Hi there! The answer is (1/2)
I suppose you mean the slope of a line that is parallel to y = (1/2)x + 3.
This equation is written in slope-intercept form, which means that the number in front of x represents the slope of the line. The other number represents the y-intercept.
A line that is parallel to another line, will be a line with the same slope. Since the slope of y = (1/2)x + 3 is (1/2), the slope of a line parallel to this line is (1/2) as well.
~ Hope this helps you!
D. 2 is the biggest number available there, so it would produce the narrowest graph.
Answer: A. Use Pythagorean Theorem to prove that KL is equal to c.
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Explanation:
If we could show that KL = c, then we can tie together the following pairs of segments
- EG = KM = a
- GF = ML = b
- EF = KL = c
Then we'd use the SSS congruence theorem to prove the triangles are congruent. The last step is to use CPCTC to conclude that angle EGF is a 90 degree angle.
Keep in mind that we need to know the actual numeric values of 'a' and 'b' to be able to determine the value for c. So without the numbers, the Pythagorean theorem isn't really useful; however, I can see where your teacher is going with this line of logic. Your teacher is effectively just laying out a basic outline more or less.
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Notes:
- SSS = side side side
- CPCTC = corresponding parts of congruent triangles are congruent
The given info is sufficient to warrant the conclusion that both triangles are 45-45-90 triangles.
The measure of angle B is 45 degrees, or pi/4 radians.
The cosine of this angle B is 1/√2, or √(2)/2. This is approx. 0.707.
