Question 1

)Given points(5,-11),and (11,-5)form the vertices of the base of a triangle,find a third point so that the three points form the vertices of an isosceles triangle. ​

Accepted Answer

The midpoint of the base formed by the points (5, -11) and (11, -5) is (8, -8), which would be the apex of an isosceles triangle with equal sides.

Question 2

Find the midpoint of the line segment joining the points (3,6)and (9,-4). ​

Accepted Answer

The midpoint of a line segment is found by averaging the x-coordinates and the y-coordinates of the endpoints. For the points (3,6) and (9,-4), the midpoint is ((3+9)/2, (6-4)/2) = (6,1).

Question 3

Use the graph,which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007.​  ​ Approximate the percent change in the price of milk from the price in 2000 to the highest price shown in the graph.
​

Accepted Answer

The answer of Use the graph,which shows the average retail...

Question 4

The Coca-Cola Company had sales of $19,999 million in 1999 and $29,511 million in 2007.Use the Midpoint Formula to estimate the sales in 2003.Assume that the sales followed a linear pattern. ​

Accepted Answer

The answer of The Coca-Cola Company had sales of $19,999...

Question 5

Find the coordinates of the point that is located 8 units below the x-axis and 3 units to the left of the y-axis. ​
​

Accepted Answer

The point that is 8 units below the x-axis will have a negative y-coordinate and the point that is 3 units to the left of the y-axis will have a negative x-coordinate. Therefore, the coordinates of the point will be (-3, -8). The correct choice is E.

Question 6

A soccer player passes the ball from a point that is 13 yards from the end line and 16 yards from the sideline.The pass is received by a teammate who is 48 yards from the same end line and 39 yards from the same sideline,as shown in the figure.How long is the pass??  (a,b): (13,16) (c,d): (48,39)
?

Accepted Answer

The answer of A soccer player passes the ball from...

Question 7

Find the coordinates of the vertices of the polygon in its new position. ​
Original coordinates of vertices: (6,5), (3,2), (4,2), (5,2)​
Shift: six units downward,two units to the left
​

Accepted Answer

Shifting a point six units downward subtracts 6 from its y-coordinate, and shifting it two units to the left subtracts 2 from its x-coordinate. Applying this to each point: (6-2, 5-6) = (4, -1), (3-2, 2-6) = (1, -4), (4-2, 2-6) = (2, -4), (5-2, 2-6) = (3, -4).

Question 8

The graph shows the numbers of performers who were elected to the Rock and Roll Hall of Fame from 1991 through 2008.Describe any trends in the data.From these trends,predict the number of performers elected in 2009.

Accepted Answer

The answer of The graph shows the numbers of performers...

Question 9

Determine the quadrant(s)in which (x,y)is located so that the condition is satisfied. x = 2 and y < -8

Accepted Answer

Given x = 2, this means the point is to the right of the y-axis. Given y < -8, this means the point is below the x-axis. The only quadrant that satisfies both conditions is Quadrant IV.

Question 10

Find the coordinates of the vertices of the polygon in its new position. ​
Original coordinates of vertices: (-5,-3), (-3,6), (-5,-4), (-4,-7)
Shift: three units to the right,four units upward
​

Accepted Answer

To shift the polygon three units to the right, we will add 3 to the x-coordinate of each vertex. To shift it four units upwards, we will add 4 to the y-coordinate of each vertex. Therefore:
(-5,-3) becomes (-2,1)
(-3,6) becomes (0,10)
(-5,-4) becomes (-2,0)
(-4,-7) becomes (-1,-3)

Thus, the coordinates of the vertices in the new position are: (-2,1), (0,10), (-2,0), and (-1,-3), which is exactly the same as the coordinates in choice A.

Question 11

Use the graph,which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007.​  ​ Approximate the lowest price of a gallon of whole milk shown in the graph.When did this occur?
​

Accepted Answer

The lowest price of a gallon of whole milk shown in the graph is approximately $2.67 / gal, which occurred in 1997.

Question 12

Find the midpoint of the line segment joining the points (5.5,4.3)and (13.6,-1.2). ​

Accepted Answer

Using the midpoint formula gives:
Midpoint = ((5.5+13.6)/2 , (4.3-1.2)/2) = (9.55, 1.55)
Therefore, the answer is D.

Question 13

A quarterback is standing in the middle of the field 41 yards from his goal line.He passes the ball to a player 8 yards to his left on the 26 yard line.How long was the pass? ​

Accepted Answer

The answer of A quarterback is standing in the middle...

Question 14

Find the distance between the points (4,-3)and (11,-3). ?

Accepted Answer

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane is given by the formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. For the points (4,-3) and (11,-3), the distance is $\sqrt{(11 - 4)^2 + (-3 + 3)^2} = \sqrt{7^2 + 0^2} = 7$.

Question 15

Plot the point (-3,1)on the Cartesian plane. ​

Accepted Answer

The answer of Plot the point (-3,1)on the Cartesian plane....

Question 16

Use the Midpoint Formula to estimate the sales of Dollar Tree Stores,Inc.in 2005,given the sales in 2003 and 2007.Assume that the sales followed a linear pattern. Dollar tree
Year
Sales (in millions)
2003
2200
2007
4283

Accepted Answer

The midpoint formula is $\frac{x_1 + x_2}{2}$ for the average of two numbers. Here, $x_1 = 2200$ million and $x_2 = 4283$ million for the years 2003 and 2007, respectively. Thus, the estimated sales for 2005 is $\frac{2200 + 4283}{2} = \frac{6483}{2} = 3241.5$ million.

Question 17

Find the distance between the points (4,-5)and (9,0).Round the answer to the nearest tenth. ​

Accepted Answer

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Plugging in the given points (4, -5) and (9, 0), we get $\sqrt{(9 - 4)^2 + (0 + 5)^2} = \sqrt{25 + 25} = \sqrt{50}$, which is approximately 7.1 when rounded to the nearest tenth.

Question 18

Find the coordinates of the point C shown below.​  ​ ​

Accepted Answer

The answer of Find the coordinates of the point C...

Question 19

Use the Midpoint Formula to estimate the sales of Big Lots,Inc.in 2005,given the sales in 2003 and 2007.Assume that the sales followed a linear pattern. Big Lots
Year
Sales (in millions)
2003
4174
2007
4700

Accepted Answer

We can use the midpoint formula to estimate the sales of Big Lots in 2005:

Midpoint = (Sales in 2003 + Sales in 2007) / 2
Midpoint = (4174 + 4700) / 2
Midpoint = 4437

Therefore, the estimated sales of Big Lots in 2005 is $4437 million. The correct answer is D).

Question 20

​Find the distance between the points.Round to the nearest hundredth,if necessary. ​
(-8,-8), (-1,9)
​

Accepted Answer

To find the distance between two points we use the distance formula: 
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values given in the problem:
d = sqrt((-1 - (-8))^2 + (9 - (-8))^2)
d = sqrt(49 + 289)
d = sqrt(338)
d ≈ 18.38
Rounding to the nearest hundredth gives us choice C.

Quiz 1: Rectangular Coordinates

) Given points(5,-11) ,and (11,-5) form the vertices of the base of a triangle,find a third point so that the three points form the vertices of an isosceles triangle.

Find the midpoint of the line segment joining the points (3,6) and (9,-4) .

Use the graph,which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007. Approximate the percent change in the price of milk from the price in 2000 to the highest price shown in the graph.

The Coca-Cola Company had sales of $19,999 million in 1999 and $29,511 million in 2007.Use the Midpoint Formula to estimate the sales in 2003.Assume that the sales followed a linear pattern.

Find the coordinates of the point that is located 8 units below the x-axis and 3 units to the left of the y-axis.

Find the coordinates of the vertices of the polygon in its new position. Original coordinates of vertices: (6,5) , (3,2) , (4,2) , (5,2) Shift: six units downward,two units to the left

The graph shows the numbers of performers who were elected to the Rock and Roll Hall of Fame from 1991 through 2008.Describe any trends in the data.From these trends,predict the number of performers elected in 2009.

Determine the quadrant(s) in which (x,y) is located so that the condition is satisfied. x = 2 and y < -8

Find the coordinates of the vertices of the polygon in its new position. Original coordinates of vertices: (-5,-3) , (-3,6) , (-5,-4) , (-4,-7) Shift: three units to the right,four units upward

Use the graph,which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007. Approximate the lowest price of a gallon of whole milk shown in the graph.When did this occur?

Find the midpoint of the line segment joining the points (5.5,4.3) and (13.6,-1.2) .

A quarterback is standing in the middle of the field 41 yards from his goal line.He passes the ball to a player 8 yards to his left on the 26 yard line.How long was the pass?

Find the distance between the points (4,-3) and (11,-3) . ?

Plot the point (-3,1) on the Cartesian plane.

Use the Midpoint Formula to estimate the sales of Dollar Tree Stores,Inc.in 2005,given the sales in 2003 and 2007.Assume that the sales followed a linear pattern. Dollar tree Year Sales (in millions) 2003 2200 2007 4283

Find the distance between the points (4,-5) and (9,0) .Round the answer to the nearest tenth.

Find the coordinates of the point C shown below.

Use the Midpoint Formula to estimate the sales of Big Lots,Inc.in 2005,given the sales in 2003 and 2007.Assume that the sales followed a linear pattern. Big Lots Year Sales (in millions) 2003 4174 2007 4700

Find the distance between the points.Round to the nearest hundredth,if necessary. (-8,-8) , (-1,9)

Quiz 1: Rectangular Coordinates

) Given points(5,-11) ,and (11,-5) form the vertices of the base of a triangle,find a third point so that the three points form the vertices of an isosceles triangle. ​

Find the midpoint of the line segment joining the points (3,6) and (9,-4) . ​

Use the graph,which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007.​ ​ Approximate the percent change in the price of milk from the price in 2000 to the highest price shown in the graph. ​

The Coca-Cola Company had sales of $19,999 million in 1999 and $29,511 million in 2007.Use the Midpoint Formula to estimate the sales in 2003.Assume that the sales followed a linear pattern. ​

Find the coordinates of the point that is located 8 units below the x-axis and 3 units to the left of the y-axis. ​ ​

Find the coordinates of the vertices of the polygon in its new position. ​ Original coordinates of vertices: (6,5) , (3,2) , (4,2) , (5,2) ​ Shift: six units downward,two units to the left ​

The graph shows the numbers of performers who were elected to the Rock and Roll Hall of Fame from 1991 through 2008.Describe any trends in the data.From these trends,predict the number of performers elected in 2009.

Determine the quadrant(s) in which (x,y) is located so that the condition is satisfied. x = 2 and y < -8

Find the coordinates of the vertices of the polygon in its new position. ​ Original coordinates of vertices: (-5,-3) , (-3,6) , (-5,-4) , (-4,-7) Shift: three units to the right,four units upward ​

Use the graph,which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007.​ ​ Approximate the lowest price of a gallon of whole milk shown in the graph.When did this occur? ​

Find the midpoint of the line segment joining the points (5.5,4.3) and (13.6,-1.2) . ​

A quarterback is standing in the middle of the field 41 yards from his goal line.He passes the ball to a player 8 yards to his left on the 26 yard line.How long was the pass? ​

Find the distance between the points (4,-3) and (11,-3) . ?

Plot the point (-3,1) on the Cartesian plane. ​

Use the Midpoint Formula to estimate the sales of Dollar Tree Stores,Inc.in 2005,given the sales in 2003 and 2007.Assume that the sales followed a linear pattern. Dollar tree Year Sales (in millions) 2003 2200 2007 4283

Find the distance between the points (4,-5) and (9,0) .Round the answer to the nearest tenth. ​

Find the coordinates of the point C shown below.​ ​ ​

Use the Midpoint Formula to estimate the sales of Big Lots,Inc.in 2005,given the sales in 2003 and 2007.Assume that the sales followed a linear pattern. Big Lots Year Sales (in millions) 2003 4174 2007 4700

​Find the distance between the points.Round to the nearest hundredth,if necessary. ​ (-8,-8) , (-1,9) ​

) Given points(5,-11) ,and (11,-5) form the vertices of the base of a triangle,find a third point so that the three points form the vertices of an isosceles triangle.

Find the midpoint of the line segment joining the points (3,6) and (9,-4) .

Use the graph,which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007. Approximate the percent change in the price of milk from the price in 2000 to the highest price shown in the graph.

The Coca-Cola Company had sales of $19,999 million in 1999 and $29,511 million in 2007.Use the Midpoint Formula to estimate the sales in 2003.Assume that the sales followed a linear pattern.

Find the coordinates of the point that is located 8 units below the x-axis and 3 units to the left of the y-axis.

Find the coordinates of the vertices of the polygon in its new position. Original coordinates of vertices: (6,5) , (3,2) , (4,2) , (5,2) Shift: six units downward,two units to the left

Find the coordinates of the vertices of the polygon in its new position. Original coordinates of vertices: (-5,-3) , (-3,6) , (-5,-4) , (-4,-7) Shift: three units to the right,four units upward

Use the graph,which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007. Approximate the lowest price of a gallon of whole milk shown in the graph.When did this occur?

Find the midpoint of the line segment joining the points (5.5,4.3) and (13.6,-1.2) .

A quarterback is standing in the middle of the field 41 yards from his goal line.He passes the ball to a player 8 yards to his left on the 26 yard line.How long was the pass?

Plot the point (-3,1) on the Cartesian plane.

Find the distance between the points (4,-5) and (9,0) .Round the answer to the nearest tenth.

Find the coordinates of the point C shown below.

Find the distance between the points.Round to the nearest hundredth,if necessary. (-8,-8) , (-1,9)