Answer:
m∠B = 119°
Step-by-step explanation:
- the measure of c and 112 are on the straight angle and they are both equal 180°
c = 180 - 112 = 68
∠c = 68°
- the sum of the interior angles of a triangle is 180°
- the measure of third angle = the sum of the interior angles - the sum of two angles
a = 180 - (51 + 68) = 61
∠a = 61°
- the measure of 61 and b are on the straight angle and they are both equal 180°
b = 180 - 61 = 119
∠b = 119°
also you can go on other way
- an exterior angle of a triangle is equal to the sum of the opposite interior angles
51 + 68 = 119
Answer:
Well, one way to use reasonableness is to estimate the answer to see if your answer is an outrageous answer or not. So, looking at your problem, you see that you are multiplying a two hundred something number by 4 and then subtracting 10 from it.
Step-by-step explanation:
Answer:
x=20
m<B=92 degrees
m<C=40 degrees
Step-by-step explanation:
48+6x-28+2x=180
20+8x=180
8x=160
x=20
(6(20)-28)=92
2(20)=40
So, x=20, m<B=92 degrees and m<C=40 degrees
The median is the middle number
Answer:
Probability=2/5
Step-by-step explanation:
Let the line segment be AB of uniform length and x is distance
so
![P(\frac{min(x,L-x)}{max(x,L-x)} )](https://tex.z-dn.net/?f=P%28%5Cfrac%7Bmin%28x%2CL-x%29%7D%7Bmax%28x%2CL-x%29%7D%20%29%3C1%2F4)
Case 1 min(x,L-x) then
![=\frac{x}{L-x}\leq 1/4\\x](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%7D%7BL-x%7D%5Cleq%20%201%2F4%5C%5Cx%3CL%2F5)
Case 2 min(x,L-x)=L-x then
![=\frac{L-x}{x}\frac{4L}{5}\\](https://tex.z-dn.net/?f=%3D%5Cfrac%7BL-x%7D%7Bx%7D%3C1%2F4%5C%5C%20x%3E%5Cfrac%7B4L%7D%7B5%7D%5C%5C)
So Probability
![P=\int\limits^{L/5}_0 {f(x)} \, dx+\int\limits^{L}_{4L/5} {f(x)} \, dx\\ P=\int\limits^{L/5}_0 {\frac{1}{L} } \, dx+\int\limits^L_{4L/5} {\frac{1}{L} } \, dx\\ P=\frac{1}{L}(\frac{L}{5} -0+L-\frac{4L}{5} )\\ P=\frac{1}{L} (2L/5)\\P=\frac{2}{5}](https://tex.z-dn.net/?f=P%3D%5Cint%5Climits%5E%7BL%2F5%7D_0%20%7Bf%28x%29%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5E%7BL%7D_%7B4L%2F5%7D%20%7Bf%28x%29%7D%20%5C%2C%20dx%5C%5C%20%20P%3D%5Cint%5Climits%5E%7BL%2F5%7D_0%20%7B%5Cfrac%7B1%7D%7BL%7D%20%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5EL_%7B4L%2F5%7D%20%7B%5Cfrac%7B1%7D%7BL%7D%20%7D%20%5C%2C%20dx%5C%5C%20%20P%3D%5Cfrac%7B1%7D%7BL%7D%28%5Cfrac%7BL%7D%7B5%7D%20-0%2BL-%5Cfrac%7B4L%7D%7B5%7D%20%29%5C%5C%20P%3D%5Cfrac%7B1%7D%7BL%7D%20%282L%2F5%29%5C%5CP%3D%5Cfrac%7B2%7D%7B5%7D)