Two angles are supplementary to each other. If one angle is 25 degrees more than half the other, what is the measure of each angle to the nearest tenth of a degree?

Step-by-step explanation:

Supplementary angles add up to 180. so if you let the second angle = x, you can define the first one as 0.5x+25.

Then you can write an equation:

x + 0.5x + 25 = 180

combine x's and subtract 25 from both sides:

1.5x = 155

divide by 1.5 to solve for x

x = 103.3

that is angle #2

for angle #1, you divide by 2 and add 25

103.3 / 2 = 51.65 + 25 = 76.65, round to the nearest tenth, 76.7

check by adding and you get

103.3 + 76.7 = 180

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}