The distance between the points ( 0 , 0 ) , ( 4 , 2 ) .

Question

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Answer 1

Question

Chapter 2, Problem 1RE

a.

To determine

The distance between the points $(0,0),(4,2)$ .

a.

Expert Solution

Answer to Problem 1RE

The distance between the points $(0,0),(4,2)$ is $25_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the distance between the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $d=(x2−x1)2+(y2−y1)2$ .

$d=(4−0)2+(2−0)2=16+4=20=4⋅5=25$

Thus, the distance between the points $(0,0),(4,2)$ is $25_$ .

b.

To determine

The midpoint of the line segment connecting the points $(0,0),(4,2)$ .

b.

Expert Solution

Answer to Problem 1RE

The midpoint of the line segment connecting the points $(0,0),(4,2)$ is $(2,1)_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the midpoint of the line segment connecting the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $(x,y)=(x1+x22,y1+y22)$ .

$(x,y)=(0+42,0+22)=(42,22)=(2,1)$

Thus, the midpoint of the line segment connecting the points $(0,0),(4,2)$ is $(2,1)_$ .

c.

To determine

The slope of the line containing the points $(0,0),(4,2)$ .

c.

Expert Solution

Answer to Problem 1RE

The slope of the line containing the points $(0,0),(4,2)$ is $m=12_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the slope of the line containing the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $m=y2−y1x2−x1$ .

$m=2−04−0=24=12$

Thus, the slope of the line containing the points $(0,0),(4,2)$ is $m=12_$ .

d.

To determine

To interpret: The slope found in part (c).

d.

Expert Solution

Explanation of Solution

From part (c), the slope of the line containing the points $(0,0),(4,2)$ is $m=12$ .

For every 2 units changes in x, y will change by 1 unit.

That is, if x increases by 2 units, then y will decreases by 1 unit.

Thus, the average rate of change of y with respect to x is $12$

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In simplest terms, Sketch the graph of the parabola. Then, determine its equation. opens downward, vertex is (- 4, 7), passes through point (0, - 39)

Answer 2

Question

Chapter 2, Problem 1RE

a.

To determine

The distance between the points $(0,0),(4,2)$ .

a.

Expert Solution

Answer to Problem 1RE

The distance between the points $(0,0),(4,2)$ is $25_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the distance between the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $d=(x2−x1)2+(y2−y1)2$ .

$d=(4−0)2+(2−0)2=16+4=20=4⋅5=25$

Thus, the distance between the points $(0,0),(4,2)$ is $25_$ .

b.

To determine

The midpoint of the line segment connecting the points $(0,0),(4,2)$ .

b.

Expert Solution

Answer to Problem 1RE

The midpoint of the line segment connecting the points $(0,0),(4,2)$ is $(2,1)_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the midpoint of the line segment connecting the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $(x,y)=(x1+x22,y1+y22)$ .

$(x,y)=(0+42,0+22)=(42,22)=(2,1)$

Thus, the midpoint of the line segment connecting the points $(0,0),(4,2)$ is $(2,1)_$ .

c.

To determine

The slope of the line containing the points $(0,0),(4,2)$ .

c.

Expert Solution

Answer to Problem 1RE

The slope of the line containing the points $(0,0),(4,2)$ is $m=12_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the slope of the line containing the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $m=y2−y1x2−x1$ .

$m=2−04−0=24=12$

Thus, the slope of the line containing the points $(0,0),(4,2)$ is $m=12_$ .

d.

To determine

To interpret: The slope found in part (c).

d.

Expert Solution

Explanation of Solution

From part (c), the slope of the line containing the points $(0,0),(4,2)$ is $m=12$ .

For every 2 units changes in x, y will change by 1 unit.

That is, if x increases by 2 units, then y will decreases by 1 unit.

Thus, the average rate of change of y with respect to x is $12$

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Answer 3

Question

Chapter 2, Problem 1RE

a.

To determine

The distance between the points $(0,0),(4,2)$ .

a.

Expert Solution

Answer to Problem 1RE

The distance between the points $(0,0),(4,2)$ is $25_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the distance between the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $d=(x2−x1)2+(y2−y1)2$ .

$d=(4−0)2+(2−0)2=16+4=20=4⋅5=25$

Thus, the distance between the points $(0,0),(4,2)$ is $25_$ .

b.

To determine

The midpoint of the line segment connecting the points $(0,0),(4,2)$ .

b.

Expert Solution

Answer to Problem 1RE

The midpoint of the line segment connecting the points $(0,0),(4,2)$ is $(2,1)_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the midpoint of the line segment connecting the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $(x,y)=(x1+x22,y1+y22)$ .

$(x,y)=(0+42,0+22)=(42,22)=(2,1)$

Thus, the midpoint of the line segment connecting the points $(0,0),(4,2)$ is $(2,1)_$ .

c.

To determine

The slope of the line containing the points $(0,0),(4,2)$ .

c.

Expert Solution

Answer to Problem 1RE

The slope of the line containing the points $(0,0),(4,2)$ is $m=12_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the slope of the line containing the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $m=y2−y1x2−x1$ .

$m=2−04−0=24=12$

Thus, the slope of the line containing the points $(0,0),(4,2)$ is $m=12_$ .

d.

To determine

To interpret: The slope found in part (c).

d.

Expert Solution

Explanation of Solution

From part (c), the slope of the line containing the points $(0,0),(4,2)$ is $m=12$ .

For every 2 units changes in x, y will change by 1 unit.

That is, if x increases by 2 units, then y will decreases by 1 unit.

Thus, the average rate of change of y with respect to x is $12$

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Answer 4

Question

Chapter 2, Problem 1RE

a.

To determine

The distance between the points $(0,0),(4,2)$ .

a.

Expert Solution

Answer to Problem 1RE

The distance between the points $(0,0),(4,2)$ is $25_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the distance between the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $d=(x2−x1)2+(y2−y1)2$ .

$d=(4−0)2+(2−0)2=16+4=20=4⋅5=25$

Thus, the distance between the points $(0,0),(4,2)$ is $25_$ .

b.

To determine

The midpoint of the line segment connecting the points $(0,0),(4,2)$ .

b.

Expert Solution

Answer to Problem 1RE

The midpoint of the line segment connecting the points $(0,0),(4,2)$ is $(2,1)_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the midpoint of the line segment connecting the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $(x,y)=(x1+x22,y1+y22)$ .

$(x,y)=(0+42,0+22)=(42,22)=(2,1)$

Thus, the midpoint of the line segment connecting the points $(0,0),(4,2)$ is $(2,1)_$ .

c.

To determine

The slope of the line containing the points $(0,0),(4,2)$ .

c.

Expert Solution

Answer to Problem 1RE

The slope of the line containing the points $(0,0),(4,2)$ is $m=12_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the slope of the line containing the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $m=y2−y1x2−x1$ .

$m=2−04−0=24=12$

Thus, the slope of the line containing the points $(0,0),(4,2)$ is $m=12_$ .

d.

To determine

To interpret: The slope found in part (c).

d.

Expert Solution

Explanation of Solution

From part (c), the slope of the line containing the points $(0,0),(4,2)$ is $m=12$ .

For every 2 units changes in x, y will change by 1 unit.

That is, if x increases by 2 units, then y will decreases by 1 unit.

Thus, the average rate of change of y with respect to x is $12$

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Answer 5

Chapter 2, Problem 1RE

a.

To determine

The distance between the points $(0,0),(4,2)$ .

a.

Expert Solution

Answer to Problem 1RE

The distance between the points $(0,0),(4,2)$ is $25_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the distance between the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $d=(x2−x1)2+(y2−y1)2$ .

$d=(4−0)2+(2−0)2=16+4=20=4⋅5=25$

Thus, the distance between the points $(0,0),(4,2)$ is $25_$ .

b.

To determine

The midpoint of the line segment connecting the points $(0,0),(4,2)$ .

b.

Expert Solution

Answer to Problem 1RE

The midpoint of the line segment connecting the points $(0,0),(4,2)$ is $(2,1)_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the midpoint of the line segment connecting the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $(x,y)=(x1+x22,y1+y22)$ .

$(x,y)=(0+42,0+22)=(42,22)=(2,1)$

Thus, the midpoint of the line segment connecting the points $(0,0),(4,2)$ is $(2,1)_$ .

c.

To determine

The slope of the line containing the points $(0,0),(4,2)$ .

c.

Expert Solution

Answer to Problem 1RE

The slope of the line containing the points $(0,0),(4,2)$ is $m=12_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the slope of the line containing the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $m=y2−y1x2−x1$ .

$m=2−04−0=24=12$

Thus, the slope of the line containing the points $(0,0),(4,2)$ is $m=12_$ .

d.

To determine

To interpret: The slope found in part (c).

d.

Expert Solution

Explanation of Solution

From part (c), the slope of the line containing the points $(0,0),(4,2)$ is $m=12$ .

For every 2 units changes in x, y will change by 1 unit.

That is, if x increases by 2 units, then y will decreases by 1 unit.

Thus, the average rate of change of y with respect to x is $12$

Answer 6

Chapter 2, Problem 1RE

a.

To determine

The distance between the points $(0,0),(4,2)$ .

a.

Expert Solution

Answer to Problem 1RE

The distance between the points $(0,0),(4,2)$ is $25_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the distance between the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $d=(x2−x1)2+(y2−y1)2$ .

$d=(4−0)2+(2−0)2=16+4=20=4⋅5=25$

Thus, the distance between the points $(0,0),(4,2)$ is $25_$ .

Answer 7

Chapter 2, Problem 1RE

a.

To determine

The distance between the points $(0,0),(4,2)$ .

Answer 8

a.

Expert Solution

Answer to Problem 1RE

The distance between the points $(0,0),(4,2)$ is $25_$ .

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the distance between the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $d=(x2−x1)2+(y2−y1)2$ .

$d=(4−0)2+(2−0)2=16+4=20=4⋅5=25$

Thus, the distance between the points $(0,0),(4,2)$ is $25_$ .

Answer 13

b.

To determine

The midpoint of the line segment connecting the points $(0,0),(4,2)$ .

b.

Expert Solution

Answer to Problem 1RE

The midpoint of the line segment connecting the points $(0,0),(4,2)$ is $(2,1)_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the midpoint of the line segment connecting the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $(x,y)=(x1+x22,y1+y22)$ .

$(x,y)=(0+42,0+22)=(42,22)=(2,1)$

Thus, the midpoint of the line segment connecting the points $(0,0),(4,2)$ is $(2,1)_$ .

Answer 14

b.

To determine

The midpoint of the line segment connecting the points $(0,0),(4,2)$ .

Answer 15

b.

Expert Solution

Answer to Problem 1RE

The midpoint of the line segment connecting the points $(0,0),(4,2)$ is $(2,1)_$ .

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the midpoint of the line segment connecting the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $(x,y)=(x1+x22,y1+y22)$ .

$(x,y)=(0+42,0+22)=(42,22)=(2,1)$

Thus, the midpoint of the line segment connecting the points $(0,0),(4,2)$ is $(2,1)_$ .

Answer 20

c.

To determine

The slope of the line containing the points $(0,0),(4,2)$ .

c.

Expert Solution

Answer to Problem 1RE

The slope of the line containing the points $(0,0),(4,2)$ is $m=12_$ .

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the slope of the line containing the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $m=y2−y1x2−x1$ .

$m=2−04−0=24=12$

Thus, the slope of the line containing the points $(0,0),(4,2)$ is $m=12_$ .

Answer 21

c.

To determine

The slope of the line containing the points $(0,0),(4,2)$ .

Answer 22

c.

Expert Solution

Answer to Problem 1RE

The slope of the line containing the points $(0,0),(4,2)$ is $m=12_$ .

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

The given points are $(0,0),(4,2)$ .

Obtain the slope of the line containing the points $(0,0),(4,2)$ as follows.

Substitute $(x1,y1)=(0,0) and (x2,y2)=(4,2)$ in $m=y2−y1x2−x1$ .

$m=2−04−0=24=12$

Thus, the slope of the line containing the points $(0,0),(4,2)$ is $m=12_$ .

Answer 27

d.

To determine

To interpret: The slope found in part (c).

d.

Expert Solution

Explanation of Solution

From part (c), the slope of the line containing the points $(0,0),(4,2)$ is $m=12$ .

For every 2 units changes in x, y will change by 1 unit.

That is, if x increases by 2 units, then y will decreases by 1 unit.

Thus, the average rate of change of y with respect to x is $12$

Answer 28

d.

To determine

To interpret: The slope found in part (c).

Answer 29

d.

Expert Solution

Explanation of Solution

From part (c), the slope of the line containing the points $(0,0),(4,2)$ is $m=12$ .

For every 2 units changes in x, y will change by 1 unit.

That is, if x increases by 2 units, then y will decreases by 1 unit.

Thus, the average rate of change of y with respect to x is $12$

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

Ch. 2.1 - On the real number line, the origin is assigned...Ch. 2.1 - If –3 and 5 are the coordinates of two points on...Ch. 2.1 - If 3 and 4 are the legs of a right triangle, the...Ch. 2.1 - Use the converse of the Pythagorean Theorem to...Ch. 2.1 - The area A of a triangle whose base is b and whose...Ch. 2.1 - True or False Two triangles are congruent if two...Ch. 2.1 - If (x, y) are the coordinates of a point P in the...Ch. 2.1 - The coordinate axes partition the xy-plane into...Ch. 2.1 - If three distinct points P, Q, and R all lie on a...Ch. 2.1 - True or False The distance between two points is...

The distance between the points ( 0 , 0 ) , ( 4 , 2 ) .

Answer to Problem 1RE

Explanation of Solution

Answer to Problem 1RE

Explanation of Solution

Answer to Problem 1RE

Explanation of Solution

To interpret: The slope found in part (c).

Explanation of Solution

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Chapter 2 Solutions