Question 1

Solve the problem.

-If a ≤ b, is it always true that $a ^ { 2 } \leq b ^ { 2 } ? \text { Explain. }$

Accepted Answer

The answer of Solve the problem.

-If a ≤ b, is...

Question 2

Answer the question or solve the problem.
-If x > 5 then 5x > 25.

Accepted Answer

The statement is true. When x is greater than 5, then multiplying x by 5 will result in a value greater than 25.

Question 3

Solve the problem.

-In solving the inequality 8x ≤ -32 $$\text { would you have to reverse the inequality symbol? }$$

Accepted Answer

The answer of Solve the problem.

-In solving the inequality 8x...

Question 4

Solve the problem.

-Andy has some $10 bills and some $20 bills in a shoebox under his bed. He has a total of 53 bills worth a total of $700. How many $20 bills does he have?

Accepted Answer

Let x be the number of $10 bills and y be the number of $20 bills.

We know that:

x + y = 53 (total number of bills)
10x + 20y = 700 (total value of the bills)

Simplify the first equation:

x = 53 - y

Substitute into the second equation:

10(53 - y) + 20y = 700

Distribute the 10:

530 - 10y + 20y = 700

Combine like terms:

10y = 170

Divide both sides by 10:

y = 17

So Andy has 17 $20 bills. The best choice is C.

Question 5

Solve the problem.

-If a ≤ b, is it always true that a $- 7 \leq b - 7 ? \text { Explain }$

Accepted Answer

The answer of Solve the problem.

-If a ≤ b, is...

Question 6

Solve the problem.

-On her way to a holiday weekend, Nancy drove $2 \frac { 1 } { 2 }$ hours in rush-hour traffic. When traffic eased up, she was able to increase her speed by 42 miles per hour and drove another $4 \frac { 1 } { 2 }$ hours. If the entire trip was 343 miles, how fast did she drive in rush-hour traffic?

Accepted Answer

The answer of Solve the problem.

-On her way to a...

Question 7

Solve the problem.

-$\text { If } b < 0 \text {, is it true that } b ^ { 2 } > b \text { ? Explain. }$

Accepted Answer

The answer of Solve the problem.

-\(\text { If } b...

Question 8

Solve the problem.

-The three-part inequality $\mathrm { a } < \mathrm { x } \leq \mathrm { b }$ means " $\mathrm { a }$ is less than $\mathrm { x }$ and $\mathrm { x }$ is less than or equal to $\mathrm { b }$ ". Which of these inequalities has no solution?
(a) $- 5 < x \leq - 11$
(b) $- 8 < x \leq - 7$
(c) $0 < x \leq 4$
(d) $- 2 < x \leq 6$

Accepted Answer

The answer of Solve the problem.

-The three-part inequality \(\mathrm {...

Question 9

Solve the problem.

-There are two types of tickets for a school play: student tickets and tickets for the general public. The total cost for one student ticket and one general public ticket is $9. The total cost for 13 student
Tickets and 12 general public tickets is $110. How much does a student ticket cost?

Accepted Answer

Let x be the cost of a student ticket and y be the cost of a general public ticket. We have the equations: x + y = 9 and 13x + 12y = 110. Solving these simultaneously, we find x = $2.

Question 10

Answer the question or solve the problem.
-If x < 4 then -5x < -20.

Accepted Answer

The answer of Answer the question or solve the problem.
-If...

Question 11

Solve the problem.

-If a ≤ b, is it always true that $- 7 a \leq - 7 b ? \text { Explain. }$

Accepted Answer

The answer of Solve the problem.

-If a ≤ b, is...

Question 12

Solve the problem.

-There are two types of tickets for a school play: child tickets that sell for $2 each and adult tickets that sell for $7 each. A total of 80 tickets are sold, bringing in a total of $410. How many adult
Tickets are sold?

Accepted Answer

The problem can be solved using a system of equations. Let x be the number of child tickets and y be the number of adult tickets. We have two equations: x + y = 80 (since a total of 80 tickets are sold) and 2x + 7y = 410 (since child tickets are $2 each and adult tickets are $7 each, and the total revenue is $410). Solving this system of equations, we find that y = 50, meaning 50 adult tickets were sold.

Question 13

Answer the question or solve the problem.
-From a point on a straight road, John and Fred ride bicycles in opposite directions. John rides 7 miles per hour and Fred rides 5 miles per hour. In how many hours will they be 60 miles apart?

Accepted Answer

We can use the formula: distance = rate x time
Let's assume that they will be 60 miles apart after t hours.
John will have covered a distance of 7t miles
Fred will have covered a distance of 5t miles
The total distance between them will be the sum of their distances:
7t + 5t = 12t miles
We want to find when this distance is equal to 60 miles:
12t = 60
t = 5
Therefore, they will be 60 miles apart after 5 hours.

Question 14

Solve the problem.

-If $a < b$, is it always true that $\frac { 1 } { a } > \frac { 1 } { b }$ ? Explain.

Accepted Answer

The answer of Solve the problem.

-If $a < b$, is...

Question 15

Answer the question or solve the problem.
-From a point on a river, two boats are driven in opposite directions, one at 7 miles per hour and the other at 6 miles per hour. In how many hours will they be 52 miles apart?

Accepted Answer

We can use the formula distance = rate x time. Let t be the time in hours. Then the distance travelled by the first boat is 7t and the distance travelled by the second boat is 6t. The total distance between them is 7t + 6t = 13t. We want this distance to be 52 miles, so:

13t = 52
t = 4

Therefore, they will be 52 miles apart in 4 hours. The correct answer is choice C.

Question 16

Solve the problem.

-There are two types of tickets for a school play: student tickets and tickets for the general public. The total cost for one student ticket and one general public ticket is $11. The total cost for 11
Student tickets and 9 general public tickets is $107. How much does a general public ticket cost?

Accepted Answer

The system of equations based on the given information is: S + G = 11 (where S is the cost of a student ticket and G is the cost of a general public ticket) and 11S + 9G = 107. Solving these equations simultaneously, we find that G = $7, which means the cost of a general public ticket is $7.

Question 17

Answer the question or solve the problem.
-From a point on a straight road, two cars are driven in opposite directions, one at 55 miles per hour and the other at 51 miles per hour. In how many hours will they be 530 miles apart?

Accepted Answer

Since the cars are going in opposite directions their distance apart will increase at a rate of 55 mph + 51 mph = 106 mph. To travel 530 miles at a rate of 106 mph it will take 530/106 = 5 hours.

Question 18

Answer the question or 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 60° larger than each of A and B. What are the
Measures of the three angles?

Accepted Answer

Let x be the measure of angles A and B. Then the measure of angle C is x + 60. The sum of the measures of the angles is x + x + (x + 60) = 180. Simplifying the equation, we get 3x + 60 = 180. Subtracting 60 from both sides, we get 3x = 120. Dividing by 3, we get x = 40. Therefore, the measures of the three angles are A and B: 40°, C: 100°. The answer is choice D.

Question 19

Solve the problem.

-A car traveling 69 miles per hour passes a bus traveling 61 in the same direction on the highway. If they maintain their speeds, how long will it take them to be 20 miles apart?

Accepted Answer

Since the car is moving faster than the bus, the distance between them is increasing at a rate of 69 - 61 = 8 miles per hour. To be 20 miles apart, it will take: 
Time = Distance / Rate 
Time = 20 / 8 
Time = 2.5 hours

Question 20

Solve the problem.

-Under what conditions must the inequality symbol be reversed when solving an
inequality?

Accepted Answer

The answer of Solve the problem.

-Under what conditions must the...

Quiz 2: Linear Equations

Solve the problem. -If a ≤ b, is it always true that $a ^ { 2 } \leq b ^ { 2 } ? \text { Explain. }$

Answer the question or solve the problem. -If x > 5 then 5x > 25.

Solve the problem. -In solving the inequality 8x ≤ -32 $\text { would you have to reverse the inequality symbol? }$

Solve the problem. -Andy has some $10 bills and some $20 bills in a shoebox under his bed. He has a total of 53 bills worth a total of $700. How many $20 bills does he have?

Solve the problem. -If a ≤ b, is it always true that a $- 7 \leq b - 7 ? \text { Explain }$

Solve the problem. - $\text { If } b < 0 \text {, is it true that } b ^ { 2 } > b \text { ? Explain. }$

Answer the question or solve the problem. -If x < 4 then -5x < -20.

Solve the problem. -If a ≤ b, is it always true that $- 7 a \leq - 7 b ? \text { Explain. }$

Solve the problem. -There are two types of tickets for a school play: child tickets that sell for $2 each and adult tickets that sell for $7 each. A total of 80 tickets are sold, bringing in a total of $410. How many adult Tickets are sold?

Answer the question or solve the problem. -From a point on a straight road, John and Fred ride bicycles in opposite directions. John rides 7 miles per hour and Fred rides 5 miles per hour. In how many hours will they be 60 miles apart?

Solve the problem. -If $a < b$ , is it always true that $\frac { 1 } { a } > \frac { 1 } { b }$ ? Explain.

Answer the question or solve the problem. -From a point on a river, two boats are driven in opposite directions, one at 7 miles per hour and the other at 6 miles per hour. In how many hours will they be 52 miles apart?

Answer the question or solve the problem. -From a point on a straight road, two cars are driven in opposite directions, one at 55 miles per hour and the other at 51 miles per hour. In how many hours will they be 530 miles apart?

Answer the question or 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 60° larger than each of A and B. What are the Measures of the three angles?

Solve the problem. -A car traveling 69 miles per hour passes a bus traveling 61 in the same direction on the highway. If they maintain their speeds, how long will it take them to be 20 miles apart?

Solve the problem. -Under what conditions must the inequality symbol be reversed when solving an inequality?

Quiz 2: Linear Equations

Solve the problem. -If a ≤ b, is it always true that a2≤b2? Explain. a ^ { 2 } \leq b ^ { 2 } ? \text { Explain. }a2≤b2? Explain.

Answer the question or solve the problem. -If x > 5 then 5x > 25.

Solve the problem. -In solving the inequality 8x ≤ -32 would you have to reverse the inequality symbol? \text { would you have to reverse the inequality symbol? } would you have to reverse the inequality symbol?

Solve the problem. -Andy has some $10 bills and some $20 bills in a shoebox under his bed. He has a total of 53 bills worth a total of $700. How many $20 bills does he have?

Solve the problem. -If a ≤ b, is it always true that a −7≤b−7? Explain - 7 \leq b - 7 ? \text { Explain }−7≤b−7? Explain

Solve the problem. - If b<0, is it true that b2>b ? Explain. \text { If } b < 0 \text {, is it true that } b ^ { 2 } > b \text { ? Explain. } If b<0, is it true that b2>b ? Explain.

Answer the question or solve the problem. -If x < 4 then -5x < -20.

Solve the problem. -If a ≤ b, is it always true that −7a≤−7b? Explain. - 7 a \leq - 7 b ? \text { Explain. }−7a≤−7b? Explain.

Solve the problem. -There are two types of tickets for a school play: child tickets that sell for $2 each and adult tickets that sell for $7 each. A total of 80 tickets are sold, bringing in a total of $410. How many adult Tickets are sold?

Answer the question or solve the problem. -From a point on a straight road, John and Fred ride bicycles in opposite directions. John rides 7 miles per hour and Fred rides 5 miles per hour. In how many hours will they be 60 miles apart?

Solve the problem. -If a<ba < ba<b , is it always true that 1a>1b\frac { 1 } { a } > \frac { 1 } { b }a1​>b1​ ? Explain.

Answer the question or solve the problem. -From a point on a river, two boats are driven in opposite directions, one at 7 miles per hour and the other at 6 miles per hour. In how many hours will they be 52 miles apart?

Answer the question or solve the problem. -From a point on a straight road, two cars are driven in opposite directions, one at 55 miles per hour and the other at 51 miles per hour. In how many hours will they be 530 miles apart?

Answer the question or 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 60° larger than each of A and B. What are the Measures of the three angles?

Solve the problem. -A car traveling 69 miles per hour passes a bus traveling 61 in the same direction on the highway. If they maintain their speeds, how long will it take them to be 20 miles apart?

Solve the problem. -Under what conditions must the inequality symbol be reversed when solving an inequality?

Solve the problem. -If a ≤ b, is it always true that $a ^ { 2 } \leq b ^ { 2 } ? \text { Explain. }$

Solve the problem. -In solving the inequality 8x ≤ -32 $\text { would you have to reverse the inequality symbol? }$

Solve the problem. -If a ≤ b, is it always true that a $- 7 \leq b - 7 ? \text { Explain }$

Solve the problem. - $\text { If } b < 0 \text {, is it true that } b ^ { 2 } > b \text { ? Explain. }$

Solve the problem. -If a ≤ b, is it always true that $- 7 a \leq - 7 b ? \text { Explain. }$

Solve the problem. -If $a < b$ , is it always true that $\frac { 1 } { a } > \frac { 1 } { b }$ ? Explain.