Answer:
the unknown side of the triangle is ![2\sqrt{21}](https://tex.z-dn.net/?f=2%5Csqrt%7B21%7D)
Step-by-step explanation:
![a^2+b^2=c^2](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E2)
![4^2+b^2=10^2](https://tex.z-dn.net/?f=4%5E2%2Bb%5E2%3D10%5E2)
![16+b^2=100](https://tex.z-dn.net/?f=16%2Bb%5E2%3D100)
![b^2=100-16](https://tex.z-dn.net/?f=b%5E2%3D100-16)
![b^2=84](https://tex.z-dn.net/?f=b%5E2%3D84)
or ![2\sqrt{21}](https://tex.z-dn.net/?f=2%5Csqrt%7B21%7D)
Answer:
Step-by-step explanation:
<u>Area formula:</u>
<u>The height is:</u>
- h = (x + 2)sin 45° = √2(x + 2)/2
<u>Substitute the area value an set an equation:</u>
- 4√2 = (2x - 3)√2(x + 2)/2
- (2x - 3)(x + 2) = 8
- 2x² + x - 6 = 8
- 2x² + x - 14 = 0
- D = 1 + 4*2*14 = 113
- x = (-1 + √113)/4 = 2.41 (rounded)
Note. the second root ignored as negative
Total number of chips = 4+ 6 = 10
Number of white chips = 4
Probability of picking a white chip =
![\frac{4}{10}= \frac{2}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B10%7D%3D%20%5Cfrac%7B2%7D%7B5%7D%20%20)
This white chip is not replaced back into the bag. This will reduce the number of white chips in the bag by 1 and reduce the total number of chips in the bag by 1.
So, now the total number of chips in the bag = 3 + 6 = 9
Number of white chips in the bag = 3
Probability of picking a white chip =
![\frac{3}{9}= \frac{1}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B9%7D%3D%20%5Cfrac%7B1%7D%7B3%7D%20%20)
Thus, the probability of picking two white chips will be =
Therefore, option B gives the correct answer.
Answer:
cos(θ) = (√33)/7
Step-by-step explanation:
The relevant relation is ...
cos(θ) = √(1 -sin²(θ))
cos(θ) = √(1 -(4/7)²) = √(1 -16/49) = √(33/49)
cos(θ) = (√33)/7