Answer:
a= 25.69, b=23.12, c=131.119
Step-by-step explanation:
![cosa=\frac{B^{2} +C^{2} -A^{2} }{2BC} \\ =\frac{79.59}{88.32} \\ a = 25.69](https://tex.z-dn.net/?f=cosa%3D%5Cfrac%7BB%5E%7B2%7D%20%2BC%5E%7B2%7D%20-A%5E%7B2%7D%20%7D%7B2BC%7D%20%5C%5C%20%20%20%20%20%20%20%20%3D%5Cfrac%7B79.59%7D%7B88.32%7D%20%5C%5C%20%20%20%20%20%20%20a%20%3D%2025.69)
![cos(b)=\frac{A^{2} +C^{2} -B^{2} }{2AC} \\ =\frac{89.69}{97.52}\\ b=23.12\\c=180-23.12-25.69\\ = 131.119](https://tex.z-dn.net/?f=cos%28b%29%3D%5Cfrac%7BA%5E%7B2%7D%20%2BC%5E%7B2%7D%20-B%5E%7B2%7D%20%7D%7B2AC%7D%20%5C%5C%20%20%20%20%20%20%20%20%3D%5Cfrac%7B89.69%7D%7B97.52%7D%5C%5C%20%20%20%20%20%20b%3D23.12%5C%5Cc%3D180-23.12-25.69%5C%5C%20%20%20%3D%20131.119)
Answer:
10
Step-by-step explanation:
d = √(x2 -x1)² + (y2 - y1)²
√(-6 - 0)² + [1 - (-7)]²
√(-6)² + (8)²
√(36) + (64)
√100
= 10
Answer: Y=-1 or Y=-1+4
Step-by-step explanation:
<h3>Use the formula y2- y1 over x2-x1 so it should look like this 1-3 over 3-1 which is -2 over 2 then you divide that which is -1 and if you have to find one all you have to do is use one point label which is x and y so I pick (1,3) so you put 3=-1(1) once you have that you multipy so -1 times 1 is -1 so your gonna add 1 to the -1 and the three the -1 cancel out because it is a zero pair 3+1 is 4 so B=4 </h3>
Answer:
Step-by-step explanation:
Assuming that each draw is independent of the last and that each ball is equally likely to be selected makes this a binomial distribution
a.) first find the probability of selecting a black ball, 2/10 or .2
![{10\choose{4}}.2^4*.8^6=.08808384](https://tex.z-dn.net/?f=%7B10%5Cchoose%7B4%7D%7D.2%5E4%2A.8%5E6%3D.08808384)
b.) Probability of slecting a red ball: 1/10 or .1
Less than 2 is X=0 + X=1
![{10\choose0}*.2^0*.8^{10}+{10\choose1}*.2*.8^9=.3758096384](https://tex.z-dn.net/?f=%7B10%5Cchoose0%7D%2A.2%5E0%2A.8%5E%7B10%7D%2B%7B10%5Cchoose1%7D%2A.2%2A.8%5E9%3D.3758096384)
i will leave you to do the rounding
Answer:
DE = 20 units
Step-by-step explanation:
<u><em>GIVEN</em></u><em> :-</em>
- D & E are the mid-points of AB & BC respectively.
- DE = 4x + 4
- AC = x + 36
<u><em>TO FIND</em></u><em> :-</em>
<u><em>FACTS TO KNOW BEFORE SOLVING</em></u><em> :-</em>
- The midsegment of a triangle is a line constructed by connecting the midpoints of any two sides of the triangle.
- The Triangle Midsegment Theorem tells us that a midsegment is one-half the length of the third side (the base), and it is also parallel to the base.
<u><em>PROCEDURE</em></u><em> :-</em>
According to Triangle Midsegment Theorem ,
![DE = \frac{AC}{2}](https://tex.z-dn.net/?f=DE%20%3D%20%5Cfrac%7BAC%7D%7B2%7D)
![=> 4x + 4 = \frac{x + 36}{2}](https://tex.z-dn.net/?f=%3D%3E%204x%20%2B%204%20%3D%20%5Cfrac%7Bx%20%2B%2036%7D%7B2%7D)
Multiplying 2 on both the sides ,
![=> 2(4x + 4) = x + 36](https://tex.z-dn.net/?f=%3D%3E%202%284x%20%2B%204%29%20%3D%20x%20%2B%2036)
![=> 8x + 8 = x + 36](https://tex.z-dn.net/?f=%3D%3E%208x%20%2B%208%20%3D%20x%20%2B%2036)
![=> 8x - x = 36 - 8](https://tex.z-dn.net/?f=%3D%3E%208x%20-%20x%20%3D%2036%20-%208)
![=> 7x = 28](https://tex.z-dn.net/?f=%3D%3E%207x%20%3D%2028)
![=> x = \frac{28}{7} = 4](https://tex.z-dn.net/?f=%3D%3E%20x%20%3D%20%5Cfrac%7B28%7D%7B7%7D%20%3D%204)
∴ DE = 4×4 + 4 = 20 units