If 5/8 x a =1 what does a equal
1 answer:
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Answer:
(x, y) = (-1, 4), (2, -1), (5, -6)
Step-by-step explanation:
You can choose any value you like for either x or y, then solve for the other value. I like to plot points with integer coefficients, so I would look for sets of those.
The nature of this equation is that it will have integer solutions with x-values spaced 3 apart and y-values spaced 5 apart. (The spacing of each corresponds to the coefficient of the other.) So, the trick is to find an x-value that gives an integer solution for y. (You will need to try at most 3 consecutive integers.)
Solving the equation for y, we get ...
y = -5/3x +7/3
Right away, we know that x=0 will not give an integer solution for y. Nor does x=1. The third consecutive integer that is easy to try is x = -1, so ...
y = (-5/3)(-1) +7/3 = (5+7)/3 = 4 . . . . an integer value for y
Our first point is then (x, y) = (-1, 4).
Since the slope is negative, we know that increasing x will decrease y. Thus we can simply add (3, -5) to any point to get another point on the line.
Two more points on the line are ...
(-1, 4) +(3, -5) = (2, -1)
(2, -1) +(3, -5) = (5, -6)
Three integer-valued points on this line are (-1, 4), (2, -1), (5, -6).
This is the good part of Trigonometry, actually measuring triangles. It's much better than all the identities around sine and cosine and the rest, which actually have more to do with circles than triangles.
This part of trig has a short menu:
Law of Cosines. Three ways to write it, one is
Law of Sines:
Triangle angles:
and two special cases of the Law of Cosines, the Pythagorean Theorem
and the Collinear Points Theorem:
Here we choose Triangle Angles followed by Law of Sines:
A = 180 - 105 -15 = 60 degrees
Answer: 1.8 cm
When I was a student we'd be expected to get exactly and get
But that was before online homework.