The numbers divisible by 3 are multiples of 3.
Answer: (10 - 6i)/5
(x + yi) + (4(x + yi) + 6i) = 10
⇔ 5(x + yi) + 6i = 10
⇔ 5(x + yi) = 10 - 6i
⇔ x + yi = (10 - 6i)/5
Step-by-step explanation:
mechanic #1's rate = x
mechanic #2's rate = y
* Their rate is dollars per hour ($/hr)
mechanic #1 worked for 20 hours (hr × $/hr = $)
20x = money earned by mech#1
and mechanic #2 worked for 5 hours
5y = money earned by mech#2
together they charged a total of $1150. So the amount of money earned by both mechanics.
20x + 5y = 1150
the sum of the two rates was $95 per hour.
x + y = 95
which means
x = 95 - y
plug (95 - y) in for "x" in the other equation to get everything in terms of one variable.
20(95 - y) + 5y = 1150
solve for y
1900 - 20y + 5y = 1150
1900 - 15y = 1150
-15y = 1150 - 1900
-15y = -750
y = -750/-15
y = 50 $/hr
Now use this to solve for x
x + y = 95
x + 50 = 95
x = 95 - 50
x = 45 $/hr
mech#1 charged 45$/hr
mech #2 charged 50$/hr
Answer:
c
Step-by-step explanation:
First, we need to find the other sides. Since 30° is given to us, we can use sine and cosine to figure out the other side.
To find the side opposite to the angle, we use sine, which is opposite/hypotenuse. It is given that the hypotenuse is 12, so therefore:
sin(30°)=x/12
x = 12sin(30) = 6
To find the side adjacent to the angle, we use cosine, which is adjacent/hypotenuse. Since hypotenuse is 12, we get:
cos(30°)=x/12
x = 12cos(30) = (12√3)/2 = 6√3
Therefore, the perimeter of the triangle is 12+6+6√3 = 18+6√3
