Answer:
37/24
Step-by-step explanation:
Since the denomenators must be consistent, both 8 and 12 have the common factor of 24.
the denominator of 8 must be multiplied by 3 to get to 24, but to multiply the denominator you must multiply the numerator by 3 which gives you
15/24
the denominator of 12 must be multiplied by 2 to get 24, so you must multiply 11 by 2 as well to get
22/24
add them together to get 37/24
By solving a system of equations, we will see that m measures 12 units.
<h3>
How to get the measure of m?</h3>
Notice that we have 3 right triangles.
Then we can write the equations:
cos(a) = 6/m
For the small triangle on the left, where m is the hypotenuse.
cos(a) = m/(6 + 18)
For the larger triangle (the one composed of the two triangles).
Where in both equations, angle "a" is the one in the top left.
Then we have the system of equations:
cos(a) = 6/m
cos(a) = m/(6 + 18)
Then we can write:
6/m = m/(6 + 18)
If we simplify the expression, we get:
6*(6 + 18) = m^2
6*(24) = m^2
144 = m^2
√144 = m = 12
Then we conclude that m measures 12 units.
If you want to learn more about right triangles:
brainly.com/question/2217700
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40 mph
First you have 1200/30. You are trying to get to 1 hour, so in order to get 30 to one, you must divide 30 by 30 and 1200 by thirty as well. You get 40 miles per hour.
