Multiply 3 times 6 times 3 to get the total number of choices.
Since there can only be one meat, one vegetable, and one cheese, the chances are 1/54.
Answer:
The value of x is ![\frac{10}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B3%7D)
Step-by-step explanation:
Given,
![\frac{1}{250}:2=\frac{1}{150}:x](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B250%7D%3A2%3D%5Cfrac%7B1%7D%7B150%7D%3Ax)
![\frac{1/250}{2}=\frac{1/150}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B1%2F250%7D%7B2%7D%3D%5Cfrac%7B1%2F150%7D%7Bx%7D)
![\frac{1}{500}=\frac{1}{150x}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B500%7D%3D%5Cfrac%7B1%7D%7B150x%7D)
By cross multiplication,
![150x = 500](https://tex.z-dn.net/?f=150x%20%3D%20500)
![x=\frac{500}{150}=\frac{500\div 50}{150\div 50}=\frac{10}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B500%7D%7B150%7D%3D%5Cfrac%7B500%5Cdiv%2050%7D%7B150%5Cdiv%2050%7D%3D%5Cfrac%7B10%7D%7B3%7D)
Answer:
1.) x = 14.96ft
2.) The shorter leg is 6 meters
Step-by-step explanation:
1.) a^2 + b^2 = c^2
- a and b = legs of the triangle
- c = hypotenuse the longest side
15ft^2 + x^2 = (2x +1)^2
- 225 = 2x^2 + 1 - x^2
- 225 = x^2 + 1
- 225 - 1 = x^2 +1 - 1
- √224 = √x^2
- x = 14.9662...
2.) Longer leg a = x+2, shorter leg b = x, Hyp. c= 2x-2
Equation:
Solve:
- (x+2)(x+2) + x^2 = (2x-2)(2x-2)
- x^2 + 4x + 4 + x^2 = 4x^2 - 8x +4
- 2x^2 + 4x + 4 = 4x^2 - 8x +4
- 2x^2 + 4x + 4 - 4x^2 +8x - 4 = 4x^2 - 4x^2 - 8x + 8x + 4 - 4
- -2x^2 + 12x = 0
- 2x (-x + 6) = 0
Answers:
- 2x = 0
- -x + 6 = 0
- <u>x=0 -or- x=6</u>
<u>Since x cannot equal 0 due to the known length of the triangle needs to be more than 0 the answer for x equals 0.</u>
<u>B=6</u>
Check:
- A = x + 2: A= 6 +2 = 8
- B= 6
- C = 2x -2: C= 2(6) -2 = 10
8^2 + 6^2 = 10^2
These inequalities are not compatible: you are looking for a number that is less than 2, but more than 7. This is impossible, because if a number is less than 2, it can't be more than 7.
Conversely, if a number is more than 7, it can't be less than 2.