The length of OM is 4/3 the length of OJ, and the length of ON is 4/3 the length of OK. Thus, two pairs of sides from the triangles are proportional to each other.
Also, angle O from one of the triangles is equal to angle O of the other triangle because they are the same angle.
Thus, the two triangles are similar by SAS (side-angle-side) similarity theorem. This theorem is quite similar to the SAS congruence theorem.
To make a similarity statement, we just have to match corresponding parts when naming the triangle.
Similarity statement: ΔOJK~ΔOMN
Simplifying
12x + 10 + 3 + 8x = 0
Reorder the terms:
10 + 3 + 12x + 8x = 0
Combine like terms: 10 + 3 = 13
13 + 12x + 8x = 0
Combine like terms: 12x + 8x = 20x
13 + 20x = 0
Solving
13 + 20x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-13' to each side of the equation.
13 + -13 + 20x = 0 + -13
Combine like terms: 13 + -13 = 0
0 + 20x = 0 + -13
20x = 0 + -13
Combine like terms: 0 + -13 = -13
20x = -13
Divide each side by '20'.
x = -0.65
Simplifying
x = -0.65
Well, we can see that the y-intercept is (0, -4) which means that the line must be:
y=mx-4
And since only one answer has -4 as the y-intercept, y=x-4 is the answer :P
Answer:
21
Step-by-step explanation:
21 water stations
Step-by-step explanation:
From the question, we are informed that a marathon is 26.2 miles long and that there is a water station every 1 1/4miles along the race route and at the finish line.
To get the number of water stations that are needed for this marathon, we divide 26.2 miles by 1 1/4miles. This will be:
= 26.2miles/1 1/4 miles
= 26.2 miles/1.25 miles
= 20.96
= 21 water stations
