The vertex where the two triangles touch forms a pair of vertical angles, so that the angles on opposites sides of the vertex are congruent. You're shown that two legs of both triangles are congruent. All this tells you that the two triangles are isosceles, and furthermore that they are similar because of the congruence of their "base" angles.
This means




(1) y² + x² = 53
(2) y - x = 5 ⇒ y = x + 5
subtitute (2) to (1)
(x + 5)² + x² = 53 |use (a + b)² = a² + 2ab + b²
x² + 2x·5 + 5² + x² = 53
2x² + 10x + 25 = 53 |subtract 53 from both sides
2x² + 10x - 28 =0 |divide both sides by 2
x² + 5x - 14 = 0
x² - 2x+ 7x - 14 = 0
x(x - 2) + 7(x - 2) = 0
(x - 2)(x + 7) = 0 ⇔ x - 2 = 0 or x + 7 = 0 ⇔ x = 2 or x = -7
subtitute the values of y to (2)
for x = 2, y = 5 + 2 = 7
for x = -7, y = 5 + (-7) = 5 - 2 = 3
Answer: x = 2 and y = 7 or x = -7 and y = 3
29 percent = 29/100
So 29/100 x 20
= 5.8
Answer:
Option D, x = 4
Step-by-step explanation:
Option A: y = 4 doesn't work because that line would be horizontal
Option B: y = 4x doesn't work because that would be diagnol
Option C: x = -4 doesn't work because that would a vertical line at -4
<em>Option D: x = 4 works because that would a vertical line at 4</em>
<em />
Answer: Option D, x = 4
Answer:
4 hours
Step-by-step explanation:
If it took them together with a total of 6 hours and Oliver is half as fast meaning Jose is faster it will take Jose 4 hours.
A simple equation is
6= 4+2
And the 2 would be Oliver since Oliver is half as fast.