Question 1

A person sold their house for $100,000 and made a profit of 35%. How much did they pay for their home?

Accepted Answer

To find the original price, divide the selling price by 1 plus the profit percentage (1.35). $100,000 / 1.35 = $74,074.07.

Question 2

Solve by using the quadratic formula. $6 x ^ { 2 } - x - 3 = 0$
A) $\left\{ \frac { 1 \pm \sqrt { 73 } } { 6 } \right\}$

B) $\left\{ \frac { - 1 \pm \sqrt { 73 } } { 12 } \right\}$

C) $\left\{ \frac { 1 \pm \sqrt { 73 } } { 12 } \right\}$

D) $\left\{ \frac { - 1 \pm \sqrt { 73 } } { 6 } \right\}$

Accepted Answer

The answer of Solve by using the quadratic formula. \(6...

Question 3

Show the solutions using a graph: $- 1 < x \leq 5$
A)

B)

C)

D)

Accepted Answer

The answer of Show the solutions using a graph: \(-...

Question 4

An arithmetic student needs at least a 70% average to receive credit for the course. If she scored 85%, 79%, and 69% on the first three exams, what is the lowest score she can get on the fourth exam to receive credit for the course?

Accepted Answer

The student needs an average of 70% on four exams to receive credit for the course. The student has already taken three exams and scored 85%, 79%, and 69%. The average of these three scores is (85 + 79 + 69) / 3 = 77.67%. To receive credit for the course, the student needs to score at least (70 - 77.67) * 100 / (100 - 77.67) = 47.33% on the fourth exam. The lowest score the student can get on the fourth exam to receive credit for the course is 47%.

Question 5

The time to complete a project is inversely proportional to the number of people who are working on the project. A class project can be completed by 3 students in 24 days. In order to finish the project in 6 days, how many more students should the group add?

Accepted Answer

The answer of The time to complete a project is...

Question 6

A person drives 5,000 miles in 6 months. How many miles will that person drive in 3 years?

Accepted Answer

If a person drives 5,000 miles in 6 months, they would drive 10,000 miles in 1 year (since 5,000 miles x 2 = 10,000 miles). Over 3 years, they would drive 30,000 miles (10,000 miles/year x 3 years = 30,000 miles).

Question 7

The simple interest (I) on a certain amount of money (p) that is invested at a specified interest rate (r) for a specific period of time (t) can be found by the formula I = prt. Find the interest on a principal of $100 invested at 3% yearly for 7 years.

Accepted Answer

The simple interest is calculated using the formula I = prt. Here, p = $100, r = 3% = 0.03, and t = 7 years. So, I = 100 * 0.03 * 7 = $21.00.

Question 8

State whether the equation is a linear equation in one variable or not.
$$2 x = 7 ( x - 2 )$$

Accepted Answer

The equation is linear because it can be written in the form ax + b = 0, where a and b are constants. In this case, a = 2 and b = -14.

Question 9

$$\text { Evaluate the formula } F V = P ( 1 + r ) ^ { n } \text { when } P = \$ 100,000 , r = 0.08 \text {, and } n = 9$$

Accepted Answer

The answer of \[\text { Evaluate the formula } F...

Question 10

Simplify the expression. $- 3 r ^ { 2 } + 2 r + 7 - 9 + 4 r + r ^ { 2 }$
A) $- 2 r ^ { 2 } + 6 r + 2$
B) $- 2 r ^ { 2 } + 6 r - 2$
C) $2 r ^ { 2 } + 6 r - 2$
D) $2 r ^ { 2 } + 6 r + 2$

Accepted Answer

The answer of Simplify the expression. \(- 3 r ^...

Question 11

Solve by factoring.
$\frac { 1 } { 5 } x ^ { 2 } + \frac { 14 } { 5 } x + 9 = 0$

Accepted Answer

The answer of Solve by factoring.
\(\frac { 1 } {...

Question 12

If everyone had the same body proportions, your weight in pounds would vary directly with the cube of your height in feet. Assume the average height and weight of a female in your math class is 5'5" and 125 pounds. Use this information to write a variation equation then use it to find the weight of the female below if they had the same body type as the average female. Round answer to the nearest pound. Kelly 5'3"

Accepted Answer

The answer of If everyone had the same body proportions,...

Question 13

Simplify: $5 x - \frac { 1 } { 2 } + \frac { 5 } { 2 } ( 2 x - 2 )$
A) $8 x - \frac { 11 } { 2 }$

B) $10 x - \frac { 7 } { 2 }$

C) $6 x - \frac { 11 } { 2 }$

D) $10 x - \frac { 11 } { 2 }$

Accepted Answer

The answer of Simplify: \(5 x - \frac { 1...

Question 14

List the coefficients in the expression.
$$\frac { 4 } { 5 } x + y - 5.8 z$$

A) $\frac { 4 } { 5 } , 1 , - 5.8$

В) $\frac { 4 } { 5 } , - 5.8$

C) $\frac { 4 } { 5 } , 0 , - 5.8$

D) $+ , + , -$

Accepted Answer

The answer of List the coefficients in the expression.
\[\frac {...

Question 15

Simplify: -18a + 14a + 15a.

Accepted Answer

The expression simplifies to 11a by combining like terms: -18a + 14a + 15a = 11a.

Question 16

Solve.
$$5 x - 4 = 2 ( x - 2 ) + 3 x$$
A) identity; $\{ x \mid x$ is a real number $\}$
B) contradiction; $\varnothing$

Accepted Answer

The answer of Solve.
\[5 x - 4 = 2 (...

Question 17

Solve for $y : 2 x + 5 = 3 y - 1$
A) $\frac { 2 x + 5 } { 3 } + 1$

B) $\frac { 3 y - 6 } { 2 }$

C) $\frac { 2 x + 6 } { 3 }$

D) $\frac { 2 } { 3 } x + 6$

Accepted Answer

The answer of Solve for \(y : 2 x +...

Question 18

Gail is trying to stay between 400 calories and 600 calories for lunch. She selects a sandwich for 150 calories and a salad for 50 calories. How many calories can she have for dessert?

Accepted Answer

The answer of Gail is trying to stay between 400...

Question 19

Solve by using the quadratic formula.
$$0.8 x ^ { 2 } - 1.2 = - 0.7 x$$
A) $\left\{ \frac { 7 \pm \sqrt { 433 } } { 32 } \right\}$

B) $\left\{ \frac { 7 \pm \sqrt { 433 } } { 16 } \right\}$

C) $\left\{ \frac { - 7 \pm \sqrt { 433 } } { 16 } \right\}$

D) $\left\{ \frac { - 7 \pm \sqrt { 433 } } { 32 } \right\}$

Accepted Answer

The answer of Solve by using the quadratic formula.
\[0.8 x...

Question 20

Under certain conditions, the pressure of gas varies inversely with its volume. If a gas with a volume of 150 cubic inches has 29 pounds of pressure, find the amount of pressure 145 cubic inches of gas is under. A) $\frac { 1 } { 29 } \mathrm { lb }$

B) $30 \mathrm { lb }$

C) $\frac { 1 } { 30 } \mathrm { lb }$

D) $29 \mathrm { lb }$

Accepted Answer

The answer of Under certain conditions, the pressure of gas...

Quiz 6: Topics in Algebra

A person sold their house for $100,000 and made a profit of 35%. How much did they pay for their home?

Solve by using the quadratic formula. $6 x ^ { 2 } - x - 3 = 0$ A) $\left\{ \frac { 1 \pm \sqrt { 73 } } { 6 } \right\}$ B) $\left\{ \frac { - 1 \pm \sqrt { 73 } } { 12 } \right\}$ C) $\left\{ \frac { 1 \pm \sqrt { 73 } } { 12 } \right\}$ D) $\left\{ \frac { - 1 \pm \sqrt { 73 } } { 6 } \right\}$

An arithmetic student needs at least a 70% average to receive credit for the course. If she scored 85%, 79%, and 69% on the first three exams, what is the lowest score she can get on the fourth exam to receive credit for the course?

The time to complete a project is inversely proportional to the number of people who are working on the project. A class project can be completed by 3 students in 24 days. In order to finish the project in 6 days, how many more students should the group add?

A person drives 5,000 miles in 6 months. How many miles will that person drive in 3 years?

The simple interest (I) on a certain amount of money (p) that is invested at a specified interest rate (r) for a specific period of time (t) can be found by the formula I = prt. Find the interest on a principal of $100 invested at 3% yearly for 7 years.

State whether the equation is a linear equation in one variable or not. $2 x = 7 ( x - 2 )$

$\text { Evaluate the formula } F V = P ( 1 + r ) ^ { n } \text { when } P = \$ 100,000 , r = 0.08 \text {, and } n = 9$

Simplify the expression. $- 3 r ^ { 2 } + 2 r + 7 - 9 + 4 r + r ^ { 2 }$ A) $- 2 r ^ { 2 } + 6 r + 2$ B) $- 2 r ^ { 2 } + 6 r - 2$ C) $2 r ^ { 2 } + 6 r - 2$ D) $2 r ^ { 2 } + 6 r + 2$

Solve by factoring. $\frac { 1 } { 5 } x ^ { 2 } + \frac { 14 } { 5 } x + 9 = 0$

Simplify: $5 x - \frac { 1 } { 2 } + \frac { 5 } { 2 } ( 2 x - 2 )$ A) $8 x - \frac { 11 } { 2 }$ B) $10 x - \frac { 7 } { 2 }$ C) $6 x - \frac { 11 } { 2 }$ D) $10 x - \frac { 11 } { 2 }$

List the coefficients in the expression. $\frac { 4 } { 5 } x + y - 5.8 z$ A) $\frac { 4 } { 5 } , 1 , - 5.8$ В) $\frac { 4 } { 5 } , - 5.8$ C) $\frac { 4 } { 5 } , 0 , - 5.8$ D) $+ , + , -$

Simplify: -18a + 14a + 15a.

Solve. $5 x - 4 = 2 ( x - 2 ) + 3 x$ A) identity; $\{ x \mid x$ is a real number $\}$ B) contradiction; $\varnothing$

Solve for $y : 2 x + 5 = 3 y - 1$ A) $\frac { 2 x + 5 } { 3 } + 1$ B) $\frac { 3 y - 6 } { 2 }$ C) $\frac { 2 x + 6 } { 3 }$ D) $\frac { 2 } { 3 } x + 6$

Gail is trying to stay between 400 calories and 600 calories for lunch. She selects a sandwich for 150 calories and a salad for 50 calories. How many calories can she have for dessert?

Quiz 6: Topics in Algebra

A person sold their house for $100,000 and made a profit of 35%. How much did they pay for their home?

Show the solutions using a graph: −1<x≤5- 1 < x \leq 5−1<x≤5 A) B) C) D)

An arithmetic student needs at least a 70% average to receive credit for the course. If she scored 85%, 79%, and 69% on the first three exams, what is the lowest score she can get on the fourth exam to receive credit for the course?

The time to complete a project is inversely proportional to the number of people who are working on the project. A class project can be completed by 3 students in 24 days. In order to finish the project in 6 days, how many more students should the group add?

A person drives 5,000 miles in 6 months. How many miles will that person drive in 3 years?

The simple interest (I) on a certain amount of money (p) that is invested at a specified interest rate (r) for a specific period of time (t) can be found by the formula I = prt. Find the interest on a principal of $100 invested at 3% yearly for 7 years.

State whether the equation is a linear equation in one variable or not. 2x=7(x−2) 2 x = 7 ( x - 2 ) 2x=7(x−2)

Evaluate the formula FV=P(1+r) n when P=$100,000,r=0.08, and n=9\text { Evaluate the formula } F V = P ( 1 + r ) ^ { n } \text { when } P = \$ 100,000 , r = 0.08 \text {, and } n = 9 Evaluate the formula FV=P(1+r) n when P=$100,000,r=0.08, and n=9

Solve by factoring. 15x2+145x+9=0\frac { 1 } { 5 } x ^ { 2 } + \frac { 14 } { 5 } x + 9 = 051​x2+514​x+9=0

Simplify: 5x−12+52(2x−2)5 x - \frac { 1 } { 2 } + \frac { 5 } { 2 } ( 2 x - 2 )5x−21​+25​(2x−2) A) 8x−1128 x - \frac { 11 } { 2 }8x−211​ B) 10x−7210 x - \frac { 7 } { 2 }10x−27​ C) 6x−1126 x - \frac { 11 } { 2 }6x−211​ D) 10x−11210 x - \frac { 11 } { 2 }10x−211​

List the coefficients in the expression. 45x+y−5.8z\frac { 4 } { 5 } x + y - 5.8 z54​x+y−5.8z A) 45,1,−5.8\frac { 4 } { 5 } , 1 , - 5.854​,1,−5.8 В) 45,−5.8\frac { 4 } { 5 } , - 5.854​,−5.8 C) 45,0,−5.8\frac { 4 } { 5 } , 0 , - 5.854​,0,−5.8 D) +,+,−+ , + , -+,+,−

Simplify: -18a + 14a + 15a.

Solve. 5x−4=2(x−2)+3x5 x - 4 = 2 ( x - 2 ) + 3 x5x−4=2(x−2)+3x A) identity; {x∣x\{ x \mid x{x∣x is a real number }\}} B) contradiction; ∅\varnothing∅

Solve for y:2x+5=3y−1y : 2 x + 5 = 3 y - 1y:2x+5=3y−1 A) 2x+53+1\frac { 2 x + 5 } { 3 } + 132x+5​+1 B) 3y−62\frac { 3 y - 6 } { 2 }23y−6​ C) 2x+63\frac { 2 x + 6 } { 3 }32x+6​ D) 23x+6\frac { 2 } { 3 } x + 632​x+6

Gail is trying to stay between 400 calories and 600 calories for lunch. She selects a sandwich for 150 calories and a salad for 50 calories. How many calories can she have for dessert?

State whether the equation is a linear equation in one variable or not. $2 x = 7 ( x - 2 )$

$\text { Evaluate the formula } F V = P ( 1 + r ) ^ { n } \text { when } P = \$ 100,000 , r = 0.08 \text {, and } n = 9$

Solve by factoring. $\frac { 1 } { 5 } x ^ { 2 } + \frac { 14 } { 5 } x + 9 = 0$

Simplify: $5 x - \frac { 1 } { 2 } + \frac { 5 } { 2 } ( 2 x - 2 )$ A) $8 x - \frac { 11 } { 2 }$ B) $10 x - \frac { 7 } { 2 }$ C) $6 x - \frac { 11 } { 2 }$ D) $10 x - \frac { 11 } { 2 }$

List the coefficients in the expression. $\frac { 4 } { 5 } x + y - 5.8 z$ A) $\frac { 4 } { 5 } , 1 , - 5.8$ В) $\frac { 4 } { 5 } , - 5.8$ C) $\frac { 4 } { 5 } , 0 , - 5.8$ D) $+ , + , -$

Solve. $5 x - 4 = 2 ( x - 2 ) + 3 x$ A) identity; $\{ x \mid x$ is a real number $\}$ B) contradiction; $\varnothing$

Solve for $y : 2 x + 5 = 3 y - 1$ A) $\frac { 2 x + 5 } { 3 } + 1$ B) $\frac { 3 y - 6 } { 2 }$ C) $\frac { 2 x + 6 } { 3 }$ D) $\frac { 2 } { 3 } x + 6$