Answer:
x = 1/2
and
y = -1
Step-by-step explanation:
8x + 3y = 1
4x + 2y = 0
Multiply 4x + 2y = 0 by 2
8x + 3y = 1
8x + 4y = 0
8x + 4y = 0 minus 8x + 3y = 1
y = -1
For 8x + 3y = 1 plug in y = -1
8x + 3(-1) = 1
8x - 3 x 1 = 1
8x - 3 = 1
Add 3 to both sides
8x - 3 + 3 = 1 + 3
8x = 4
Divide both sides by 8
8x/8 (cancels out) = 4/8
x = 1/2
Answer:
Hey! What you have here are Alternate Exterior Angels!
Alternate Exterior Angles are on the exterior of the figure, and since there are 2 parallel lines that the line is passing though, the angles A and B are congruent!
Hope this Helped and Let me know if you have any questions!
Godspeed!
-SongBird
Answer:
Step-by-step explanation:
The shaded area is the difference of areas of the rectangle and the square.
<u>Rectangle:</u>
- A₁ = (x + 10)(2x + 5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50
<u>Square:</u>
- A₂ = (x + 1)² = x² + 2x + 1
<u>Shaded region:</u>
- A₁ - A₂ =
- 2x² + 25x + 50 - (x² + 2x + 1) =
- 2x² + 25x + 50 - x² - 2x - 1 =
- x² + 23x + 49
Answer:
The proportion of student heights that are between 94.5 and 115.5 is 86.64%
Step-by-step explanation:
We have a mean and a standard deviation . For a value x we compute the z-score as , so, for x = 94.5 the z-score is (94.5-105)/7 = -1.5, and for x = 115.5 the z-score is (115.5-105)/7 = 1.5. We are looking for P(-1.5 < z < 1.5) = P(z < 1.5) - P(z < -1.5) = 0.9332 - 0.0668 = 0.8664. Therefore, the proportion of student heights that are between 94.5 and 115.5 is 86.64%