Question 1

How long will it take an object to hit the ground if it is dropped from a height of 1024 feet? (Use $d = r t + 16 t ^ { 2 }$.) Assume the object initially is held still.
A) 8 sec
B) 4 sec
C) 16 sec
D) 32 sec

Accepted Answer

The formula $d = 16t^2$ is used since the initial velocity $r$ is 0. Solving $1024 = 16t^2$ gives $t^2 = 64$, so $t = 8$ seconds.

Question 2

The heat energy from electricity is given by the formula $E = 0.238 I ^ { 2 } R t$. Find $E$ when $I = 50 \mathrm { amps } , R = 19 \mathrm { ohms }$, and $t = 100 \mathrm {~s}$. Round answer to the nearest hundredth.
A) 1,243,550.00
B) 1,130,500.00
C) 1,017,450.00
D) 22,610.00

Accepted Answer

The answer of The heat energy from electricity is given...

Question 3

A community college has 3,000 students and 90 instructors. The college plans that enrollment will be 3,500 next year. How many new instructors should be hired if the college wants to keep the same student to instructor ratio?
A) 13 instructors
B) 77 instructors
C) 105 instructors
D) 15 instructors

Accepted Answer

The current student to instructor ratio is 3000 students / 90 instructors = 33.33 students per instructor. To maintain this ratio with 3500 students, the college needs 3500 / 33.33 ≈ 105 instructors. Therefore, they need to hire 105 - 90 = 15 new instructors.

Question 4

$$\text { The formula for the average } a \text { of two numbers } n \text { and } s \text { is } a = \frac { n + s } { 2 } \text {. Solve for } s \text {. }$$
A) a + 2 + n
B) 2a + n
C) 2a - n
D) a + 2 - n

Accepted Answer

The answer of \[\text { The formula for the average...

Question 5

Solve the proportion. $\frac { 3 } { x - 1 } = \frac { 7 } { x + 2 }$
A) $\frac { 3 } { 4 }$

B) 4

C) $\frac { 1 } { 4 }$

D) $\frac { 13 } { 4 }$

Accepted Answer

The answer of Solve the proportion. \(\frac { 3 }...

Question 6

Write the phrase in symbols: Eight less than three times a number. A) $3 ( 8 - x )$
B) $3 x - 8$
C) $3 ( x - 8 )$
D) $8 - 3 x$

Accepted Answer

The answer of Write the phrase in symbols: Eight less...

Question 7

$$\text { Solve: } - 7 + x = - 6$$
A) {1}
B) {13}
C) {-1}
D) {-13}

Accepted Answer

Add 7 to both sides of the equation to solve for x.-7 + x = -6-7 + 7 + x = -6 + 70 + x = 1x = 1

Question 8

Steve earned scores of 84 and 75 on his first two exams. What will his average grade be if he gets a 78 on his third exam?
A) 84
B) 78
C) 79
D) 75

Accepted Answer

The average grade is calculated by adding all the scores and dividing by the number of exams: (84 + 75 + 78) / 3 = 79.

Question 9

Solve: $- \frac { 2 } { 5 } x = 18$
A) $\{ 45 \}$

В) $\left\{ - \frac { 36 } { 5 } \right\}$

C) $\{ - 45 \}$

D) $\left\{ \frac { 36 } { 5 } \right\}$

Accepted Answer

The answer of Solve: \(- \frac { 2 } {...

Question 10

Write the ratio as a fraction and reduce to lowest terms. 4 feet to 20 inches A) $\frac { 12 } { 5 }$

B) $\frac { 5 } { 1 }$

C) $\frac { 1 } { 5 }$

D) $\frac { 5 } { 12 }$

Accepted Answer

The answer of Write the ratio as a fraction and...

Question 11

A bus leaves from campus headed east at 25 miles per hour and another bus leaves from campus headed south at 35 miles per hour. How long will it take for the buses to be 172 miles apart? Round answer to the nearest hour.
A) 4 hours
B) 3 hours
C) 2 hours
D) 8 hours

Accepted Answer

Using the Pythagorean theorem, the distance between the buses is given by the equation: $d = \sqrt{(25t)^2 + (35t)^2}$. Setting $d = 172$, we solve for $t$: $\sqrt{(25t)^2 + (35t)^2} = 172$. Simplifying gives $t = 4$ hours.

Question 12

$$\text { Evaluate the formula } P = 2 l + 2 w \text { when } l = 7 \text { in. and } w = 5 \text { in. }$$
A) 12 in.
B) 24 in.
C) 19 in.
D) 17 in.

Accepted Answer

The formula for the perimeter of a rectangle is $ P = 2l + 2w $. Substituting $ l = 7 $ in. and $ w = 5 $ in., we get $ P = 2(7) + 2(5) = 14 + 10 = 24 $ in.

Question 13

Solve. $\quad - 10 - x > - 7$ A) $\{ \mathrm { x } \mid x < - 3 \}$ B) $\{ x \mid x < - 17 \}$ C) $\{ x \mid x > - 3 \}$ D) $\{ x \mid x > - 17 \}$

Accepted Answer

The answer of Solve. \(\quad - 10 - x >...

Question 14

Solve: $4 + 3 ( 2 x + 1 ) = x - 8$
A) $\left\{ - \frac { 3 } { 5 } \right\}$

B) $\{ - 3 \}$

C) $\left\{ - \frac { 13 } { 5 } \right\}$

D) $\left\{ - \frac { 1 } { 5 } \right\}$

Accepted Answer

The answer of Solve: \(4 + 3 ( 2 x...

Question 15

List the coefficients in the expression.
$$17 x ^ { 3 } - 18 x ^ { 2 } + 7$$
A) $17 , - 18,7$

B) $17,18,7$

C) $17 x ^ { 3 } , - 18 x ^ { 2 } , 7$

D) $+ , - , +$

Accepted Answer

The answer of List the coefficients in the expression.
\[17 x...

Question 16

$$\text { Simplify: } 3 ( x - 1 ) - ( x - 4 )$$ A) $2 x - 7$
B) $2 x + 7$
C) $2 x + 1$
D) $2 x - 1$

Accepted Answer

The answer of \[\text { Simplify: } 3 ( x...

Question 17

Use the formula F = ma to solve. Find the acceleration for a force F = 585 newtons and a mass of 45 kg. A) $169 \mathrm {~m} / \mathrm { s } ^ { 2 }$

B) $585 \mathrm {~m} / \mathrm { s } ^ { 2 }$

C) $2025 \mathrm {~m} / \mathrm { s } ^ { 2 }$

D) $13 \mathrm {~m} / \mathrm { s } ^ { 2 }$

Accepted Answer

The answer of Use the formula F = ma to...

Question 18

Which two terms in the expression are like terms?
$$7 z + 7 z ^ { 2 } - 5 z + 5$$
A) $7 z$ and $- 5 z$
B) there are no like terms
C) $- 5 z$ and 5
D) $7 z$ and $7 z ^ { 2 }$

Accepted Answer

The answer of Which two terms in the expression are...

Question 19

$$\text { Evaluate: } - 4 x - 2 \text { when } x = 1$$
A) 8
B) -2
C) -6
D) 2

Accepted Answer

The answer of \[\text { Evaluate: } - 4 x...

Question 20

Solve the inequality. $4 ( x + 2 ) - 5 > 3 x + 8$
A) $\{ \mathrm { x } \mid x > - 5 \}$
B) $\{ \mathrm { x } \mid x > 20 \}$
C) $\{ x \mid x > 5 \}$
D) $\{ \mathrm { x } \mid x > 11 \}$

Accepted Answer

The answer of Solve the inequality. \(4 ( x +...

Quiz 6: Topics in Algebra

How long will it take an object to hit the ground if it is dropped from a height of 1024 feet? (Use $d = r t + 16 t ^ { 2 }$ .) Assume the object initially is held still.

The heat energy from electricity is given by the formula $E = 0.238 I ^ { 2 } R t$ . Find $E$ when $I = 50 \mathrm { amps } , R = 19 \mathrm { ohms }$ , and $t = 100 \mathrm {~s}$ . Round answer to the nearest hundredth.

A community college has 3,000 students and 90 instructors. The college plans that enrollment will be 3,500 next year. How many new instructors should be hired if the college wants to keep the same student to instructor ratio?

$\text { The formula for the average } a \text { of two numbers } n \text { and } s \text { is } a = \frac { n + s } { 2 } \text {. Solve for } s \text {. }$

Solve the proportion. $\frac { 3 } { x - 1 } = \frac { 7 } { x + 2 }$ A) $\frac { 3 } { 4 }$ B) 4 C) $\frac { 1 } { 4 }$ D) $\frac { 13 } { 4 }$

Write the phrase in symbols: Eight less than three times a number. A) $3 ( 8 - x )$ B) $3 x - 8$ C) $3 ( x - 8 )$ D) $8 - 3 x$

$\text { Solve: } - 7 + x = - 6$

Steve earned scores of 84 and 75 on his first two exams. What will his average grade be if he gets a 78 on his third exam?

Solve: $- \frac { 2 } { 5 } x = 18$ A) $\{ 45 \}$ В) $\left\{ - \frac { 36 } { 5 } \right\}$ C) $\{ - 45 \}$ D) $\left\{ \frac { 36 } { 5 } \right\}$

Write the ratio as a fraction and reduce to lowest terms. 4 feet to 20 inches A) $\frac { 12 } { 5 }$ B) $\frac { 5 } { 1 }$ C) $\frac { 1 } { 5 }$ D) $\frac { 5 } { 12 }$

A bus leaves from campus headed east at 25 miles per hour and another bus leaves from campus headed south at 35 miles per hour. How long will it take for the buses to be 172 miles apart? Round answer to the nearest hour.

$\text { Evaluate the formula } P = 2 l + 2 w \text { when } l = 7 \text { in. and } w = 5 \text { in. }$

Solve. $\quad - 10 - x > - 7$ A) $\{ \mathrm { x } \mid x < - 3 \}$ B) $\{ x \mid x < - 17 \}$ C) $\{ x \mid x > - 3 \}$ D) $\{ x \mid x > - 17 \}$

Solve: $4 + 3 ( 2 x + 1 ) = x - 8$ A) $\left\{ - \frac { 3 } { 5 } \right\}$ B) $\{ - 3 \}$ C) $\left\{ - \frac { 13 } { 5 } \right\}$ D) $\left\{ - \frac { 1 } { 5 } \right\}$

List the coefficients in the expression. $17 x ^ { 3 } - 18 x ^ { 2 } + 7$ A) $17 , - 18,7$ B) $17,18,7$ C) $17 x ^ { 3 } , - 18 x ^ { 2 } , 7$ D) $+ , - , +$

$\text { Simplify: } 3 ( x - 1 ) - ( x - 4 )$ A) $2 x - 7$ B) $2 x + 7$ C) $2 x + 1$ D) $2 x - 1$

Use the formula F = ma to solve. Find the acceleration for a force F = 585 newtons and a mass of 45 kg. A) $169 \mathrm {~m} / \mathrm { s } ^ { 2 }$ B) $585 \mathrm {~m} / \mathrm { s } ^ { 2 }$ C) $2025 \mathrm {~m} / \mathrm { s } ^ { 2 }$ D) $13 \mathrm {~m} / \mathrm { s } ^ { 2 }$

Which two terms in the expression are like terms? $7 z + 7 z ^ { 2 } - 5 z + 5$ A) $7 z$ and $- 5 z$ B) there are no like terms C) $- 5 z$ and 5 D) $7 z$ and $7 z ^ { 2 }$

$\text { Evaluate: } - 4 x - 2 \text { when } x = 1$

Solve the inequality. $4 ( x + 2 ) - 5 > 3 x + 8$ A) $\{ \mathrm { x } \mid x > - 5 \}$ B) $\{ \mathrm { x } \mid x > 20 \}$ C) $\{ x \mid x > 5 \}$ D) $\{ \mathrm { x } \mid x > 11 \}$

Quiz 6: Topics in Algebra

How long will it take an object to hit the ground if it is dropped from a height of 1024 feet? (Use d=rt+16t2d = r t + 16 t ^ { 2 }d=rt+16t2 .) Assume the object initially is held still.

The heat energy from electricity is given by the formula E=0.238I2RtE = 0.238 I ^ { 2 } R tE=0.238I2Rt . Find EEE when I=50amps,R=19ohmsI = 50 \mathrm { amps } , R = 19 \mathrm { ohms }I=50amps,R=19ohms , and t=100 st = 100 \mathrm {~s}t=100 s . Round answer to the nearest hundredth.

A community college has 3,000 students and 90 instructors. The college plans that enrollment will be 3,500 next year. How many new instructors should be hired if the college wants to keep the same student to instructor ratio?

Solve the proportion. 3x−1=7x+2\frac { 3 } { x - 1 } = \frac { 7 } { x + 2 }x−13​=x+27​ A) 34\frac { 3 } { 4 }43​ B) 4 C) 14\frac { 1 } { 4 }41​ D) 134\frac { 13 } { 4 }413​

Write the phrase in symbols: Eight less than three times a number. A) 3(8−x)3 ( 8 - x )3(8−x) B) 3x−83 x - 83x−8 C) 3(x−8)3 ( x - 8 )3(x−8) D) 8−3x8 - 3 x8−3x

Solve: −7+x=−6\text { Solve: } - 7 + x = - 6 Solve: −7+x=−6

Steve earned scores of 84 and 75 on his first two exams. What will his average grade be if he gets a 78 on his third exam?

Solve: −25x=18- \frac { 2 } { 5 } x = 18−52​x=18 A) {45}\{ 45 \}{45} В) {−365}\left\{ - \frac { 36 } { 5 } \right\}{−536​} C) {−45}\{ - 45 \}{−45} D) {365}\left\{ \frac { 36 } { 5 } \right\}{536​}

Write the ratio as a fraction and reduce to lowest terms. 4 feet to 20 inches A) 125\frac { 12 } { 5 }512​ B) 51\frac { 5 } { 1 }15​ C) 15\frac { 1 } { 5 }51​ D) 512\frac { 5 } { 12 }125​

A bus leaves from campus headed east at 25 miles per hour and another bus leaves from campus headed south at 35 miles per hour. How long will it take for the buses to be 172 miles apart? Round answer to the nearest hour.

Evaluate the formula P=2l+2w when l=7 in. and w=5 in. \text { Evaluate the formula } P = 2 l + 2 w \text { when } l = 7 \text { in. and } w = 5 \text { in. } Evaluate the formula P=2l+2w when l=7 in. and w=5 in.

Solve. −10−x>−7\quad - 10 - x > - 7−10−x>−7 A) {x∣x<−3}\{ \mathrm { x } \mid x < - 3 \}{x∣x<−3} B) {x∣x<−17}\{ x \mid x < - 17 \}{x∣x<−17} C) {x∣x>−3}\{ x \mid x > - 3 \}{x∣x>−3} D) {x∣x>−17}\{ x \mid x > - 17 \}{x∣x>−17}

Solve: 4+3(2x+1)=x−84 + 3 ( 2 x + 1 ) = x - 84+3(2x+1)=x−8 A) {−35}\left\{ - \frac { 3 } { 5 } \right\}{−53​} B) {−3}\{ - 3 \}{−3} C) {−135}\left\{ - \frac { 13 } { 5 } \right\}{−513​} D) {−15}\left\{ - \frac { 1 } { 5 } \right\}{−51​}

List the coefficients in the expression. 17x3−18x2+717 x ^ { 3 } - 18 x ^ { 2 } + 717x3−18x2+7 A) 17,−18,717 , - 18,717,−18,7 B) 17,18,717,18,717,18,7 C) 17x3,−18x2,717 x ^ { 3 } , - 18 x ^ { 2 } , 717x3,−18x2,7 D) +,−,++ , - , ++,−,+

Simplify: 3(x−1)−(x−4)\text { Simplify: } 3 ( x - 1 ) - ( x - 4 ) Simplify: 3(x−1)−(x−4) A) 2x−72 x - 72x−7 B) 2x+72 x + 72x+7 C) 2x+12 x + 12x+1 D) 2x−12 x - 12x−1

Which two terms in the expression are like terms? 7z+7z2−5z+57 z + 7 z ^ { 2 } - 5 z + 57z+7z2−5z+5 A) 7z7 z7z and −5z- 5 z−5z B) there are no like terms C) −5z- 5 z−5z and 5 D) 7z7 z7z and 7z27 z ^ { 2 }7z2

Evaluate: −4x−2 when x=1\text { Evaluate: } - 4 x - 2 \text { when } x = 1 Evaluate: −4x−2 when x=1

Solve the inequality. 4(x+2)−5>3x+84 ( x + 2 ) - 5 > 3 x + 84(x+2)−5>3x+8 A) {x∣x>−5}\{ \mathrm { x } \mid x > - 5 \}{x∣x>−5} B) {x∣x>20}\{ \mathrm { x } \mid x > 20 \}{x∣x>20} C) {x∣x>5}\{ x \mid x > 5 \}{x∣x>5} D) {x∣x>11}\{ \mathrm { x } \mid x > 11 \}{x∣x>11}

How long will it take an object to hit the ground if it is dropped from a height of 1024 feet? (Use $d = r t + 16 t ^ { 2 }$ .) Assume the object initially is held still.

The heat energy from electricity is given by the formula $E = 0.238 I ^ { 2 } R t$ . Find $E$ when $I = 50 \mathrm { amps } , R = 19 \mathrm { ohms }$ , and $t = 100 \mathrm {~s}$ . Round answer to the nearest hundredth.

Solve the proportion. $\frac { 3 } { x - 1 } = \frac { 7 } { x + 2 }$ A) $\frac { 3 } { 4 }$ B) 4 C) $\frac { 1 } { 4 }$ D) $\frac { 13 } { 4 }$

Write the phrase in symbols: Eight less than three times a number. A) $3 ( 8 - x )$ B) $3 x - 8$ C) $3 ( x - 8 )$ D) $8 - 3 x$

$\text { Solve: } - 7 + x = - 6$

Solve: $- \frac { 2 } { 5 } x = 18$ A) $\{ 45 \}$ В) $\left\{ - \frac { 36 } { 5 } \right\}$ C) $\{ - 45 \}$ D) $\left\{ \frac { 36 } { 5 } \right\}$

Write the ratio as a fraction and reduce to lowest terms. 4 feet to 20 inches A) $\frac { 12 } { 5 }$ B) $\frac { 5 } { 1 }$ C) $\frac { 1 } { 5 }$ D) $\frac { 5 } { 12 }$

$\text { Evaluate the formula } P = 2 l + 2 w \text { when } l = 7 \text { in. and } w = 5 \text { in. }$

Solve. $\quad - 10 - x > - 7$ A) $\{ \mathrm { x } \mid x < - 3 \}$ B) $\{ x \mid x < - 17 \}$ C) $\{ x \mid x > - 3 \}$ D) $\{ x \mid x > - 17 \}$

Solve: $4 + 3 ( 2 x + 1 ) = x - 8$ A) $\left\{ - \frac { 3 } { 5 } \right\}$ B) $\{ - 3 \}$ C) $\left\{ - \frac { 13 } { 5 } \right\}$ D) $\left\{ - \frac { 1 } { 5 } \right\}$

List the coefficients in the expression. $17 x ^ { 3 } - 18 x ^ { 2 } + 7$ A) $17 , - 18,7$ B) $17,18,7$ C) $17 x ^ { 3 } , - 18 x ^ { 2 } , 7$ D) $+ , - , +$

$\text { Simplify: } 3 ( x - 1 ) - ( x - 4 )$ A) $2 x - 7$ B) $2 x + 7$ C) $2 x + 1$ D) $2 x - 1$

Which two terms in the expression are like terms? $7 z + 7 z ^ { 2 } - 5 z + 5$ A) $7 z$ and $- 5 z$ B) there are no like terms C) $- 5 z$ and 5 D) $7 z$ and $7 z ^ { 2 }$

$\text { Evaluate: } - 4 x - 2 \text { when } x = 1$

Solve the inequality. $4 ( x + 2 ) - 5 > 3 x + 8$ A) $\{ \mathrm { x } \mid x > - 5 \}$ B) $\{ \mathrm { x } \mid x > 20 \}$ C) $\{ x \mid x > 5 \}$ D) $\{ \mathrm { x } \mid x > 11 \}$