Question 1

After opening the parachute, the descent of a parachutist follows a linear model.At 7:28 P.M., the height of the parachutist is 6150 feet.At 7:31 P.M., the height is 3450 feet.Use a linear equation that gives the height of the parachutist in terms of the time to find the time when the parachutist will reach the ground.

Accepted Answer

We can use the two given data points to find the slope of the linear equation:

slope = (3450 - 6150) / (3 minutes * 60 seconds/minute) = -900 feet/minute

Next, we can use the point-slope form of the linear equation:

y - y1 = m(x - x1)

where (x1, y1) is one of the data points and m is the slope. Let's use the first data point (7:28 P.M., 6150 feet):

y - 6150 = -900/60 (x - 7*60 - 28)   // convert minutes to seconds

Simplifying the equation, we get:

y = -15x + 7260

To find the time when the parachutist will reach the ground, we need to find the value of x when y = 0 (since height is 0 when the parachutist reaches the ground):

0 = -15x + 7260

x = 484 seconds = 8 minutes and 4 seconds

Therefore, the parachutist will reach the ground at 7:31 P.M. + 8 minutes and 4 seconds = 7:34:50 P.M.

Hence, the answer is B.

Question 2

The table below shows the velocities, in feet per second, of a ball that is thrown horizontally from the top of a 50 foot building and the distances, in feet, that it lands from the base of the building.Compute the linear regression equation for these data.

Accepted Answer

The answer of The table below shows the velocities, in...

Question 3

Find the slope of the line that passes through the points

Accepted Answer

The answer of Find the slope of the line that...

Question 4

Use the point on the line and the slope of the line to determine whether any of the three additional points lies on the line. Point
Slope   I:  II:  III:

Accepted Answer

Using the point-slope form of a line, we can write the equation of the line passing through the given point as:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is the given point on the line.
Substituting the given values, we get:
y - 3 = 2(x - 4)
Simplifying further, we get:
y - 3 = 2x - 8
y = 2x - 5
Now, substituting the x and y-coordinates of the three additional points into this equation, we can check whether they lie on the line or not.

For point I (3, -1), we have:
y = 2x - 5
-1 = 2(3) - 5
-1 = 1
This is false. Therefore, point I does NOT lie on the line.

For point II (2, -2), we have:
y = 2x - 5
-2 = 2(2) - 5
-2 = -1
This is false. Therefore, point II does NOT lie on the line.

For point III (5, 5), we have:
y = 2x - 5
5 = 2(5) - 5
5 = 5
This is true. Therefore, point III lies on the line.

Hence, the answer is A) Only point I lies on the line.

Question 5

Determine if lines  and  are parallel, perpendicular, or neither.

Accepted Answer

The answer of Determine if lines  and  are...

Question 6

Determine whether lines L₁ and L₂ passing through the pairs of points are parallel, perpendicular, or neither. L₁: (-1, 8), (9, -4) L₂: (0, 9), (1, -1)

Accepted Answer

To determine whether the two lines are parallel, perpendicular or neither, we need to find the slopes of the lines. For L₁: Slope = (y2 - y1)/(x2 - x1) = (-4 - 8)/(9 - (-1)) = -12/10 = -6/5 For L₂: Slope = (y2 - y1)/(x2 - x1) = (-1 - 9)/(1 - 0) = -10 Now, we see that the slopes are not the same (not parallel) and not negative reciprocals (not perpendicular). Hence, the lines are neither parallel nor perpendicular.

Question 7

Determine whether lines L₁ and L₂ passing through the pairs of points are parallel, perpendicular, or neither. L₁: (1, 2), (1, 4) L₂: (-7, -8), (-9, -8)

Accepted Answer

The answer of Determine whether lines L₁ and L₂ passing...

Question 8

Determine whether lines L₁ and L₂ passing through the pairs of points are parallel, perpendicular, or neither. L₁: (-5, -5), (4, 6) L₂: (-9, 8), (-18, -3)

Accepted Answer

The answer of Determine whether lines L₁ and L₂ passing...

Question 9

Find the slope and y-intercept of the equation of the line.

Accepted Answer

The equation of the line can be written in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept. The given equation can be rewritten as y = -6x + 4, so the slope is -6 and the y-intercept is 4. Choice C matches these values.

Question 10

Plot the points and find the slope of the line passing through the pair of points. (3, -2), (-4, -2)

Accepted Answer

The points (3, -2) and (-4, -2) lie on a horizontal line. The slope of a horizontal line is always 0. Therefore, the answer is (A) slope: 0.

Question 11

Which of the following graphs below can be approximated by a linear model? I  II  III

Accepted Answer

The answer of Which of the following graphs below can...

Question 12

Write the equation that expresses the relationship between the variables described below, then use the given data to solve for the variation of constant. "t varies directly as  , and  when  "

Accepted Answer

The answer of Write the equation that expresses the relationship...

Question 13

Suppose the average remaining lifetime for women in a given country is given in the following table.  Compute the linear regression equation for these data, where x is the age, in years, and A is the remaining lifetime, in years.Round parameters to the nearest hundredth.

Accepted Answer

The answer of Suppose the average remaining lifetime for women...

Question 14

The simple interest on an investment is directly proportional to the amount of the investment.By investing $5750 in a certain certificate of deposit, you obtained an interest payment of $172.50 after 1 year.Determine a mathematical model that gives the interest, I, for this CD after 1 year in terms of the amount invested, P.

Accepted Answer

The answer of The simple interest on an investment is...

Question 15

Find the slope and y-intercept of the equation of the line. -y - 8x = -2

Accepted Answer

First, solve for y in terms of x to get the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Starting with -y - 8x = -2, add y to both sides and add 2 to both sides to get y = 8x + 2. Thus, the slope (m) is 8, and the y-intercept (b) is 2.

Question 16

A motorcycle was purchased for $39,000.Assuming the motorcycle depreciates at a rate of $4680 per year (straight-line depreciation) for the first 7 years, write the value v of the motorcycle as a function of the time t (measured in years) for

Accepted Answer

The answer of A motorcycle was purchased for $39,000.Assuming the...

Question 17

Assume that y is directly proportional to x.If  and  , determine a linear model that relates y and x.

Accepted Answer

The answer of Assume that y is directly proportional to...

Question 18

The sales tax on an item with a retail price of $908 is $99.88.Create a mathematical model that gives the retail price, y, in terms of the sales tax, x, and use it to determine the retail price of an item that has a sales tax of $113.50.

Accepted Answer

The answer of The sales tax on an item with...

Question 19

Graph y as a function of x by finding the slope and y-intercept of the line below.

Accepted Answer

The answer of Graph y as a function of x...

Question 20

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is  x-intercept: (3, 0) y-intercept: (0, 5)

Accepted Answer

The answer of Use the intercept form to find the...

Quiz 2: Functions and Graphs

The table below shows the velocities, in feet per second, of a ball that is thrown horizontally from the top of a 50 foot building and the distances, in feet, that it lands from the base of the building.Compute the linear regression equation for these data.

Find the slope of the line that passes through the points

Use the point on the line and the slope of the line to determine whether any of the three additional points lies on the line. Point Slope I: II: III:

Determine if lines and are parallel, perpendicular, or neither.

Determine whether lines L₁ and L₂ passing through the pairs of points are parallel, perpendicular, or neither. L₁: (-1, 8) , (9, -4) L₂: (0, 9) , (1, -1)

Determine whether lines L₁ and L₂ passing through the pairs of points are parallel, perpendicular, or neither. L₁: (1, 2) , (1, 4) L₂: (-7, -8) , (-9, -8)

Determine whether lines L₁ and L₂ passing through the pairs of points are parallel, perpendicular, or neither. L₁: (-5, -5) , (4, 6) L₂: (-9, 8) , (-18, -3)

Find the slope and y-intercept of the equation of the line.

Plot the points and find the slope of the line passing through the pair of points. (3, -2) , (-4, -2)

Which of the following graphs below can be approximated by a linear model? I II III

Write the equation that expresses the relationship between the variables described below, then use the given data to solve for the variation of constant. "t varies directly as , and when "

Suppose the average remaining lifetime for women in a given country is given in the following table. Compute the linear regression equation for these data, where x is the age, in years, and A is the remaining lifetime, in years.Round parameters to the nearest hundredth.

Find the slope and y-intercept of the equation of the line. -y - 8x = -2

A motorcycle was purchased for $39,000.Assuming the motorcycle depreciates at a rate of $4680 per year (straight-line depreciation) for the first 7 years, write the value v of the motorcycle as a function of the time t (measured in years) for

Assume that y is directly proportional to x.If and , determine a linear model that relates y and x.

The sales tax on an item with a retail price of $908 is $99.88.Create a mathematical model that gives the retail price, y, in terms of the sales tax, x, and use it to determine the retail price of an item that has a sales tax of $113.50.

Graph y as a function of x by finding the slope and y-intercept of the line below.

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is x-intercept: (3, 0) y-intercept: (0, 5)

Quiz 2: Functions and Graphs

The table below shows the velocities, in feet per second, of a ball that is thrown horizontally from the top of a 50 foot building and the distances, in feet, that it lands from the base of the building.Compute the linear regression equation for these data.

Find the slope of the line that passes through the points

Use the point on the line and the slope of the line to determine whether any of the three additional points lies on the line. Point Slope I: II: III:

Determine if lines and are parallel, perpendicular, or neither.

Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (-1, 8) , (9, -4) L2 : (0, 9) , (1, -1)

Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (1, 2) , (1, 4) L2 : (-7, -8) , (-9, -8)

Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (-5, -5) , (4, 6) L2 : (-9, 8) , (-18, -3)

Find the slope and y-intercept of the equation of the line.

Plot the points and find the slope of the line passing through the pair of points. (3, -2) , (-4, -2)

Which of the following graphs below can be approximated by a linear model? I II III

Write the equation that expresses the relationship between the variables described below, then use the given data to solve for the variation of constant. "t varies directly as , and when "

Suppose the average remaining lifetime for women in a given country is given in the following table. Compute the linear regression equation for these data, where x is the age, in years, and A is the remaining lifetime, in years.Round parameters to the nearest hundredth.

Find the slope and y-intercept of the equation of the line. -y - 8x = -2

A motorcycle was purchased for $39,000.Assuming the motorcycle depreciates at a rate of $4680 per year (straight-line depreciation) for the first 7 years, write the value v of the motorcycle as a function of the time t (measured in years) for

Assume that y is directly proportional to x.If and , determine a linear model that relates y and x.

The sales tax on an item with a retail price of $908 is $99.88.Create a mathematical model that gives the retail price, y, in terms of the sales tax, x, and use it to determine the retail price of an item that has a sales tax of $113.50.

Graph y as a function of x by finding the slope and y-intercept of the line below.

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is x-intercept: (3, 0) y-intercept: (0, 5)

Determine whether lines L₁ and L₂ passing through the pairs of points are parallel, perpendicular, or neither. L₁: (-1, 8) , (9, -4) L₂: (0, 9) , (1, -1)

Determine whether lines L₁ and L₂ passing through the pairs of points are parallel, perpendicular, or neither. L₁: (1, 2) , (1, 4) L₂: (-7, -8) , (-9, -8)

Determine whether lines L₁ and L₂ passing through the pairs of points are parallel, perpendicular, or neither. L₁: (-5, -5) , (4, 6) L₂: (-9, 8) , (-18, -3)