Find the measures of the angles of a triangle if the measure of one angle is twice the measure of a second angle and the third a
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In this relationship between the number of miles per gallon on the highway and that in the city for some cars are:
For each additional city mpg, the highway value goes up by
0.9478 mpg.
And It is inappropriate to interpret the intercept because no cars get 0 mpg in the city.
According to the statement
we have given that the relationship between the number of miles per gallon on the highway in the graphical representation and that in the city for some cars.
And we have to give some reasons for the given statements.
So, For this purpose, we know that the
A. In this statement we have to tell that the what is shown in the given relationship in the graph.
So, For each additional city mpg, the highway value goes up by
0.9478 mpg.
And the second statement is
B. I this we have to tell the intercept of the plane in the given Relationship.
So, It is inappropriate to interpret the intercept because no cars get 0 mpg in the city.
So, In this relationship between the number of miles per gallon on the highway and that in the city for some cars are:
For each additional city mpg, the highway value goes up by
0.9478 mpg.
And It is inappropriate to interpret the intercept because no cars get 0 mpg in the city.
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Question:
The figure shows the relationship between the number of miles per gallon on the highway and that in the city for some cars.
a. Report the slope and explain what it means.
b. Either interpret the intercept (7.792) or explain why it is not appropriate to interpret the intercept.
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These are a huge pain. First set up your initial triangle with A and B as your base angles and C as your vertex angle. Now drop an altitude and call it h. You need to solve for h. Use sin 56 = h/13 to get that h = 10.8. The rule is that if the side length of a is greater than the height but less than the side length of b, you have 2 triangles. h<a<b --> 10.8<12<13. Those are true statements so we have 2 triangles. Side a is the side that swings, this is the one we "move", forming the second triangle. First we have to solve the first triangle using the Law of Sines, then we can solve the second. 
to get that angle B is 64 degrees. Now find C: 180-56-64=60. And now for side c: 
and c=12.5. That's your first triangle. In the second triangle, side a is the swinging side and that length doesn't change. Neither does the angle measure. Angle B has a supplement of 180-64 which is 116. So the new angle B in the second triangle is 116, but the length of b doesn't change, either. I'll show you how you know you're right about that in just a sec. The only angle AND side that both change are C and c. If our new triangle has angles 56 and 116, then C has to be 8 degrees. Using the Law of Sines again, we can solve for c:
and c = 2.0. We can look at this new triangle and determine the side measures are correct because the longest side will always be across from the largest angle, and the shortest side will always be across from the smallest angle. The new angle B is 116, which is across from the longest side of 13. These are hard. Ugh.