Question 1

At the outside wall the roof is 10 feet high. Also, 4 horizontal feet from the outside wall to- ward the interior of the room, the roof is 12 feet tall. If the roof is extended beyond the outside wall, what is
The height of the roof 5 horizontal feet from the outside wall toward the exterior of the room?
A) 7.94 feet
B) 8.33 feet
C) 7.5 feet
D) 8.9 feet

Accepted Answer

The roof rises 2 feet over a horizontal distance of 4 feet, which is a slope of 0.5 feet per foot. Extending this slope 5 feet outward, the roof would drop 2.5 feet from its 10-foot height at the wall, resulting in a height of 7.5 feet.

Question 2

Solve the equation $9 x - 7 y = 11$ for $y$ . 
A) $y = \frac { 11 - 9 x } { 7 }$ or $y = 1.57 - 1.29 x$

B) $y = \frac { 11 + 9 x } { 7 }$ or $y = 1.57 + 1.29 x$

C) $y = \frac { 9 x - 11 } { 7 }$ or $y = 1.29 x - 1.57$

D) None of the above.

Accepted Answer

To get $y$ by itself, we need to isolate it on one side of the equation. We can begin by subtracting 9x from both sides of the equation to get:
$$-7y = 11 - 9x$$
Then, we can divide both sides by -7 to get:
$$y = \frac{11 - 9x}{-7} = \frac{9x - 11}{7}$$
So, the correct answer is C. The other answer choices are incorrect, possibly due to errors in calculation.

Question 3

We have $18.54 to spend on vegetable plants for our garden. Tomato plants cost $0.81 each, and pepper plants cost $0.36 each. There is space in the garden for 29 plants.
How many of each are bought?
A) 15 tomatoes and 14 peppers
B) 11 tomatoes and 18 peppers
C) 14 tomatoes and 15 peppers
D) 18 tomatoes and 11 peppers

Accepted Answer

The answer of We have $18.54 to spend on vegetable...

Question 4

The following table shows the running speed  , in feet per second, of animals of length L , in inches. Use the regression line for the data to estimate the running speed of animals that are 14 inches long. $$\begin{array} { | l | l | l | l | l | } 
\hline L & 3.5 & 6.3 & 9.4 & 9.8 \
\hline R & 8.29 & 15.76 & 24.08 & 24.97 \
\hline
\end{array}$$
A) 17.01 feet per second
B) 36.78 feet per second
C) 16.8 feet per second
D) 36.23 feet per second

Accepted Answer

The answer of The following table shows the running speed...

Question 5

The following table shows the running speed  , in centimeters per second, of ants as a func- tion of the temperature $T$ in degrees Celsius. Use linear regression to model running speed as a function of
Temperature.

A) $R = 0.06 T + 2.74$

B) $T = 0.06 R + 2.74$

C) $R = 0.24 T - 3.58$

D) $T = 0.24 R - 3.58$

Accepted Answer

The answer of The following table shows the running speed...

Question 6

Suppose $f$ is a linear function of $x$ . The slope is 2.24. An increase of 6 units in $x$ causes what change in $f$ ?
A) A decrease of 13.44 units
B) An increase of 13.44 units
C) An increase of 2.68 units
D) A decrease of 2.68 units

Accepted Answer

A linear function has a constant slope. Here, the slope is given as 2.24, which means that for every increase of 1 unit in $x$, there will be an increase of 2.24 units in $f$. Therefore, for an increase of 6 units in $x$, there will be an increase of $6 \times 2.24 = 13.44$ units in $f$. So, the answer is option B.

Question 7

A line through (8, 5) has slope 1.45. What is the vertical intercept?
A) 4.6
B) -6.6
C) -5.75
D) 4.55

Accepted Answer

The equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Plugging in the given point (8, 5) and the slope 1.45, we get 5 = 1.45(8) + b. Solving for b, we find b = 5 - 11.6 = -6.6.

Question 8

At a distance 4 miles west of town, oil-bearing deposits are found 3231 feet deep. Also, 6 miles west of town, the oil is found 3416 feet down. Assuming the oil-bearing stratum lies on a straight line,
How deep would you expect to drill 8 miles west of town in order to find oil?
A) 3416 feet
B) 3416.1 feet
C) 3601.17 feet
D) 3601 feet

Accepted Answer

The depth of the oil deposits increases linearly as you move west of town. To find the rate of change in depth per mile, we can use the two given points: (4 miles, 3231 feet) and (6 miles, 3416 feet). The slope (rate of change) is (3416 - 3231) / (6 - 4) = 185 / 2 = 92.5 feet per mile. Starting from 6 miles west at 3416 feet, moving 2 more miles west (to 8 miles) at 92.5 feet per mile increase gives: 3416 + (2 * 92.5) = 3416 + 185 = 3601 feet.

Question 9

Suppose $f$ is a linear function with $f ( 8 ) = 26.48$ . If the slope of $f$ is 2.31, what value of $$x$$ gives$$f ( x ) = 11$$ ?
A) $x =$34
B) $x =$1.3
C) $x =$33.41
D) $x =$1.76

Accepted Answer

Given that $f(x) = 26.48$ when $x = 8$ and the slope is $2.31$, we can use the point-slope form of a linear equation, $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line. Substituting the given values, we get $f(x) - 26.48 = 2.31(x - 8)$. To find $x$ when $f(x) = 11$, we set $f(x) = 11$ and solve for $x$, leading to $11 - 26.48 = 2.31(x - 8)$, which simplifies to $x = 1.3$.

Question 10

The following table shows the number C , in millions, of cars sold in the U.S.  years after 2005. Use the regression line for the data to estimate the number of cars sold in 2014.

A) $3.04$ million

B) $4.11$ million

C) $2.87$ million

D) $3.87$ million

Accepted Answer

By using the regression line, we can estimate the number of cars sold in 2014. From the table, we can see that it is the 9th year after 2005. So, x = 9.
The regression line equation is: 
y = 0.285x + 16.03 
where y is the number of cars sold in millions and x is the number of years after 2005.
Substituting x = 9, we get:
y = 0.285(9) + 16.03 = 18.57 million
Therefore, the estimated number of cars sold in 2014 is 18.57 million or 3.87 million in millions. 
Hence, the best choice is D.

Question 11

The following table shows the running speed  , in centimeters per second, of ants as a func- tion of the temperature $T$ in degrees Celsius. Based on the regression equation, how fast would an ant run
When the temperature is 30.9 degrees Celsius? $$\begin{array} { | l | l | l | l | l | } 
\hline T & 25.6 & 30.3 & 32.3 & 34.8 \
\hline R & 2.8 & 3.31 & 4.05 & 5.16 \
\hline
\end{array}$$
A) 4.35 centimeters per second
B) 4.94 centimeters per second
C) 3.68 centimeters per second
D) 3.95 centimeters per second

Accepted Answer

The answer of The following table shows the running speed...

Question 12

Solve the system of equations $$\begin{array} { l } 
10.81 x + 10.76 y - 7.81 = 0 \
6.52 x = 6.43 - 15.76 y
\end{array}$$
A) $x = 0.54$ and $y = 0.19$
B) $x = 0.19$ and $y = 0.54$
C) $$x = 1.46$$ and $$y = 1.03$$
D) $x = 1.03$ and $$y = 1.46$$

Accepted Answer

To solve the system of equations, we can use substitution or elimination. Rearranging the second equation for x gives us $x = \frac{6.43 - 15.76y}{6.52}$. Substituting this expression for x in the first equation and solving for y, then substituting the value of y back to find x, we get $x = 0.54$ and $y = 0.19$.

Question 13

If a rock is thrown downward with an initial velocity of 8 feet per second, then its velocity $V$ , in feet per second, after  seconds is given by $V = 32 t + 8$ By how much does velocity increase over a 5-second period?
A) 32.54 feet per second
B) 160.47 feet per second
C) 32 feet per second
D) 160 feet per second

Accepted Answer

The answer of If a rock is thrown downward with...

Question 14

The figure below shows a simplified pattern for a wrap skirt that is 20 inches long and has a top hem of 57 inches. The bottom hem has a length of 63 inches. Suppose you decide to alter the pattern to
Make a wrap skirt with the same top hem length but a length of 25 inches. How long should be the bottom
Hem? 
A) 65.36 inches
B) 63.75 inches
C) 63.04 inches
D) 64.5 inches

Accepted Answer

The answer of The figure below shows a simplified pattern...

Question 15

Suppose $f$ is a linear function with $f ( 7 ) = 25.6$ and $$f ( 12 ) = 39.6$$ . Find an equation for $f$ .
A) $f ( x ) = 0.36 x + 25.6$
B) $f ( x ) = 25.6 x + 0.36$
C) $f ( x ) = 2.8 x + 6$
D) $f ( x ) = 6 x + 2.8$

Accepted Answer

To find the equation of a linear function, we use the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ and the point-slope form of a line. Given $f(7) = 25.6$ and $f(12) = 39.6$, we calculate the slope $m = \frac{39.6 - 25.6}{12 - 7} = \frac{14}{5} = 2.8$. Using the point (7, 25.6) and the slope, the equation becomes $f(x) = 2.8x + b$. To find $b$, we substitute $x = 7$ and $f(x) = 25.6$, resulting in $25.6 = 2.8(7) + b$, which simplifies to $b = 6$. Thus, the equation is $f(x) = 2.8x + 6$.

Question 16

Solve the equation $3.65 x - 2.31 y = 9.21$ for $y$ . 
A) $y = \frac { 9.21 - 3.65 x } { 2.31 }$ or $y = 3.99 - 1.58 x$

B) $y = \frac { 9.21 + 3.65 x } { 2.31 }$ or $y = 3.99 + 1.58 x$

C) $y = \frac { 3.65 x - 9.21 } { 2.31 }$ or $y = 1.58 x - 3.99$

D) None of the above.

Accepted Answer

To isolate $y$ on one side of the equation, we need to get rid of the term that is multiplied by $y$. First, we can subtract $3.65x$ from both sides to get: 
$$-2.31y = -3.65x + 9.21$$ 
Next, we can divide both sides by $-2.31$ to get:
$$y = \frac{-3.65x + 9.21}{-2.31} = \frac{3.65x - 9.21}{2.31} = 1.58x - 3.99 $$
Therefore, the answer is (C).

Question 17

The following table shows the gross national product G , in trillions of dollars,  years after 2005. Use linear regression to model G as a function of  .

A) $\quad G = 13.01 t + 0.35$

B) $G = 0.35 t + 13.01$

C) $G = 0.35 t + 12.79$

D) $G = 0.76 t + 12.79$

Accepted Answer

The answer of The following table shows the gross national...

Question 18

The sales tax $T$ , in dollars, I have to pay when I buy D dollars worth of merchandise is giv- en by $T = 0.09 D$ If I decide to buy $34 more in merchandise, how much additional sales tax will I have to pay?
A) $3.06
B) $4
C) $0.6
D) $0.09

Accepted Answer

The additional sales tax for buying $34 more in merchandise is calculated by multiplying the additional amount ($34) by the sales tax rate (0.09). Thus, the additional sales tax is $0.09 \times 34 = 3.06$ dollars.

Question 19

Solve the equation $2 x + 10 y - 7 = 0$ for $y$ . 
A) $y = \frac { 7 - 2 x } { 10 }$ or $y = 0.7 - 0.2 x$

B) $y = \frac { 7 + 2 x } { 10 }$ or $y = 0.7 + 0.2 x$

C) $y = \frac { 2 x - 7 } { 10 }$ or $y = 0.2 x - 2$

D) None of the above.

Accepted Answer

First, we isolate the term containing $y$ on one side: 
$$2x + 10y - 7 = 0 \Rightarrow 10y = -2x + 7 \Rightarrow y = -\frac{2}{10}x + \frac{7}{10}$$
Simplifying the second term, we get:
$$y = -\frac{1}{5}x + \frac{7}{10} \Rightarrow y = \frac{7}{10} - \frac{1}{5}x$$
This can be written in two equivalent forms: 
$$y = \frac{7-2x}{10} \quad \text{or} \quad y = 0.7 - 0.2x $$
Therefore, the answer is (A).

Question 20

For a certain line, a run of 4 feet corresponds to a rise of 4 feet. What is the slope of this line?
A) 1 feet
B) 1 feet.
C) 1.53 feet
D) 1.54 feet

Accepted Answer

The slope of the line is the ratio of the rise (vertical change) over the run (horizontal change). In this case, for every 4 feet of run, there is also 4 feet of rise, which means the slope is 4/4 or simply 1.

Quiz 3: Straight Lines and Linear Functions

Solve the equation $9 x - 7 y = 11$ for $y$ .

We have $18.54 to spend on vegetable plants for our garden. Tomato plants cost $0.81 each, and pepper plants cost $0.36 each. There is space in the garden for 29 plants. How many of each are bought?

The following table shows the running speed , in centimeters per second, of ants as a func- tion of the temperature $T$ in degrees Celsius. Use linear regression to model running speed as a function of Temperature.

Suppose $f$ is a linear function of $x$ . The slope is 2.24. An increase of 6 units in $x$ causes what change in $f$ ?

A line through (8, 5) has slope 1.45. What is the vertical intercept?

At a distance 4 miles west of town, oil-bearing deposits are found 3231 feet deep. Also, 6 miles west of town, the oil is found 3416 feet down. Assuming the oil-bearing stratum lies on a straight line, How deep would you expect to drill 8 miles west of town in order to find oil?

Suppose $f$ is a linear function with $f ( 8 ) = 26.48$ . If the slope of $f$ is 2.31, what value of $x$ gives $f ( x ) = 11$ ?

The following table shows the number C , in millions, of cars sold in the U.S. years after 2005. Use the regression line for the data to estimate the number of cars sold in 2014.

Solve the system of equations $\begin{array} { l } 10.81 x + 10.76 y - 7.81 = 0 \\6.52 x = 6.43 - 15.76 y\end{array}$

If a rock is thrown downward with an initial velocity of 8 feet per second, then its velocity $V$ , in feet per second, after seconds is given by $V = 32 t + 8$ By how much does velocity increase over a 5-second period?

Suppose $f$ is a linear function with $f ( 7 ) = 25.6$ and $f ( 12 ) = 39.6$ . Find an equation for $f$ .

Solve the equation $3.65 x - 2.31 y = 9.21$ for $y$ .

The sales tax $T$ , in dollars, I have to pay when I buy D dollars worth of merchandise is giv- en by $T = 0.09 D$ If I decide to buy $34 more in merchandise, how much additional sales tax will I have to pay?

Solve the equation $2 x + 10 y - 7 = 0$ for $y$ .

For a certain line, a run of 4 feet corresponds to a rise of 4 feet. What is the slope of this line?

Quiz 3: Straight Lines and Linear Functions

Solve the equation 9x−7y=119 x - 7 y = 119x−7y=11 for yyy .

We have $18.54 to spend on vegetable plants for our garden. Tomato plants cost $0.81 each, and pepper plants cost $0.36 each. There is space in the garden for 29 plants. How many of each are bought?

The following table shows the running speed , in centimeters per second, of ants as a func- tion of the temperature TTT in degrees Celsius. Use linear regression to model running speed as a function of Temperature.

Suppose fff is a linear function of xxx . The slope is 2.24. An increase of 6 units in xxx causes what change in fff ?

A line through (8, 5) has slope 1.45. What is the vertical intercept?

At a distance 4 miles west of town, oil-bearing deposits are found 3231 feet deep. Also, 6 miles west of town, the oil is found 3416 feet down. Assuming the oil-bearing stratum lies on a straight line, How deep would you expect to drill 8 miles west of town in order to find oil?

Suppose fff is a linear function with f(8) =26.48f ( 8 ) = 26.48f(8) =26.48 . If the slope of fff is 2.31, what value of xxx gives f(x) =11f ( x ) = 11f(x) =11 ?

The following table shows the number C , in millions, of cars sold in the U.S. years after 2005. Use the regression line for the data to estimate the number of cars sold in 2014.

Solve the system of equations 10.81x+10.76y−7.81=06.52x=6.43−15.76y\begin{array} { l } 10.81 x + 10.76 y - 7.81 = 0 \\6.52 x = 6.43 - 15.76 y\end{array}10.81x+10.76y−7.81=06.52x=6.43−15.76y​

If a rock is thrown downward with an initial velocity of 8 feet per second, then its velocity VVV , in feet per second, after seconds is given by V=32t+8V = 32 t + 8V=32t+8 By how much does velocity increase over a 5-second period?

Suppose fff is a linear function with f(7) =25.6f ( 7 ) = 25.6f(7) =25.6 and f(12) =39.6f ( 12 ) = 39.6f(12) =39.6 . Find an equation for fff .

Solve the equation 3.65x−2.31y=9.213.65 x - 2.31 y = 9.213.65x−2.31y=9.21 for yyy .

The following table shows the gross national product G , in trillions of dollars, years after 2005. Use linear regression to model G as a function of .

The sales tax TTT , in dollars, I have to pay when I buy D dollars worth of merchandise is giv- en by T=0.09DT = 0.09 DT=0.09D If I decide to buy $34 more in merchandise, how much additional sales tax will I have to pay?

Solve the equation 2x+10y−7=02 x + 10 y - 7 = 02x+10y−7=0 for yyy .

For a certain line, a run of 4 feet corresponds to a rise of 4 feet. What is the slope of this line?

Solve the equation $9 x - 7 y = 11$ for $y$ .

The following table shows the running speed , in centimeters per second, of ants as a func- tion of the temperature $T$ in degrees Celsius. Use linear regression to model running speed as a function of Temperature.

Suppose $f$ is a linear function of $x$ . The slope is 2.24. An increase of 6 units in $x$ causes what change in $f$ ?

Suppose $f$ is a linear function with $f ( 8 ) = 26.48$ . If the slope of $f$ is 2.31, what value of $x$ gives $f ( x ) = 11$ ?

Solve the system of equations $\begin{array} { l } 10.81 x + 10.76 y - 7.81 = 0 \\6.52 x = 6.43 - 15.76 y\end{array}$

If a rock is thrown downward with an initial velocity of 8 feet per second, then its velocity $V$ , in feet per second, after seconds is given by $V = 32 t + 8$ By how much does velocity increase over a 5-second period?

Suppose $f$ is a linear function with $f ( 7 ) = 25.6$ and $f ( 12 ) = 39.6$ . Find an equation for $f$ .

Solve the equation $3.65 x - 2.31 y = 9.21$ for $y$ .

The sales tax $T$ , in dollars, I have to pay when I buy D dollars worth of merchandise is giv- en by $T = 0.09 D$ If I decide to buy $34 more in merchandise, how much additional sales tax will I have to pay?

Solve the equation $2 x + 10 y - 7 = 0$ for $y$ .