Answer:
x = 70°
Step-by-step explanation:
The relevant relations are ...
- base angles of an isosceles triangle are congruent
- consecutive interior angles where parallel lines meet a transversal are supplementary
__
Triangle OBQ is isosceles, so angle OQB = 40°. Triangle OPQ is isosceles, so angle OQP is x. The sum of angles OQB and OQP is angle BQP, which is supplementary to angle OPQ. That is, ...
(40° +x) +x = 180°
2x = 140° . . . . . . subtract 40°
x = 70° . . . . . . divide by 2
_____
There are many ways to find x. The one shown here is just one of them. In general, right triangles, isosceles triangles, symmetry, inscribed angles can all be used to write relations involving the known angles and x.
D
He washes 60 sq ft in 1/4 of an hour. Multiply 60 by 4 and you get 240 per hour
Answer:
Kyle’s fixed monthly salary in dollars is $1800
Step-by-step explanation:
let a be the fixed monthly salary
let b% represent the fixed percentage of sales
a+(b%*15000)=2550
a+(b%*25000)=3050
a+(b/100*15000)=2550
a+150b=2550
a+(b/100*25000)=3050
a+250b=3050
now we have
a+150b=2550
a+250b=3050
let subtract a+150b=2550 from a+250b=3050
100b=500
b=500/100=5%
then a+(5%*15000)=2550
a+750=2550
a=2550-750=$1800
Very interesting question!
Let's try to get something that would work for just 5 for now.
Any of these numbers would leave a remainder of 1 when divided by just 5:
6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, ...
Notice that they all look like 5*(something) + 1. Basically, they are all multiples of 5 plus 1.
Let's see what would work for just 8:
9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, ...
Are there any matches... AHA! It's 81. This is the lowest positive integer greater than 1 that follows the rule for both 5 and 8.
