Answer:
Set builder notation: {a | a ≥ -21}
Interval notation: [-21, ∞)
Step-by-step explanation:
A set represents a collection of things, objects, or numbers. A set builder notation is in the form y = {x | x is an odd number between 8 and 10}, which means y contains all the odd numbers between 8 and 10.
Interval notation is a way to define a set of numbers between a lower limit and an upper limit using end-point values. for example (8, 20) means numbers between 8 and 20.
Given -3a-15≤-2a+6; solving :
-3a - 15 ≤ -2a + 6
-3a + 2a ≤ 6 + 15
-a ≤ 21
dividing through by -1:
a ≥ -21
The solution is:
Set builder notation: {a | a ≥ -21}
Interval notation: [-21, ∞)
Greatest common factor (or denominator) is 6,
least common multiple is 180
hmm
(note:
I spent like 30 mins trying to use a math only of finding the values
but it didn't work so I did a force brute and elimination method
explained below)
so
a and b must be multiples of 6
so list all the multiples of 6
wait
180=6*30
and 30's factors are 1,2,3,5,6,10,15,30 so only list the numbers that
are the result of multiplying 6 and any of those numbers in that list
(so we can have the lcm of 180)
so
6*1=6
6*2=12
6*3=18
6*5=30
6*6=36
6*10=60
6*15=90
6*30=180
these are our possible candidates for the 2 numbers
now we must find the pair that has a GCD of only 6
doing the math is long and tedious so do it yourself (trial and error)
we see that our choices that fulfill both requirements (GCD of 6 and LCM of 180) are
90&12
60&18
30&36
sum them to find the least one
90+12=102
60+18=78
30+36=66
the least possible sum is 66
Answer:
Step-by-step explanation:
<u>A three tern ratio</u>
What is a three term ratio?
A three-term ratio compares three quantities measured in the
same units.
The ratio of 18 rides, 30 games, and 8 water slides. can be written as
18:30:8
in the simplest form it is expressed as
9:15:4
in other way it is expressed as
9 to 15 to 4
another type of ratio is the two term ratio
e,g 1:2
<u>Given:</u>
Zoe gets paid a 1% commission for every sale she makes in addition to base pay.
She sold $8,000 worth of computers on a day and made $140 that day.
<u>To find:</u>
A function P(x) representing total pay on a day where she sells x dollars worth of computers.
<u>Solution:</u>
To determine the function P(x) we need to determine how much Zoe's base pay per day is.
One day, she sold $8,000 worth of computers and made $140 that day.
She gets a commission of 1% for $8,000.
1% of $8,000 
So she got paid $140 out of which $80 was a commission.
So her base pay 
So Zoe's base pay is $60 a day.
P(x) is the sum of her base pay and 1% of the amount of computer sales she makes ($x).
So 
, where x is the computer sales she makes in dollars. P(x) is represented in dollars.
I´d say "d" is the distance from the eye to the wall.
Now substracting 1.2-1 you´ll get the distance of the wall of the smallest triangle = 0.2 And you do 1.5-0.2= 0.3 that´s the distance of the wall of the other triangle. Then you solve everything with Pitagoras theorem. You have 2 rectangle triangles.
B+alfa=45°
tan^-1(0.2/d)=B
tan^-1(1.3/d)=alfa
THEN:
tan^-1(0.2/d)+tan^-1(1.3/d)=45°
Now you have 3 ecs and 3 variables.
alfa,B and "d"
