Answer:
a
b
d
e
Step-by-step explanation:
he triangle is isosceles.
The leg-to-hypotenuse ratio is 1:StartRoot 2 EndRoot.
The leg-to-hypotenuse ratio is 1:StartFraction StartRoot 2 EndRoot Over 2 EndRoot. The nonright angles are congruent. The ladder represents the longest length in the triangle.
If you're asking for place value:
Thousands, and Ten Thousands place.
Just value:
8,000 and 80,000
To find probability, you'd have to find the total number of marbles (5+3+6+6=20), and since there are 3 blue marbles, the probability of picking one is 3 out of 20, or 3/20
If that blue marble isn't replaced, there will then be 19 marbles, and 2 blue ones. So the probability of him picking another blue marble is 2/19
Answer:
-- Proved
![x = 10\ \ \ x = -22](https://tex.z-dn.net/?f=x%20%3D%2010%5C%20%5C%20%5C%20x%20%3D%20-22)
Step-by-step explanation:
Given
![Volume = 924cm^3](https://tex.z-dn.net/?f=Volume%20%3D%20924cm%5E3)
![Dimension: 4cm; (x+1)cm; (x+11)cm](https://tex.z-dn.net/?f=Dimension%3A%204cm%3B%20%28x%2B1%29cm%3B%20%28x%2B11%29cm)
Required
Show that ![x^2+12x-220=0](https://tex.z-dn.net/?f=x%5E2%2B12x-220%3D0)
The volume is calculated as:
![4 * (x + 1) * (x + 11) = 924](https://tex.z-dn.net/?f=4%20%2A%20%28x%20%2B%201%29%20%2A%20%28x%20%2B%2011%29%20%3D%20924)
Open the brackets
![(4x + 4) * (x + 11) = 924](https://tex.z-dn.net/?f=%284x%20%2B%204%29%20%2A%20%28x%20%2B%2011%29%20%3D%20924)
![4x^2 + 44x + 4x + 44 = 924](https://tex.z-dn.net/?f=4x%5E2%20%2B%2044x%20%2B%204x%20%2B%2044%20%3D%20924)
![4x^2 + 48x+ 44 = 924](https://tex.z-dn.net/?f=4x%5E2%20%2B%2048x%2B%2044%20%3D%20924)
Collect Like Terms
![4x^2 + 48x+ 44 - 924=0](https://tex.z-dn.net/?f=4x%5E2%20%2B%2048x%2B%2044%20-%20924%3D0)
![4x^2 + 48x -880=0](https://tex.z-dn.net/?f=4x%5E2%20%2B%2048x%20-880%3D0)
Divide through by 4
![\frac{4x^2}{4} + \frac{48x}{4} -\frac{880}{4}=0](https://tex.z-dn.net/?f=%5Cfrac%7B4x%5E2%7D%7B4%7D%20%2B%20%5Cfrac%7B48x%7D%7B4%7D%20-%5Cfrac%7B880%7D%7B4%7D%3D0)
![x^2+12x-220=0](https://tex.z-dn.net/?f=x%5E2%2B12x-220%3D0)
Solving further:
Expand the expression
![x^2 + 22x - 10x - 220 = 0](https://tex.z-dn.net/?f=x%5E2%20%2B%2022x%20-%2010x%20-%20220%20%3D%200)
Factorize:
![x(x + 22) - 10(x + 22) = 0](https://tex.z-dn.net/?f=x%28x%20%2B%2022%29%20-%2010%28x%20%2B%2022%29%20%3D%200)
![(x - 10)(x + 22) = 0](https://tex.z-dn.net/?f=%28x%20-%2010%29%28x%20%2B%2022%29%20%3D%200)
Split:
![x - 10 = 0;\ \ \ x + 22 = 0](https://tex.z-dn.net/?f=x%20-%2010%20%3D%200%3B%5C%20%5C%20%5C%20x%20%2B%2022%20%3D%200)
![x = 10\ \ \ x = -22](https://tex.z-dn.net/?f=x%20%3D%2010%5C%20%5C%20%5C%20x%20%3D%20-22)