The GCF of 16 and 40 is 8.
16/8 = 2
40/8 = 5
We can rewrite this using the distribute property like so:
<h3><u>8(2 + 5)</u></h3>
Using the distributive property:
16 + 40
16 + 40 = 56
We can also add inside the parentheses and multiply and we'll get the same answer.
8(7)
56
Solve for m:3 m + 7/2 = 5/2 - 2 m
Put each term in 3 m + 7/2 over the common denominator 2: 3 m + 7/2 = (6 m)/2 + 7/2:(6 m)/2 + 7/2 = 5/2 - 2 m
(6 m)/2 + 7/2 = (6 m + 7)/2:(6 m + 7)/2 = 5/2 - 2 m
Put each term in 5/2 - 2 m over the common denominator 2: 5/2 - 2 m = 5/2 - (4 m)/2:(6 m + 7)/2 = 5/2 - (4 m)/2
5/2 - (4 m)/2 = (5 - 4 m)/2:(6 m + 7)/2 = (5 - 4 m)/2
Multiply both sides by 2:6 m + 7 = 5 - 4 m
Add 4 m to both sides:6 m + 4 m + 7 = (4 m - 4 m) + 5
4 m - 4 m = 0:6 m + 4 m + 7 = 5
6 m + 4 m = 10 m:10 m + 7 = 5
Subtract 7 from both sides:10 m + (7 - 7) = 5 - 7
7 - 7 = 0:10 m = 5 - 7
5 - 7 = -2:10 m = -2
Divide both sides of 10 m = -2 by 10:(10 m)/10 = (-2)/10
10/10 = 1:m = (-2)/10
The gcd of -2 and 10 is 2, so (-2)/10 = (2 (-1))/(2×5) = 2/2×(-1)/5 = (-1)/5:Answer: m = (-1)/5
Answer: it will take 6 months for both gyms to cost the same.
Step-by-step explanation:
Let m represent the number of months that it will take for the cost of both gyms be the same.
At one gym, there is a $12 start-up fee, and after that each month, m, at the gym costs $20. This means that the total cost for m months is
12 + 20m
At another gym, each month at the gym costs $22. This means that the total cost for m months is 22m
For both costs to be the same, the number of months would be
12 + 20m = 22m
22m - 20m = 12
2m = 12
m = 12/2 = 6
The missing parts of the triangle ABC are A = 31.4°, B = 57.4°, C = 91.2°
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
Given that a = 8.6 in, b = 13.9 in. and c = 16.5 in. Using cosine rule:
c² = a² + b² - 2abcosC
16.5² = 8.6² + 13.9² - 2(8.6)(13.9) * cosC
C = 91.2°
Also:
a² = b² + c² - 2bccosA
8.6² = 16.5² + 13.9² - 2(16.5)(13.9) * cosA
A = 31.4°
A + B + C = 180° (angles in a triangle)
31.4 + B + 91.2 = 180
B = 57.4°
The missing parts of the triangle ABC are A = 31.4°, B = 57.4°, C = 91.2°
Find out more on equation at: brainly.com/question/2972832
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