Answer:
GCF: 1
Step-by-step explanation:
Factors are numbers that can be evenly divided into another number. The greatest common factor of a set of numbers is the biggest number than can evenly divide into all the the numbers.
Let's list the factors of 60, 45 and 82
Factors of 60:
<u>1</u>, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 45:
<u>1</u>, 3, 5, 9, 15, 45
Factors of 82:
<u>1</u>, 2, 41, 82
The greatest factor that all 3 numbers share is 1.
Let x = amount of 45% antifreezeLet y = amount of 70% antifreeze EQUATION 1: x + y = 150 (total of 150 gallons mixed) EQUATION 2: .45x + .75y = .55(x + y) Simplify and solve the system of equations Multiply second equation by 100 on both sides to remove the decimals 45x + 75y = 55(x + y) Combine like terms 45x + 75y = 55x + 55y 45x - 55x + 75y - 55y = 0 -10x + 20y = 0 Now we have the following system of equations: x + y = 150 -10x + 20y = 0 Multiply the first equation by -10 to get opposite coefficients for x; add the equations to eliminate x 10x + 10y = 1500 -10x + 20y = 0 ------------------------------ 30y = 1500 Solve for y 30y = 1500 y = 50 Since the total mixed gallons is 150, x = 150 - 50 = 100 So we need 100 gallons of the 45% antifreeze and 50 gallons of the 70% antifreeze
Answer:
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To answer your question Simplifying<span>8(5m + 10) = 0
Reorder the terms:
8(10 + 5m) = 0
(10 * 8 + 5m * 8) = 0
(80 + 40m) = 0
Solving
80 + 40m = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '-80' to each side of the equation.
80 + -80 + 40m = 0 + -80
Combine like terms: 80 + -80 = 0
0 + 40m = 0 + -80
40m = 0 + -80
Combine like terms: 0 + -80 = -80
40m = -80
Divide each side by '40'.
m = -2
Simplifying
m = -2 your welcome!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!</span>
A cyclic quadrilateral is a quadrilateral inscribed in a circle
The measure of angle A is 106
<h3>How to determine the measure of angle A</h3>
From the question, we have:
<C= 74
Opposite angles of a cyclic quadrilateral add up to 180.
So, we have:
<A + <C = 180
This gives
<A + 74 =180
Subtract 74 from both sides
<A =106
Hence, the measure of angle A is 106
Read more about cyclic quadrilaterals at:
brainly.com/question/26168678
