Ted practices two types of swimming styles for a total of 50 minutes every day. he spends 20 minutes more practicing the breast stroke than the butterfly stroke.

part a: write a pair of linear equations to show the relationship between the number of minutes ted practices the butterfly stroke every day (x) and the number of minutes he practices the breast stroke every day (y).
part b: how much time does ted spend on practicing the breast stroke every day?
part c: is it possible for ted to have spent 45 minutes practicing the butterfly stroke every day?

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}

squares, rhombus, rectangles

6(h+1)/2=a

a=area

step-by-step explanation:

its the same thing as a square or rectangle but after multiplying two sides you need to divide it by two.