Question 1

Determine whether the lines through the given pairs of points are perpendicular. A (- 3, 7), B (4, 0) and C (- 2, - 2), D (3, - 4)

Accepted Answer

A)  The lines through the given pairs of points are not perpendicular. 
B)  The lines through the given pairs of points are perpendicular. 
A)  The lines through the given pairs of points are not perpendicular. 
B)  The lines through the given pairs of points are perpendicular.

Question 2

Refer to the accompanying figure and determine the coordinates of the given point and the quadrant in which it is located.

Accepted Answer

A)  (- 5, - 3); Quadrant IV 
B)  (5, 3); Quadrant III 
C)  (5, 3); Quadrant I 
D)  (- 5, 3); Quadrant II 
A)  (- 5, - 3); Quadrant IV 
B)  (5, 3); Quadrant III 
C)  (5, 3); Quadrant I 
D)  (- 5, 3); Quadrant II

Question 3

The quantity demanded of a certain brand of DVD player is 2,200/wk when the unit price is $475. For each decrease in unit price of $28.00 below $475, the quantity demanded increases by 350 units. The suppliers will not market any DVD players if the unit price is $350 or lower. But at a unit price of $500, they are willing to make available 2,500 units in the market. The supply equation is also known to be linear.
Find the demand equation.   __________
Find the supply equation.   __________
Find the equilibrium quantity.   __________ DVD players
Find the equilibrium price.   $ __________

Accepted Answer

The answer of The quantity demanded of a certain brand...

Question 4

For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price. 2x + 9p - 93 = 0 and 3x - 14p + 108 = 0

Accepted Answer

A)  equilibrium quantity 6,000 units; equilibrium price $13 
B)  equilibrium quantity 12,000 units; equilibrium price $9 
C)  equilibrium quantity 6,000 units; equilibrium price $9 
D)  equilibrium quantity 12,000 units; equilibrium price $13 
A)  equilibrium quantity 6,000 units; equilibrium price $13 
B)  equilibrium quantity 12,000 units; equilibrium price $9 
C)  equilibrium quantity 6,000 units; equilibrium price $9 
D)  equilibrium quantity 12,000 units; equilibrium price $13

Question 5

Find the point of intersection of the pair of straight lines. 2x   8y   11   7x   3y   -23

Accepted Answer

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

Question 6

Find an equation of the line that passes through the point (1, 6) and has the slope   .

Accepted Answer

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

Question 7

Find the distance between the given points. (- 3, 1) and (9, 6)

Accepted Answer

A)  17 
B)  13 
C)  7 
D)  10 
A)  17 
B)  13 
C)  7 
D)  10

Question 8

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. Suppose C(x) = cx + F and R(x) = sx are the cost and revenue functions of a certain firm. Then, the firm is making a profit if its level of production is less than   .

Accepted Answer

A) a 
B) b 
A) a 
B) b

Question 9

Find an equation of the line that has slope   and y-intercept   .
Please enter your equation in slope-intercept form.

Accepted Answer

The answer of Find an equation of the line that...

Question 10

Write the equation   in the slope-intercept form and then find the slope and y-intercept of the corresponding line.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 11

Find the coordinates of the points that are   units away from the origin and have an x-coordinate equal to   . ​

Accepted Answer

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

Question 12

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The point (1, k) lies on the line with equation 9x + 4y = 36 if and only if   .

Accepted Answer

A)  True. If we substitute 1 instead of x and k instead of y and solve the equation for k, we will find that k is equal to   . 
B)  False. If we substitute 1 instead of x and k instead of y and solve the equation for k, we won't find that k is equal to   . 
A)  True. If we substitute 1 instead of x and k instead of y and solve the equation for k, we will find that k is equal to   . 
B)  False. If we substitute 1 instead of x and k instead of y and solve the equation for k, we won't find that k is equal to   .

Question 13

According to industry sources, online banking is expected to take off in the near future. The projected number of households (in millions) using this service is given in the following table:   (Here, x = 0 corresponds to the beginning of 1997.) Find an equation of the least-squares line for these data. Please round the coefficients in your equation to three decimal places. Use the result to estimate the number of households using online banking at the beginning of 2007, assuming the projection is accurate.

Accepted Answer

A)  y = 2.695x + 4.653; 31.603 million 
B)  y = 2.709x + 4.662; 31.729 million 
C)  y = 2.695x + 4.653; 31.566 million 
D)  y = 2.709x + 4.662; 31.752 million 
A)  y = 2.695x + 4.653; 31.603 million 
B)  y = 2.709x + 4.662; 31.729 million 
C)  y = 2.695x + 4.653; 31.566 million 
D)  y = 2.709x + 4.662; 31.752 million

Question 14

For the demand equation, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, determine the quantity demanded corresponding to the unit price p = 4. 4x + 5p - 40 = 0

Accepted Answer

A)  5,000 
B)  3,500 
C)  4,000 
D)  4,500 
A)  5,000 
B)  3,500 
C)  4,000 
D)  4,500

Question 15

Which point has a negative x-coordinate and a negative y-coordinate?

Accepted Answer

The answer of Which point has a negative x-coordinate and...

Question 16

Sketch a set of coordinate axes and plot the given point.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

Match each graph below with the letter of the corresponding slope description.
a.The slope of the line is undefined.
b.The slope of the line is positive, and its y-intercept is positive.
c.The slope of the line is negative, and its x-intercept is positive.
-

Accepted Answer

The answer of Match each graph below with the letter...

Question 18

Find the equation of the least-squares line for the data.

Accepted Answer

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

Question 19

Match each graph below with the letter of the corresponding slope description.
a.The slope of the line is undefined.
b.The slope of the line is positive, and its y-intercept is negative.
c.The slope of the line is negative, and its x-intercept is negative.
-

Accepted Answer

The answer of Match each graph below with the letter...

Question 20

Let   and   be two nonvertical straight lines in the plane with equations   and   respectively. Find conditions on   ,   ,   , and   so that   and   do not intersect.

Accepted Answer

The answer of Let   and   be...

Determine whether the lines through the given pairs of points are perpendicular. A (- 3, 7), B (4, 0) and C (- 2, - 2), D (3, - 4)

Refer to the accompanying figure and determine the coordinates of the given point and the quadrant in which it is located.

For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price. 2x + 9p - 93 = 0 and 3x - 14p + 108 = 0

Find the point of intersection of the pair of straight lines. 2x 8y 11 7x 3y -23

Find an equation of the line that passes through the point (1, 6) and has the slope .

Find the distance between the given points. (- 3, 1) and (9, 6)

Find an equation of the line that has slope and y-intercept . Please enter your equation in slope-intercept form.

Write the equation in the slope-intercept form and then find the slope and y-intercept of the corresponding line.

Find the coordinates of the points that are units away from the origin and have an x-coordinate equal to .

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The point (1, k) lies on the line with equation 9x + 4y = 36 if and only if .

For the demand equation, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, determine the quantity demanded corresponding to the unit price p = 4. 4x + 5p - 40 = 0

Which point has a negative x-coordinate and a negative y-coordinate?

Sketch a set of coordinate axes and plot the given point.

Match each graph below with the letter of the corresponding slope description. a.The slope of the line is undefined. b.The slope of the line is positive, and its y-intercept is positive. c.The slope of the line is negative, and its x-intercept is positive. -

Find the equation of the least-squares line for the data.

Match each graph below with the letter of the corresponding slope description. a.The slope of the line is undefined. b.The slope of the line is positive, and its y-intercept is negative. c.The slope of the line is negative, and its x-intercept is negative. -

Let and be two nonvertical straight lines in the plane with equations and respectively. Find conditions on , , , and so that and do not intersect.

Systems of Linear Equations and Matrices

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Sets and Counting

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

Exam 1: Straight Lines and Linear Functions

Determine whether the lines through the given pairs of points are perpendicular. A (- 3, 7), B (4, 0) and C (- 2, - 2), D (3, - 4)

Refer to the accompanying figure and determine the coordinates of the given point and the quadrant in which it is located.

For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price. 2x + 9p - 93 = 0 and 3x - 14p + 108 = 0

Find the point of intersection of the pair of straight lines. 2x 8y 11 7x 3y -23

Find an equation of the line that passes through the point (1, 6) and has the slope .

Find the distance between the given points. (- 3, 1) and (9, 6)

Find an equation of the line that has slope and y-intercept . Please enter your equation in slope-intercept form.

Write the equation in the slope-intercept form and then find the slope and y-intercept of the corresponding line.

Find the coordinates of the points that are units away from the origin and have an x-coordinate equal to . ​

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The point (1, k) lies on the line with equation 9x + 4y = 36 if and only if .

For the demand equation, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, determine the quantity demanded corresponding to the unit price p = 4. 4x + 5p - 40 = 0

Which point has a negative x-coordinate and a negative y-coordinate?

Sketch a set of coordinate axes and plot the given point.

Match each graph below with the letter of the corresponding slope description. a.The slope of the line is undefined. b.The slope of the line is positive, and its y-intercept is positive. c.The slope of the line is negative, and its x-intercept is positive. -

Find the equation of the least-squares line for the data.

Match each graph below with the letter of the corresponding slope description. a.The slope of the line is undefined. b.The slope of the line is positive, and its y-intercept is negative. c.The slope of the line is negative, and its x-intercept is negative. -

Let and be two nonvertical straight lines in the plane with equations and respectively. Find conditions on , , , and so that and do not intersect.

Systems of Linear Equations and Matrices

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Sets and Counting

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

Find the coordinates of the points that are units away from the origin and have an x-coordinate equal to .