During an evening out, dean paid a cab driver $20. he then spent $25 on dinner and half of his remaining money on a painting. he bought an umbrella for $23.75 and had $42.15 left. how much money did dean have at the beginning of the evening?

The way I see it is like this:

He ended with $42.15 -- the last thing that he did before that was buy the umbrella

$42.15 + $23.75 (umbrella) = $65.90

The next thing backwards in order is that he spent "half of his remaining money on a painting", so what he has left is one half what he had before he bought the painting.

$65.90 + $65.90 (cost of the painting) = $131.80

Before that, he spent $25 on dinner and $20 on a cab. So we add those all up:

$131.80 + $25 (dinner) + $20 (cab) = $176.80 (how much money he had at the start of the weekend)

To write it as a single equation:

$42.15 = -$23.75 + (-$25.00 + -$20.00)/2

110.90

Step-by-step explanation:

because 20.00+25.00+23.75=68.75+42.15=110.90

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841