Question 1

Substitute to find the value of the expression.
-Traveling at $r$ kilometers per hour for $t$ hours, a driver will travel $r t$ kilometers. How far will Danny travel in 16 hours at a speed of 99 kilometers per hour?
A) $115 \mathrm{~km}$
B) $1584 \mathrm{~km}$
C) $6.2 \mathrm{~km}$
D) $1584 \mathrm{mi}$

Accepted Answer

To find the distance traveled, substitute $r = 99$ km/h and $t = 16$ hours into the formula $distance = r \times t$, which gives $distance = 99 \times 16 = 1584$ kilometers.

Question 2

Substitute to find the value of the expression.
-A plane flies at 582 miles per hour. The time, in hours, for the plane to travel a distance of $d$ miles is $\frac{\mathrm{d}}{582}$. How long will it take for the plane to travel 5820 miles?
A) $10 \mathrm{hr}$
B) $0.10 \mathrm{hr}$
C) $13 \mathrm{hr}$
D) $3,387,240 \mathrm{hr}$

Accepted Answer

Substituting $d = 5820$ miles into the expression $\frac{d}{582}$ gives $\frac{5820}{582} = 10$ hours.

Question 3

Substitute to find the value of the expression.
-A train must cover a distance of 2520 miles. The velocity, in miles per hour, of the train is $\frac{2520}{t}$ where $t$ is the time, in hours, to complete the trip. If the train completes the trip in 28 hours, what is its velocity?
A) $70,560 \mathrm{mph}$
B) $0.01 \mathrm{mph}$
C) $90 \mathrm{mph}$
D) $85 \mathrm{mph}$

Accepted Answer

The velocity of the train is calculated by dividing the distance by the time. Substituting $t = 28$ hours into the velocity formula $\frac{2520}{t}$ gives $\frac{2520}{28} = 90$ mph.

Question 4

Substitute to find the value of the expression.
-The area of a triangle with base $b$ and height $h$ is given by the formula $A=\frac{1}{2} b h$. Find the area of $a$ triangle when the base is 1.1 centimeters and the height is 3.3 centimeters.
A) $0.17 \mathrm{~cm}^{2}$
B) $3.63 \mathrm{~cm}^{2}$
C) $1.815 \mathrm{~cm}^{2}$
D) $1.452 \mathrm{~cm}^{2}$

Accepted Answer

The area of the triangle is calculated by substituting $b = 1.1$ cm and $h = 3.3$ cm into the formula $A = \frac{1}{2} b h$, which gives $A = \frac{1}{2} \times 1.1 \times 3.3 = 1.815 \mathrm{~cm}^{2}$.

Question 5

Substitute to find the value of the expression.
-The area of a rectangle of length land width $w$ is given by the formula $A=$ lv. Ann's backyard is rectangular with a length of 24.2 yards and a width of 17.7 yards. Find the area of Ann's backyard.
A) $428.34 \mathrm{yd}^{2}$
B) $41.9 \mathrm{yd}^{2}$
C) $428.34 \mathrm{yd}$
D) $41.9 \mathrm{yd}$

Accepted Answer

The area of a rectangle is calculated by multiplying its length by its width. For Ann's backyard, the area is $24.2 \, \text{yards} \times 17.7 \, \text{yards} = 428.34 \, \text{square yards}$.

Question 6

Substitute to find the value of the expression.
-In one store, bananas cost 60 cents per pound. The cost, in dollars, of $x$ pounds of bananas is $0.6 x$. What is the cost of 1.8 pounds of bananas?
A) $\$ 1.08$
B) $\$ 0.30$
C) $\$ 1.28$
D) $\$ 3.00$

Accepted Answer

To find the cost of 1.8 pounds of bananas, substitute $x = 1.8$ into the expression $0.6x$: $0.6 \times 1.8 = 1.08$. Therefore, the cost is $1.08.

Question 7

Substitute to find the value of the expression.
-Bill takes four times as long to do a job as Jose. Suppose $t$ represents the time it takes Bill to do the job. Then $\mathrm{t} / 4$ represents the time it takes Jose. How long does it take Jose if it takes Bill 89 minutes?
A) $356.00 \mathrm{~min}$
B) $93.00 \mathrm{~min}$
C) $85.00 \mathrm{~min}$
D) $22.25 \mathrm{~min}$

Accepted Answer

Since it takes Bill 89 minutes to do the job and Jose takes one-fourth of that time, dividing 89 by 4 gives 22.25 minutes.

Question 8

Substitute to find the value of the expression.
-Mary earns three times as much per week as Maureen. If $x$ represents the amount that Maureen earns per week, then $3 x$ represents the amount that Mary earns per week. How much does Mary earn per week if Maureen earns $\$ 346$ per week?
A) $\$ 115.33$
B) $\$ 349$
C) $\$ 1038$
D) $\$ 343$

Accepted Answer

Mary earns three times as much as Maureen. If Maureen earns $346 per week, then Mary earns $3 \times 346 = \$1038$ per week.

Question 9

Evaluate.
-$x+y$, when $x=2$ and $y=4$
A) -2
B) -6
C) 6
D) 8

Accepted Answer

When $x=2$ and $y=4$, substituting these values into the expression $x+y$ gives $2+4=6$.

Question 10

Evaluate.
-$4 x$, when $x=4$
A) 22
B) 8
C) 72
D) 16

Accepted Answer

When $x = 4$, $4x = 4 \times 4 = 16$.

Question 11

Evaluate.
-$\frac{p}{q}$, when $p=28$ and $q=4$
A) 7
B) $7 \frac{1}{4}$
C) 8
D) 6

Accepted Answer

When $p = 28$ and $q = 4$, dividing $p$ by $q$ gives $\frac{28}{4} = 7$.

Question 12

Evaluate.
-$\frac{9 m}{n}$, when $m=12$ and $n=4$
A) 54
B) 3
C) 9
D) 27

Accepted Answer

The answer of Evaluate.
-$\frac{9 m}{n}$, when $m=12$ and $n=4$
A) 54
B)...

Question 13

Evaluate.
-$\frac{x+y}{9}$, when $x=11$ and $y=52$
A) 6
B) 5
C) 8
D) 7

Accepted Answer

The answer of Evaluate.
-$\frac{x+y}{9}$, when $x=11$ and $y=52$
A) 6
B) 5
C)...

Question 14

Evaluate.
-$\frac{6 x+8 y}{9}$, when $x=72$ and $y=63$
A) 56
B) 104
C) 55
D) 936

Accepted Answer

The answer of Evaluate.
-$\frac{6 x+8 y}{9}$, when $x=72$ and $y=63$
A)...

Question 15

Translate the phrase to an algebraic expression.
-Eight multiplied by $x$
A) $8+x$
B) $\frac{8}{x}$
C) $8-x$
D) $8 x$

Accepted Answer

The phrase "Eight multiplied by $x$" translates to the algebraic expression $8x$, which means 8 times $x$.

Question 16

Translate the phrase to an algebraic expression.
-$x$ increased by four
A) $4 x$
B) $x+4$
C) $x-4$
D) 4

Accepted Answer

The phrase "x increased by four" means 4 is added to x, which is represented by the expression $x+4$.

Question 17

Translate the phrase to an algebraic expression.
-The sum of $x$ and $y$
A) $2 x y$
B) $x+y$
C) $x y$
D) $\frac{x}{y}$

Accepted Answer

The phrase "the sum of $x$ and $y$" directly translates to $x+y$, indicating addition.

Question 18

Translate to an algebraic expression.
-Robbie drove his car at $50 \mathrm{mph}$ for thours. How many miles did he travel?
A) $\frac{50}{t}$
B) $50 \mathrm{t}$
C) $50-\mathrm{t}$
D) $\frac{\mathrm{t}}{50}$

Accepted Answer

The distance traveled is calculated by multiplying the speed (50 mph) by the time in hours (t), which gives the expression $50t$.

Question 19

Translate to an algebraic expression.
-Leanne had $\$ 27$ remaining after paying $x$ dollars for a dinner and a movie. How much did she have at the start of the evening?
A) $\$ 27 x$
B) $\$ 27-\mathrm{x}$
C) $\$ 27+x$
D) $x-\$ 27$

Accepted Answer

Leanne had $27 more than what she spent (x), so the expression is $27 + x, indicating she started with x dollars and after spending, she had $27 left.

Question 20

Translate to an algebraic expression.
-Monica had $\$ 30$ before spending $x$ dollars for a snack. How much money remains?
A) $x-\$ 30$
B) $\$ 30+x$
C) $\$ 30 x$
D) $\$ 30-x$

Accepted Answer

Monica originally had $30 and spent $x, so the remaining amount is the original amount minus what was spent, which is $30 - x.

Quiz 7: Introduction to Real Numbers and Algebraic Expressions

Substitute to find the value of the expression. -Traveling at $r$ kilometers per hour for $t$ hours, a driver will travel $r t$ kilometers. How far will Danny travel in 16 hours at a speed of 99 kilometers per hour?

Substitute to find the value of the expression. -A plane flies at 582 miles per hour. The time, in hours, for the plane to travel a distance of $d$ miles is $\frac{\mathrm{d}}{582}$ . How long will it take for the plane to travel 5820 miles?

Substitute to find the value of the expression. -A train must cover a distance of 2520 miles. The velocity, in miles per hour, of the train is $\frac{2520}{t}$ where $t$ is the time, in hours, to complete the trip. If the train completes the trip in 28 hours, what is its velocity?

Substitute to find the value of the expression. -The area of a triangle with base $b$ and height $h$ is given by the formula $A=\frac{1}{2} b h$ . Find the area of $a$ triangle when the base is 1.1 centimeters and the height is 3.3 centimeters.

Substitute to find the value of the expression. -The area of a rectangle of length land width $w$ is given by the formula $A=$ lv. Ann's backyard is rectangular with a length of 24.2 yards and a width of 17.7 yards. Find the area of Ann's backyard.

Substitute to find the value of the expression. -In one store, bananas cost 60 cents per pound. The cost, in dollars, of $x$ pounds of bananas is $0.6 x$ . What is the cost of 1.8 pounds of bananas?

Substitute to find the value of the expression. -Bill takes four times as long to do a job as Jose. Suppose $t$ represents the time it takes Bill to do the job. Then $\mathrm{t} / 4$ represents the time it takes Jose. How long does it take Jose if it takes Bill 89 minutes?

Substitute to find the value of the expression. -Mary earns three times as much per week as Maureen. If $x$ represents the amount that Maureen earns per week, then $3 x$ represents the amount that Mary earns per week. How much does Mary earn per week if Maureen earns $\$ 346$ per week?

Evaluate. - $x+y$ , when $x=2$ and $y=4$

Evaluate. - $4 x$ , when $x=4$

Evaluate. - $\frac{p}{q}$ , when $p=28$ and $q=4$

Evaluate. - $\frac{9 m}{n}$ , when $m=12$ and $n=4$

Evaluate. - $\frac{x+y}{9}$ , when $x=11$ and $y=52$

Evaluate. - $\frac{6 x+8 y}{9}$ , when $x=72$ and $y=63$

Translate the phrase to an algebraic expression. -Eight multiplied by $x$

Translate the phrase to an algebraic expression. - $x$ increased by four

Translate the phrase to an algebraic expression. -The sum of $x$ and $y$

Translate to an algebraic expression. -Robbie drove his car at $50 \mathrm{mph}$ for thours. How many miles did he travel?

Translate to an algebraic expression. -Leanne had $\$ 27$ remaining after paying $x$ dollars for a dinner and a movie. How much did she have at the start of the evening?

Translate to an algebraic expression. -Monica had $\$ 30$ before spending $x$ dollars for a snack. How much money remains?

Quiz 7: Introduction to Real Numbers and Algebraic Expressions

Substitute to find the value of the expression. -Traveling at rrr kilometers per hour for ttt hours, a driver will travel rtr trt kilometers. How far will Danny travel in 16 hours at a speed of 99 kilometers per hour?

Substitute to find the value of the expression. -A plane flies at 582 miles per hour. The time, in hours, for the plane to travel a distance of ddd miles is d582\frac{\mathrm{d}}{582}582d​ . How long will it take for the plane to travel 5820 miles?

Substitute to find the value of the expression. -A train must cover a distance of 2520 miles. The velocity, in miles per hour, of the train is 2520t\frac{2520}{t}t2520​ where ttt is the time, in hours, to complete the trip. If the train completes the trip in 28 hours, what is its velocity?

Substitute to find the value of the expression. -The area of a triangle with base bbb and height hhh is given by the formula A=12bhA=\frac{1}{2} b hA=21​bh . Find the area of aaa triangle when the base is 1.1 centimeters and the height is 3.3 centimeters.

Substitute to find the value of the expression. -The area of a rectangle of length land width www is given by the formula A=A=A= lv. Ann's backyard is rectangular with a length of 24.2 yards and a width of 17.7 yards. Find the area of Ann's backyard.

Substitute to find the value of the expression. -In one store, bananas cost 60 cents per pound. The cost, in dollars, of xxx pounds of bananas is 0.6x0.6 x0.6x . What is the cost of 1.8 pounds of bananas?

Substitute to find the value of the expression. -Bill takes four times as long to do a job as Jose. Suppose ttt represents the time it takes Bill to do the job. Then t/4\mathrm{t} / 4t/4 represents the time it takes Jose. How long does it take Jose if it takes Bill 89 minutes?

Substitute to find the value of the expression. -Mary earns three times as much per week as Maureen. If xxx represents the amount that Maureen earns per week, then 3x3 x3x represents the amount that Mary earns per week. How much does Mary earn per week if Maureen earns $346\$ 346$346 per week?

Evaluate. - x+yx+yx+y , when x=2x=2x=2 and y=4y=4y=4

Evaluate. - 4x4 x4x , when x=4x=4x=4

Evaluate. - pq\frac{p}{q}qp​ , when p=28p=28p=28 and q=4q=4q=4

Evaluate. - 9mn\frac{9 m}{n}n9m​ , when m=12m=12m=12 and n=4n=4n=4

Evaluate. - x+y9\frac{x+y}{9}9x+y​ , when x=11x=11x=11 and y=52y=52y=52

Evaluate. - 6x+8y9\frac{6 x+8 y}{9}96x+8y​ , when x=72x=72x=72 and y=63y=63y=63

Translate the phrase to an algebraic expression. -Eight multiplied by xxx

Translate the phrase to an algebraic expression. - xxx increased by four

Translate the phrase to an algebraic expression. -The sum of xxx and yyy

Translate to an algebraic expression. -Robbie drove his car at 50mph50 \mathrm{mph}50mph for thours. How many miles did he travel?

Translate to an algebraic expression. -Leanne had $27\$ 27$27 remaining after paying xxx dollars for a dinner and a movie. How much did she have at the start of the evening?

Translate to an algebraic expression. -Monica had $30\$ 30$30 before spending xxx dollars for a snack. How much money remains?