Question 1

Determine whether the inequalities $- 4 ( x + 10 ) > 8$ and $x + 10 > - 2$ are equivalent.
A)not equivalent
B)equivalent

Accepted Answer

These inequalities are not equivalent because their solutions do not overlap. The first inequality implies that $x<-3$, while the second inequality implies that $x>-12$. Therefore, the values of $x$ that satisfy the first inequality (values less than $-3$) do not satisfy the second inequality (because they are not greater than $-12$), and vice versa.

Question 2

A free-falling object is described by $h = 35 t + \frac { 1 } { 2 } a t ^ { 2 }$ , where h is the height above the ground, t is the amount of time the object is falling, and a is the acceleration. Solve the equation for a .
A) $a = \frac { 2 ( h - 35 t ) } { t }$
B) $a = \frac { 2 ( h + 35 t ) } { t ^ { 2 } }$
C) $a = \frac { 2 ( h - 35 t ) } { t ^ { 2 } }$
D) $a = \frac { h - 35 t } { t ^ { 2 } }$
E) $a = \frac { h - 35 t } { 2 t ^ { 2 } }$

Accepted Answer

Firstly, taking the derivative of h with respect to t gives the velocity, v:

$$v = \frac{dh}{dt} = 35+at$$

Then, taking the derivative of v with respect to t gives the acceleration, a:

$$a = \frac{dv}{dt} = \frac{d}{dt}(35+at) = \frac{d}{dt}(35) + \frac{d}{dt}(at) = 0 + a = a$$

Therefore, the acceleration is just the coefficient of t in the equation for h:

$$a = \frac{2(h-35t)}{t^2}$$

which is choice C.

Question 3

If it takes you 12 hours to complete a job, what portion do you complete each hour?
A) 12%
B) 0.12
C) $\frac { 1 } { 12 }$
D) 11
E) 0.88

Accepted Answer

To find the portion completed each hour, we need to divide the job by the number of hours it takes to complete it. Thus, $\frac{1}{12}$ of the job is completed each hour. Choice C represents this fraction.

Question 4

A chemist wishes to mix a 30% acid solution with a 60% acid solution to obtain 60 quarts of a 39% acid solution. How many quarts of each solution should be mixed together?
A) 42 quarts of 30% solution 18 quarts of $60 \%$ solution
B) $36$ quarts of $30 \%$ solution $24$ quarts of $60 \%$ solution
C) $24$ quarts of $30 \%$ solution $36$ quarts of $60 \%$ solution
D) $30$ quarts of $30 \%$ solution $30$ quarts of $60 \%$ solution
E) $18$ quarts of $30 \%$ solution $42$ quarts of $60 \%$ solution

Accepted Answer

Let x be the number of quarts of 30% solution and y be the number of quarts of 60% solution.We have the following system of equations:x + y = 60 (total volume)0.3x + 0.6y = 0.39(60) (total amount of acid)Solving this system of equations gives x = 42 and y = 18.Therefore, the chemist should mix 42 quarts of 30% solution with 18 quarts of 60% solution.

Question 5

Determine whether the inequalities $7 x - 2 \leq 5 x + 4$ and $2 x \leq 6$ are equivalent.
A)equivalent
B)not equivalent

Accepted Answer

The answer of Determine whether the inequalities \(7 x -...

Question 6

Two cars start at the same point and travel in the same direction at average speeds of 65 miles per hour and 40 miles per hour. How much time (in hours)must elapse before the two cars are 87.5 miles apart?
A) 3.5 hours
B) 3.49 hours
C) 1.35 hours
D) $0.83$ hour
E) $2.19$ hours

Accepted Answer

The relative speed between the two cars is $65 - 40 = 25$ miles per hour. To find the time it takes for them to be 87.5 miles apart, divide the distance by the relative speed: $87.5 \div 25 = 3.5$ hours.

Question 7

Sketch the graph of $1 \leq x \leq 5$ .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Sketch the graph of \(1 \leq x...

Question 8

Ticket sales for a spaghetti dinner total $980 . There are four times as many adult tickets sold as children s tickets. The prices of the tickets for adults and children are $6 and $4 , respectively. Find the number of children s tickets sold.
A) 42 children s tickets
B) 25 children s tickets
C) 38 children s tickets
D) 35 children s tickets
E) 30 children s tickets

Accepted Answer

The answer of Ticket sales for a spaghetti dinner total...

Question 9

Which inequality has the graph that is shown? 
A) $1 < x < 4$
B) $x < 4$
C) $x \geq 4$
D) $1 \leq x \leq 4$
E) $x \leq 4$

Accepted Answer

The answer of Which inequality has the graph that is...

Question 10

Which of the following is a solution to the inequality $2 - ( x + 9 ) \geq 4$ ?
A) x=-15
B) x=-10
C) x=-8
D) x=4
E) x=0

Accepted Answer

$2 - ( x + 9 ) \geq 4$$- ( x + 9 ) \geq 2$$- x - 9 \geq 2$$- x \geq 11$$x \leq -11$Therefore, the correct choice is A.

Question 11

Solve the inequality: $x + 7 \leq - 2$
A) $x \geq - 9$
B) $x \leq - 9$
C) $x \leq 9$
D) $x \geq - 14$
E) $x \leq - \frac { 2 } { 7 }$

Accepted Answer

Subtracting 7 from both sides gives us:
x ≤ -9 
Therefore, the answer is B.

Question 12

A grocer wishes to mix two kinds of nuts costing $2.26 per pound and $3.93 per pound to make a 124 pounds of mixed nuts costing $2.36 per pound. To determine the number of pounds of the $2.26 per pound nuts in the mixture, solve for x in the equation $2.26 x + 3.93 ( 124 - x ) = 292.64$ . How many pounds of the $2.26 per pound nuts should be included in the mixture? Round to the nearest pound.
A) $7$ pounds
B) $62$ pounds
C) 5 pounds
D) $82$ pounds
E) $117$ pounds

Accepted Answer

To find the number of pounds of $2.26 per pound nuts, solve the equation: $2.26x + 3.93(124 - x) = 292.64$. Simplifying gives $2.26x + 487.32 - 3.93x = 292.64$, which simplifies to $-1.67x = -194.68$. Solving for $x$ gives $x \approx 116.58$, which rounds to 117 pounds.

Question 13

Determine if x=-6  satisfies $0 < \frac { x + 5 } { 6 } < 2$ .
A) x=-6 does satisfy the inequality.
B) x=-6 does not satisfy the inequality.

Accepted Answer

Plug in x=-6 into the inequality:

$0 < \frac { x + 5 } { 6 } < 2$

$0 < \frac { -6 + 5 } { 6 } < 2$

$0 < \frac { -1 } { 6 } < 2$

This means that $\frac{-1}{6}$ is between 0 and 2. However, -6 does not satisfy this inequality as it is outside the given range. Thus, the answer is B.

Question 14

The annual insurance premium for a policy holder was $837 . The policy holder must pay a 18% surcharge because of an accident. What is the new annual premium as a result of the accident?
A) $\$ 990.66$
B) $\$ 977.66$
C) $\$ 855.00$
D) $\$ 987.66$
E) $\$ 991.66$

Accepted Answer

First, find the amount of the surcharge by multiplying the original premium by the percentage:

$837 x 0.18 = $150.66

Then add the surcharge amount to the original premium:

$837 + $150.66 = $987.66

Therefore, the new annual premium is $987.66, which is answer choice D.

Question 15

Which of the following is a solution to the inequality $5 - \frac { 1 } { 3 } x > 0$ ?
A) x=15
B) x=5
C) x=14
D) x=9
E) x=10

Accepted Answer

The answer of Which of the following is a solution...

Question 16

Graph the inequality $x < - 2$ or $x \geq 1$ .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Graph the inequality $x < - 2$...

Question 17

Solve: $2 x < 4$
A) $x < \frac { 1 } { 2 }$
B)$x < 2$
C)  x=2
D) $x \leq 2$
E) $x > 2$

Accepted Answer

To solve the inequality $2x < 4$, divide both sides by 2 to get $x < 2$.

Question 18

Which inequality has the graph that is shown? 
A) $1 \leq x < 4$
B) $1 < x \leq 4$
C) $1 \leq x \leq 4$
D) $1 \leq x \leq 6$
E) $1 < x < 4$

Accepted Answer

The answer of Which inequality has the graph that is...

Question 19

Ticket sales for a play total $900 . There are three times as many adult tickets sold as children s tickets. The prices of the tickets for adults and children are $6 and $2 , respectively. Find the number of children s tickets sold.
A) 45 children s tickets
B) 35 children s tickets
C) 48 children s tickets
D) 52 children s tickets
E) 40 children s tickets

Accepted Answer

Let x be the number of children's tickets sold. Then the number of adult tickets sold is 3x. The total amount of money from children's tickets is 2x, and the total amount of money from adult tickets is 6(3x) = 18x. The total amount of money from all tickets is 2x + 18x = 20x. Since the total amount of money is $900, we have 20x = 900, so x = 45. Therefore, the number of children's tickets sold is 45.

Question 20

Two airplanes leave Chicago's O'Hare International Airport at the same time and fly in opposite directions. How far apart are the planes after $2 \frac { 1 } { 3 }$ hours if their average speeds are 450 miles per hour and 580 miles per hour? Round your answer to two decimal places.
A) $2,403.33$ miles
B) $1,353.33$ miles
C) $2,060.00$ miles
D) $1,050.00$ miles
E) $1,030.00$ miles

Accepted Answer

To find the total distance between the planes, add the distances each plane travels. The first plane travels $450 \times 2\frac{1}{3}$ miles, and the second plane travels $580 \times 2\frac{1}{3}$ miles. The total distance is $450 \times \frac{7}{3} + 580 \times \frac{7}{3} = 1050 + 1353.33 = 2403.33$ miles.

Quiz 2: Linear Equations and Inequalities

Determine whether the inequalities $- 4 ( x + 10 ) > 8$ and $x + 10 > - 2$ are equivalent.

A free-falling object is described by $h = 35 t + \frac { 1 } { 2 } a t ^ { 2 }$ , where h is the height above the ground, t is the amount of time the object is falling, and a is the acceleration. Solve the equation for a .

If it takes you 12 hours to complete a job, what portion do you complete each hour?

A chemist wishes to mix a 30% acid solution with a 60% acid solution to obtain 60 quarts of a 39% acid solution. How many quarts of each solution should be mixed together?

Determine whether the inequalities $7 x - 2 \leq 5 x + 4$ and $2 x \leq 6$ are equivalent.

Two cars start at the same point and travel in the same direction at average speeds of 65 miles per hour and 40 miles per hour. How much time (in hours) must elapse before the two cars are 87.5 miles apart?

Sketch the graph of $1 \leq x \leq 5$ .

Ticket sales for a spaghetti dinner total $980 . There are four times as many adult tickets sold as children s tickets. The prices of the tickets for adults and children are $6 and $4 , respectively. Find the number of children s tickets sold.

Which inequality has the graph that is shown? $Which inequality has the graph that is shown? A) 1 < x < 4 B) x < 4 C) x \geq 4 D) 1 \leq x \leq 4 E) x \leq 4$

Which of the following is a solution to the inequality $2 - ( x + 9 ) \geq 4$ ?

Solve the inequality: $x + 7 \leq - 2$

Determine if x=-6 satisfies $0 < \frac { x + 5 } { 6 } < 2$ .

The annual insurance premium for a policy holder was $837 . The policy holder must pay a 18% surcharge because of an accident. What is the new annual premium as a result of the accident?

Which of the following is a solution to the inequality $5 - \frac { 1 } { 3 } x > 0$ ?

Graph the inequality $x < - 2$ or $x \geq 1$ .

Solve: $2 x < 4$

Which inequality has the graph that is shown? $Which inequality has the graph that is shown? A) 1 \leq x < 4 B) 1 < x \leq 4 C) 1 \leq x \leq 4 D) 1 \leq x \leq 6 E) 1 < x < 4$

Ticket sales for a play total $900 . There are three times as many adult tickets sold as children s tickets. The prices of the tickets for adults and children are $6 and $2 , respectively. Find the number of children s tickets sold.

Two airplanes leave Chicago's O'Hare International Airport at the same time and fly in opposite directions. How far apart are the planes after $2 \frac { 1 } { 3 }$ hours if their average speeds are 450 miles per hour and 580 miles per hour? Round your answer to two decimal places.

Quiz 2: Linear Equations and Inequalities

Determine whether the inequalities −4(x+10) >8- 4 ( x + 10 ) > 8−4(x+10) >8 and x+10>−2x + 10 > - 2x+10>−2 are equivalent.

A free-falling object is described by h=35t+12at2h = 35 t + \frac { 1 } { 2 } a t ^ { 2 }h=35t+21​at2 , where h is the height above the ground, t is the amount of time the object is falling, and a is the acceleration. Solve the equation for a .

If it takes you 12 hours to complete a job, what portion do you complete each hour?

A chemist wishes to mix a 30% acid solution with a 60% acid solution to obtain 60 quarts of a 39% acid solution. How many quarts of each solution should be mixed together?

Determine whether the inequalities 7x−2≤5x+47 x - 2 \leq 5 x + 47x−2≤5x+4 and 2x≤62 x \leq 62x≤6 are equivalent.

Two cars start at the same point and travel in the same direction at average speeds of 65 miles per hour and 40 miles per hour. How much time (in hours) must elapse before the two cars are 87.5 miles apart?

Sketch the graph of 1≤x≤51 \leq x \leq 51≤x≤5 .

Ticket sales for a spaghetti dinner total $980 . There are four times as many adult tickets sold as children s tickets. The prices of the tickets for adults and children are $6 and $4 , respectively. Find the number of children s tickets sold.

Which inequality has the graph that is shown?

Which of the following is a solution to the inequality 2−(x+9) ≥42 - ( x + 9 ) \geq 42−(x+9) ≥4 ?

Solve the inequality: x+7≤−2x + 7 \leq - 2x+7≤−2

Determine if x=-6 satisfies 0<x+56<20 < \frac { x + 5 } { 6 } < 20<6x+5​<2 .