
B) 40.5°
C) 81°
D) 8.2°

Accepted Answer

Let the angle be $x$ degrees. Its complement is $90 - x$ and its supplement is $180 - x$. According to the problem, the supplement is 11 times the complement, so $180 - x = 11(90 - x)$. Solving this equation gives $x = 81$.

Question 6

Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-Find the measure of an angle if its supplement measures 50° less than 3 times its complement.
A) 166°
B) 20°
C) 83°
D) 10°

Accepted Answer

Let the angle be x. Its supplement is 180° - x, and its complement is 90° - x. According to the problem, the supplement is 50° less than 3 times the complement: 180° - x = 3(90° - x) - 50°. Solving this equation gives x = 20°.

Question 7

Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-Find the measure of an angle such that the difference between its supplement and 3 times its complement is 50°.
A) 70°
B) 83°
C) 166°
D) 35°

Accepted Answer

The supplement of an angle is 180° minus the angle, and the complement is 90° minus the angle. Let x be the angle. The equation based on the given information is: (180 - x) - 3(90 - x) = 50. Solving this equation gives x = 70°.

Question 8

Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-Find the measure of an angle, if its supplement measures 42° more than twice its complement.
A) 48°
B) 42°
C) 84°
D) 52°

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 9

Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-Find the measure of an angle such that the sum of the measures of its complement and its supplement is 176°.
A) 4°
B) 47°
C) 2°
D) 42°

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 10

Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-The sum of the measures of the angles of any triangle is 180°. In triangle ABC, angles A and B have the same measure, while the measure of angle C is 45° larger than each of A and B. What are the measures of the three angles?
A) A and C: 70°; B: 55°
B) A and B: 45°; C: 90°
C) A and B: 90°; C: 45°
D) A and B: 55°; C: 70°

Accepted Answer

Angles A and B are equal, and angle C is 45° larger than each of A and B. Let A = B = x, then C = x + 45°. The equation is x + x + (x + 45°) = 180°. Solving gives x = 45°, so A and B are 45° each, and C is 90°.

Question 11

Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-The sum of two consecutive integers is -351. Find the larger integer.
A) -175
B) -176
C) -174
D) -177

Accepted Answer

The two consecutive integers can be represented as x and x+1. Their sum is x + (x + 1) = -351. Solving for x gives 2x + 1 = -351, so 2x = -352, and x = -176. Therefore, the larger integer is x + 1 = -175.

Question 12

Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-The sum of three consecutive integers is 417. Find the integers.
A) 137, 138, 139
B) 138, 139, 140
C) 137, 139, 141
D) 139, 140, 141

Accepted Answer

The sum of three consecutive integers can be represented as $n + (n+1) + (n+2) = 417$. Simplifying, $3n + 3 = 417$, then $3n = 414$, so $n = 138$. Therefore, the integers are 138, 139, and 140.

Question 13

Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-The sum of three consecutive odd integers is 183. Find the integers.
A) 61, 63, 65
B) 59, 61, 63
C) 63, 65, 67
D) 54, 55, 56

Accepted Answer

The three consecutive odd integers can be represented as x, x+2, and x+4. Their sum is x + (x+2) + (x+4) = 3x + 6 = 183. Solving for x gives x = 59, so the integers are 59, 61, and 63.

Question 14

Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-Two pages that face each other in a book have 389 as the sum of their page numbers. What is the number of the page that comes first?
A) 192
B) 194
C) 195
D) 193

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 15

Answer the question.
-Which of the following would not be a reasonable answer in an applied problem that requires finding the number of cars parked in a parking lot?
A) -12
B) 64
C) 46
D) 5

Accepted Answer

The number of cars parked in a parking lot cannot be negative.

Question 16

Choose the one alternative that best completes the statement or answers the question.
-The following statement would be considered a step in solving an applied problem
Solve the equation.

Accepted Answer

Solving the equation is often a necessary step in addressing an applied problem, as it involves finding unknown values that can be crucial for understanding or resolving the situation at hand.

Question 17

Choose the one alternative that best completes the statement or answers the question.
-If x represents a positive integer, how would you express its negative?

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 18

Choose the one alternative that best completes the statement or answers the question.
-If x represents a negative integer, how would you express its negative?

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 19

Choose the one alternative that best completes the statement or answers the question.
-How would you express the product of two numbers, r and s?

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 20

Choose the one alternative that best completes the statement or answers the question.
-Two angles are complimentary. One of the angles is r. How do you express the other angle?

Accepted Answer

The answer of Choose the one alternative that best completes...

Quiz 3: Linear Equations and Inequalities in Two Variables; Functions

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Pennies are packaged 50 in a roll. A mother gave her son 167 pennies for his bank and had 33 pennies left over. How many rolls of pennies did she use?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Junior high classes of 25 students each met in the cafeteria to take achievement tests. If exactly 5 students sat at each table and 10 tables were used, how many classes took the tests?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find the measure of an angle whose supplement is 11 times the measure of its complement.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find the measure of an angle if its supplement measures 50° less than 3 times its complement.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find the measure of an angle such that the difference between its supplement and 3 times its complement is 50°.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find the measure of an angle, if its supplement measures 42° more than twice its complement.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find the measure of an angle such that the sum of the measures of its complement and its supplement is 176°.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -The sum of two consecutive integers is -351. Find the larger integer.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -The sum of three consecutive integers is 417. Find the integers.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -The sum of three consecutive odd integers is 183. Find the integers.

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Two pages that face each other in a book have 389 as the sum of their page numbers. What is the number of the page that comes first?

Answer the question. -Which of the following would not be a reasonable answer in an applied problem that requires finding the number of cars parked in a parking lot?

Choose the one alternative that best completes the statement or answers the question. -The following statement would be considered a step in solving an applied problem Solve the equation.

Choose the one alternative that best completes the statement or answers the question. -If x represents a positive integer, how would you express its negative?

Choose the one alternative that best completes the statement or answers the question. -If x represents a negative integer, how would you express its negative?

Choose the one alternative that best completes the statement or answers the question. -How would you express the product of two numbers, r and s?

Choose the one alternative that best completes the statement or answers the question. -Two angles are complimentary. One of the angles is r. How do you express the other angle?