Question 1

Consider a line with slope m and y-intercept (0,7).Select the graph of the distance between the origin and the line. ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 2

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​
A = (-4,-5),B = (2,7),C = (5,7)
​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 3

Consider a line with slope m and y-intercept (0,3).Find the slope that yields the maximum distance between the point (2,1)and the line. ​

Accepted Answer

A)  $m = 3$ 
B)  $m = - 1$ 
C)  $m = 2$ 
D)  $m = - 2$ 
E)  $m = 1$ 
A)  $m = 3$ 
B)  $m = - 1$ 
C)  $m = 2$ 
D)  $m = - 2$ 
E)  $m = 1$

Question 4

A straight road rises with an inclination of 0.21 radian from the horizontal (see figure).Find the slope of the road and the change in elevation (x)over a two-mile stretch of the road.Round your answer to four decimal places for the m round your answers to nearest whole number for change in elevation.​   ​ $a = 2 , b = 0.21$ ​

Accepted Answer

A)  $$\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,203 \text { feet }
\end{array}$$ 
B)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,202 \text { feet }
\end{array}$ 
C)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,200 \text { feet }
\end{array}$ 
D)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,199 \text { feet }
\end{array}$ 
E)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,201 \text { feet }
\end{array}$ 
A)  $$\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,203 \text { feet }
\end{array}$$ 
B)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,202 \text { feet }
\end{array}$ 
C)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,200 \text { feet }
\end{array}$ 
D)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,199 \text { feet }
\end{array}$ 
E)  $\begin{array} { l } 
m \approx 0.2131 \
x \approx 2,201 \text { feet }
\end{array}$

Question 5

A straight road rises with an inclination of 0.22 radian from the horizontal.Find the slope of the road and the change in elevation over a one-mile stretch of the road.Round your answer to four decimal places for the m round your answers to nearest whole number for change in elevation. ​

Accepted Answer

A)  $$\begin{array} { l } 
m \approx 0.2236 \
x \approx 1,153 \text { feet }
\end{array}$$ 
B)  $\begin{array} { l } 
m \approx 0.2236 \
x \approx 1,154 \text { feet }
\end{array}$ 
C)  $\begin{array} { l } 
m \approx 0.2236 \
x \approx 1,152 \text { feet }
\end{array}$ 
D)  $\begin{array} { l } 
m \approx 0.2236 \
x \approx 1,151 \text { feet }
\end{array}$ 
E)  $\begin{array} { l } 
m \approx 0.2236 \
x \approx 1,150 \text { feet }
\end{array}$ 
A)  $$\begin{array} { l } 
m \approx 0.2236 \
x \approx 1,153 \text { feet }
\end{array}$$ 
B)  $\begin{array} { l } 
m \approx 0.2236 \
x \approx 1,154 \text { feet }
\end{array}$ 
C)  $\begin{array} { l } 
m \approx 0.2236 \
x \approx 1,152 \text { feet }
\end{array}$ 
D)  $\begin{array} { l } 
m \approx 0.2236 \
x \approx 1,151 \text { feet }
\end{array}$ 
E)  $\begin{array} { l } 
m \approx 0.2236 \
x \approx 1,150 \text { feet }
\end{array}$

Question 6

Find the inclination $\theta$ (in radians and degrees)of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $7 x + 5 y = 0$ ​

Accepted Answer

A) ​ $\Theta \approx 2.2318 \text { radians } \approx 127.9 ^ { \circ }$ 
B)  $\theta \approx 2.2318 \text { radians } \approx 128.9 ^ { \circ }$ 
C)  $\theta \approx 2.2318 \text { radians } \approx 126.9 ^ { \circ }$ 
D)  $\theta \approx 2.2318 \text { radians } \approx 129.9 ^ { \circ }$ 
E)  $\theta \approx 2.2318 \text { radians } \approx 125.9 ^ { \circ }$ 
A) ​ $\Theta \approx 2.2318 \text { radians } \approx 127.9 ^ { \circ }$ 
B)  $\theta \approx 2.2318 \text { radians } \approx 128.9 ^ { \circ }$ 
C)  $\theta \approx 2.2318 \text { radians } \approx 126.9 ^ { \circ }$ 
D)  $\theta \approx 2.2318 \text { radians } \approx 129.9 ^ { \circ }$ 
E)  $\theta \approx 2.2318 \text { radians } \approx 125.9 ^ { \circ }$

Question 7

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane.​ $$A = \left( - \frac { 1 } { 6 } , \frac { 1 } { 7 } \right) , B = ( 6,7 ) , C = \left( \frac { 6 } { 7 } , 0 \right)$$ ​

Accepted Answer

A) ​   ​ 
B) ​   ​ 
C) ​   
D) ​   
E) ​   
A) ​   ​ 
B) ​   ​ 
C) ​   
D) ​   
E) ​

Question 8

Find the angle $$\theta$$ (in radians and degrees)between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $$\begin{array} { l } 
x - y = 10 \
3 x - 2 y = 1
\end{array}$$ ​

Accepted Answer

A)  $$\Theta \approx 0.0907 \text { radians } \approx 6.2 ^ { \circ }$$ 
B)  $$\Theta \approx 0.0907 \text { radians } \approx 4.2 ^ { \circ }$$ 
C)  $\Theta \approx 0.0907 \text { radians } \approx 5.2 ^ { \circ }$ 
D)  $\Theta \approx 0.0907 \text { radians } \approx 7.2 ^ { \circ }$ 
E)  $\Theta \approx 0.0907 \text { radians } \approx 3.2 ^ { \circ }$ 
A)  $$\Theta \approx 0.0907 \text { radians } \approx 6.2 ^ { \circ }$$ 
B)  $$\Theta \approx 0.0907 \text { radians } \approx 4.2 ^ { \circ }$$ 
C)  $\Theta \approx 0.0907 \text { radians } \approx 5.2 ^ { \circ }$ 
D)  $\Theta \approx 0.0907 \text { radians } \approx 7.2 ^ { \circ }$ 
E)  $\Theta \approx 0.0907 \text { radians } \approx 3.2 ^ { \circ }$

Question 9

Find the distance between the point and the line.Round your answer to four decimal places.​ Point Line
$( 14,12 ) \quad 11 x - y = 0$ ​

Accepted Answer

A)  $d \approx 2.1626$ 
B)  $d \approx 3.1626$ 
C)  $d \approx 1.1626$ 
D)  $d \approx 0.1626$ 
E)  $d \approx 4.1626$ 
A)  $d \approx 2.1626$ 
B)  $d \approx 3.1626$ 
C)  $d \approx 1.1626$ 
D)  $d \approx 0.1626$ 
E)  $d \approx 4.1626$

Question 10

A moving conveyor is built so that it rises 3 meter for each 5 meters of horizontal travel.The conveyor runs between two floors in a factory.The distance between the floors is 4 meters.Find the length of the conveyor.Round your answers to one decimal place. ​

Accepted Answer

A)  $24.3 \mathrm {~m}$ 
B)  $25.3 \mathrm {~m}$ 
C)  $22.3 \mathrm {~m}$ 
D)  $21.3 \mathrm {~m}$ 
E)  $23.3 \mathrm {~m}$ 
A)  $24.3 \mathrm {~m}$ 
B)  $25.3 \mathrm {~m}$ 
C)  $22.3 \mathrm {~m}$ 
D)  $21.3 \mathrm {~m}$ 
E)  $23.3 \mathrm {~m}$

Question 11

The Falls Incline Railway in Niagara Falls,Ontario,Canada is an inclined railway that was designed to carry people from the City of Niagara Falls to Queen Victoria Park.The railway is approximately 110 feet long with a 28% uphill grade (see figure).Find the change in elevation from the base to the top of the railway.Round your answers to one decimal place.​   ​ $a = 110$ ​

Accepted Answer

A)  $z \approx 29.7 \mathrm { ft }$ 
B)  $$z \approx 30.7 \mathrm { ft }$$ 
C)  $$z \approx 28.7 \mathrm { ft }$$ 
D)  $z \approx 31.7 \mathrm { ft }$ 
E)  $z \approx 27.7 \mathrm { ft }$ 
A)  $z \approx 29.7 \mathrm { ft }$ 
B)  $$z \approx 30.7 \mathrm { ft }$$ 
C)  $$z \approx 28.7 \mathrm { ft }$$ 
D)  $z \approx 31.7 \mathrm { ft }$ 
E)  $z \approx 27.7 \mathrm { ft }$

Question 12

Find the angle $$\theta$$ (in radians and degrees)between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. ​​ $$\begin{array} { l } 
6 x + y = 6 \
x - y = 5
\end{array}$$ ​

Accepted Answer

A)  $\theta \approx 0.9505 \text { radians } \approx 54.5 ^ { \circ }$ 
B)  $\theta \approx 0.9505 \text { radians } \approx 55.5 ^ { \circ }$ 
C)  $\theta \approx 0.9505 \text { radians } \approx 53.5 ^ { \circ }$ 
D)  $\theta \approx 0.9505 \text { radians } \approx 56.5 ^ { \circ }$ 
E)  $\theta \approx 0.9505 \text { radians } \approx 52.5 ^ { \circ }$ 
A)  $\theta \approx 0.9505 \text { radians } \approx 54.5 ^ { \circ }$ 
B)  $\theta \approx 0.9505 \text { radians } \approx 55.5 ^ { \circ }$ 
C)  $\theta \approx 0.9505 \text { radians } \approx 53.5 ^ { \circ }$ 
D)  $\theta \approx 0.9505 \text { radians } \approx 56.5 ^ { \circ }$ 
E)  $\theta \approx 0.9505 \text { radians } \approx 52.5 ^ { \circ }$

Question 13

A moving conveyor is built so that it rises 7 meter for each 9 meters of horizontal travel.Select a diagram that gives a visual representation of the problem. ​

Accepted Answer

A) ​   a = 7m,b = 9m 
B) ​   a = 7m,b = 9m 
C) ​   a = 7m,b = 9m 
D) ​   a = 7m,b = 9m 
E) ​   a = 7m,b = 9m 
A) ​   a = 7m,b = 9m 
B) ​   a = 7m,b = 9m 
C) ​   a = 7m,b = 9m 
D) ​   a = 7m,b = 9m 
E) ​   a = 7m,b = 9m

Question 14

Consider a line with slope m and y-intercept (0,3).Select the graph of the distance d between the point (2,1)and the line as a function of m. ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 15

Find the inclination $\theta$ (in radians and degrees)of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $( - 2,20 ) , ( 10,0 )$ ​

Accepted Answer

A)  $\theta \approx 2.1112 \text { radians } \approx 122.0 ^ { \circ }$ 
B)  $\theta \approx 2.1112 \text { radians } \approx 120.0 ^ { \circ }$ 
C)  $\theta \approx 2.1112 \text { radians } \approx 123.0 ^ { \circ }$ 
D)  $\theta \approx 2.1112 \text { radians } \approx 119.0 ^ { \circ }$ 
E)  $\theta \approx 2.1112 \text { radians } \approx 121.0 ^ { \circ }$ 
A)  $\theta \approx 2.1112 \text { radians } \approx 122.0 ^ { \circ }$ 
B)  $\theta \approx 2.1112 \text { radians } \approx 120.0 ^ { \circ }$ 
C)  $\theta \approx 2.1112 \text { radians } \approx 123.0 ^ { \circ }$ 
D)  $\theta \approx 2.1112 \text { radians } \approx 119.0 ^ { \circ }$ 
E)  $\theta \approx 2.1112 \text { radians } \approx 121.0 ^ { \circ }$

Question 16

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​
A = (0,0),B = (3,6),C = (6,0)
​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 17

Find the inclination $\theta$ (in radians and degrees)of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $( 0,200 ) , ( 20,0 )$ ​

Accepted Answer

A) ​ $\Theta \approx 1.6705 \text { radians } \approx 96.7 ^ { \circ }$ 
B)  $\theta \approx 1.6705 \text { radians } \approx 94.7 ^ { \circ }$ 
C)  $\theta \approx 1.6705 \text { radians } \approx 97.7 ^ { \circ }$ 
D)  $\theta \approx 1.6705 \text { radians } \approx 95.7 ^ { \circ }$ 
E)  $\theta \approx 1.6705 \text { radians } \approx 93.7 ^ { \circ }$ 
A) ​ $\Theta \approx 1.6705 \text { radians } \approx 96.7 ^ { \circ }$ 
B)  $\theta \approx 1.6705 \text { radians } \approx 94.7 ^ { \circ }$ 
C)  $\theta \approx 1.6705 \text { radians } \approx 97.7 ^ { \circ }$ 
D)  $\theta \approx 1.6705 \text { radians } \approx 95.7 ^ { \circ }$ 
E)  $\theta \approx 1.6705 \text { radians } \approx 93.7 ^ { \circ }$

Question 18

The Falls Incline Railway in Niagara Falls,Ontario,Canada is an inclined railway that was designed to carry people from the City of Niagara Falls to Queen Victoria Park.The railway is approximately 130 feet long with a 46% uphill grade (see figure).Find the inclination $$\theta$$ of the railway.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​   ​ $a = 130$ ​

Accepted Answer

A)  $\Theta \approx 0.4311 \text { radian, or } 25.7 ^ { \circ }$ 
B)  $\Theta \approx 0.4311 \text { radian, or } 23.7 ^ { \circ }$ 
C)  $\Theta \approx 0.4311 \text { radian, or } 26.7 ^ { \circ }$ 
D)  $\Theta \approx 0.4311 \text { radian, or } 24.7 ^ { \circ }$ 
E)  $\Theta \approx 0.4311 \text { radian, or } 22.7 ^ { \circ }$ 
A)  $\Theta \approx 0.4311 \text { radian, or } 25.7 ^ { \circ }$ 
B)  $\Theta \approx 0.4311 \text { radian, or } 23.7 ^ { \circ }$ 
C)  $\Theta \approx 0.4311 \text { radian, or } 26.7 ^ { \circ }$ 
D)  $\Theta \approx 0.4311 \text { radian, or } 24.7 ^ { \circ }$ 
E)  $\Theta \approx 0.4311 \text { radian, or } 22.7 ^ { \circ }$

Question 19

Find the inclination $\theta$ (in radians and degrees)of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $6 x + 7 y - 13 = 0$ ​

Accepted Answer

A)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$ 
B)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$ 
C)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$ 
D)  $\theta \approx 2.5536 \text { radians } \approx 146.3 ^ { \circ }$ 
E)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$ 
A)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$ 
B)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$ 
C)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$ 
D)  $\theta \approx 2.5536 \text { radians } \approx 146.3 ^ { \circ }$ 
E)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$

Question 20

Consider a line with slope m and y-intercept (0,5).Find the slope that yields the maximum distance between the origin and the line. ​

Accepted Answer

A) The maximum distance of $- \frac { 1 } { 5 }$ occurs when the slope m is $- \frac { 1 } { 5 }$ and the line through (0,5)is horizontal. 
B) The maximum distance of 5 occurs when the slope m is 0 and the line through (0,5)is horizontal. 
C) The maximum distance of $\frac { 1 } { 5 }$ occurs when the slope m is 0 and the line through (0,5)is horizontal. 
D) The maximum distance of 6 occurs when the slope m is 0 and the line through (0,6)is horizontal. 
E) The maximum distance of $- 5$ occurs when the slope m is $\frac { 1 } { 5 }$ and the line through (0,5)is horizontal. 
A) The maximum distance of $- \frac { 1 } { 5 }$ occurs when the slope m is $- \frac { 1 } { 5 }$ and the line through (0,5)is horizontal. 
B) The maximum distance of 5 occurs when the slope m is 0 and the line through (0,5)is horizontal. 
C) The maximum distance of $\frac { 1 } { 5 }$ occurs when the slope m is 0 and the line through (0,5)is horizontal. 
D) The maximum distance of 6 occurs when the slope m is 0 and the line through (0,6)is horizontal. 
E) The maximum distance of $- 5$ occurs when the slope m is $\frac { 1 } { 5 }$ and the line through (0,5)is horizontal.

Exam 59: Lines

Consider a line with slope m and y-intercept (0,7).Select the graph of the distance between the origin and the line. ​

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​ A = (-4,-5),B = (2,7),C = (5,7) ​

Consider a line with slope m and y-intercept (0,3).Find the slope that yields the maximum distance between the point (2,1)and the line. ​

A straight road rises with an inclination of 0.22 radian from the horizontal.Find the slope of the road and the change in elevation over a one-mile stretch of the road.Round your answer to four decimal places for the m round your answers to nearest whole number for change in elevation. ​

Find the inclination θ\thetaθ (in radians and degrees)of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ 7x+5y=07 x + 5 y = 07x+5y=0 ​

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane.​ A=(−16,17),B=(6,7),C=(67,0)A = \left( - \frac { 1 } { 6 } , \frac { 1 } { 7 } \right) , B = ( 6,7 ) , C = \left( \frac { 6 } { 7 } , 0 \right)A=(−61​,71​),B=(6,7),C=(76​,0) ​

Find the angle θ\thetaθ (in radians and degrees)between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ x-y=10 3x-2y=1 ​

Find the distance between the point and the line.Round your answer to four decimal places.​ Point Line (14,12)11x−y=0( 14,12 ) \quad 11 x - y = 0(14,12)11x−y=0 ​

A moving conveyor is built so that it rises 3 meter for each 5 meters of horizontal travel.The conveyor runs between two floors in a factory.The distance between the floors is 4 meters.Find the length of the conveyor.Round your answers to one decimal place. ​

Find the angle θ\thetaθ (in radians and degrees)between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. ​​ 6x+y=6 x-y=5 ​

A moving conveyor is built so that it rises 7 meter for each 9 meters of horizontal travel.Select a diagram that gives a visual representation of the problem. ​

Consider a line with slope m and y-intercept (0,3).Select the graph of the distance d between the point (2,1)and the line as a function of m. ​

Find the inclination θ\thetaθ (in radians and degrees)of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ (−2,20),(10,0)( - 2,20 ) , ( 10,0 )(−2,20),(10,0) ​

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​ A = (0,0),B = (3,6),C = (6,0) ​

Find the inclination θ\thetaθ (in radians and degrees)of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ (0,200),(20,0)( 0,200 ) , ( 20,0 )(0,200),(20,0) ​

Find the inclination θ\thetaθ (in radians and degrees)of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ 6x+7y−13=06 x + 7 y - 13 = 06x+7y−13=0 ​

Consider a line with slope m and y-intercept (0,5).Find the slope that yields the maximum distance between the origin and the line. ​

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Consider a line with slope m and y-intercept (0,7).Select the graph of the distance between the origin and the line.

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. A = (-4,-5),B = (2,7),C = (5,7)

Consider a line with slope m and y-intercept (0,3).Find the slope that yields the maximum distance between the point (2,1)and the line.

A straight road rises with an inclination of 0.22 radian from the horizontal.Find the slope of the road and the change in elevation over a one-mile stretch of the road.Round your answer to four decimal places for the m round your answers to nearest whole number for change in elevation.

Find the inclination $\theta$ (in radians and degrees)of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $7 x + 5 y = 0$

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. $A = \left( - \frac { 1 } { 6 } , \frac { 1 } { 7 } \right) , B = ( 6,7 ) , C = \left( \frac { 6 } { 7 } , 0 \right)$

Find the angle $\theta$ (in radians and degrees)between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. x-y=10 3x-2y=1

Find the distance between the point and the line.Round your answer to four decimal places. Point Line $( 14,12 ) \quad 11 x - y = 0$

A moving conveyor is built so that it rises 3 meter for each 5 meters of horizontal travel.The conveyor runs between two floors in a factory.The distance between the floors is 4 meters.Find the length of the conveyor.Round your answers to one decimal place.

A moving conveyor is built so that it rises 7 meter for each 9 meters of horizontal travel.Select a diagram that gives a visual representation of the problem.

Consider a line with slope m and y-intercept (0,3).Select the graph of the distance d between the point (2,1)and the line as a function of m.

Find the inclination $\theta$ (in radians and degrees)of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $( - 2,20 ) , ( 10,0 )$

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. A = (0,0),B = (3,6),C = (6,0)

Find the inclination $\theta$ (in radians and degrees)of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $( 0,200 ) , ( 20,0 )$

Find the inclination $\theta$ (in radians and degrees)of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $6 x + 7 y - 13 = 0$

Consider a line with slope m and y-intercept (0,5).Find the slope that yields the maximum distance between the origin and the line.