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Answer:
a) yes; 12/15/17 ~ 20/25/x; SAS
b) x = 28 1/3
Step-by-step explanation:
The left-side segments are in the ratio ...
top : bottom = 12 : 8 = 3 : 2
The right side segments are in the ratio ...
top : bottom = 15 : 10 = 3 : 2
These are the same ratio, and the angle at the peak is the same in both triangles, so the triangles are similar by the SAS postulate.
Normally, a similarity statement would identify the triangles by the labels on their vertices. Here, there are no such labels, so we choose to write the statement in terms of the side lengths, shortest to longest:
12/15/17 ~ 20/25/x
__
The sides of similar triangles are proportional, so the ratio of longest to shortest sides will be the same in the two triangles. In the smaller triangle, the longest side is 17/12 times the length of the shortest side. The value of x will be 17/12 times the length of the shortest side in the larger triangle:
x = 17/12 · 20 = 340/12
x = 28 1/3
The answer is 10 pairs of shoes.
The first ratio is 10:5. 10 socks per 5 pairs of shoes. You have 20 socks now instead of 10. You just double the ratio. 20 socks per 10 pairs of shoes. 20:10.
Answer:
<h2>y = 3</h2>
Step-by-step explanation:
If a line has slope 0, then it's a horizontal line.
A horizontal line has an equation:
<h2>y = a</h2>
where a is any real number.
The line passes through point (-12, 3) → x = -12, y = 3.
Therefore the equation is
<h2>y = 3</h2>
Answer:
(- 1, 2)
Step-by-step explanation:
Given a quadratic in standard form y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
= - 
f(x) = x² + 2x + 3 ← is in standard form
with a = 1 and b = 2, hence
= - 
= - 1
Substitute x = - 1 into f(x) for corresponding value of y
f(- 1) = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2
vertex = (- 1, 2 )
