Beth does not charge a registration fee for her dog-walking service, but she charges $5 per mile that each dog is walked. Tonya's dog-walking service charges a registration fee of $20, plus $3 per mile that each dog is walked. Write and solve an equation to find the number of miles m for which Tonya and Beth would charge the same amount.

The indifference point is 10 miles.

Step-by-step explanation:

Giving the following information:

Beth:

$5 per mile

Tonya's:

registration fee of $20

$3 per mile

First, we need to structure the income formulas:

Beth= 5x

Tonya= 20 + 3x

x= miles

Now, to determine the indifference point, we equal both formulas and isolate "x":

5x = 20 + 3x

2x= 20

x=10

The indifference point is 10 miles.

Beth= 5*10= $50

Tonya= 20 + 3*10= $50

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: