The answer is infinitely many solutions
If you divide the 2nd equation by 3, you get the first equation, meaning they are identical. That means that any value of x will be true, which means there are infinite solutions
So the first thing you do is dove the equations. Let's do the numerator equation. 8(2)-4 is simply saying 8•2-4 and i don't know if u learned this in class yet but you do multiplication and division before addition and subtraction so 8•2=16-4=12 so now 12 is our numerator. Now for the denominator, 8/4=2 so 2 is our denominator. We have 12/2 but it can be simplified to 6 because 6 goes into 12 twice and u cans check this by doing 6•2=12
Hope this helps m8 :))
Answer:
![Ratio = \frac{R^2 - r^2 }{ r^2}](https://tex.z-dn.net/?f=Ratio%20%3D%20%5Cfrac%7BR%5E2%20-%20r%5E2%20%7D%7B%20r%5E2%7D)
Step-by-step explanation:
Given
See attachment for circles
Required
Ratio of the outer sector to inner sector
The area of a sector is:
For the inner circle
![r \to radius](https://tex.z-dn.net/?f=r%20%5Cto%20radius)
The sector of the inner circle has the following area
![A_1 = \frac{\theta}{360}\pi r^2](https://tex.z-dn.net/?f=A_1%20%3D%20%5Cfrac%7B%5Ctheta%7D%7B360%7D%5Cpi%20r%5E2)
For the whole circle
![R \to Radius](https://tex.z-dn.net/?f=R%20%5Cto%20Radius)
The sector of the outer sector has the following area
![A_2 = \frac{\theta}{360}\pi (R^2 - r^2)](https://tex.z-dn.net/?f=A_2%20%3D%20%5Cfrac%7B%5Ctheta%7D%7B360%7D%5Cpi%20%28R%5E2%20-%20r%5E2%29)
So, the ratio of the outer sector to the inner sector is:
![Ratio = A_2 : A_1](https://tex.z-dn.net/?f=Ratio%20%3D%20A_2%20%3A%20A_1)
![Ratio = \frac{\theta}{360}\pi (R^2 - r^2) : \frac{\theta}{360}\pi r^2](https://tex.z-dn.net/?f=Ratio%20%3D%20%5Cfrac%7B%5Ctheta%7D%7B360%7D%5Cpi%20%28R%5E2%20-%20r%5E2%29%20%3A%20%5Cfrac%7B%5Ctheta%7D%7B360%7D%5Cpi%20r%5E2)
Cancel out common factor
![Ratio = R^2 - r^2 : r^2](https://tex.z-dn.net/?f=Ratio%20%3D%20R%5E2%20-%20r%5E2%20%3A%20r%5E2)
Express as fraction
![Ratio = \frac{R^2 - r^2 }{ r^2}](https://tex.z-dn.net/?f=Ratio%20%3D%20%5Cfrac%7BR%5E2%20-%20r%5E2%20%7D%7B%20r%5E2%7D)
1) number of cards that aren't : number of cards that are 3
we have 48 cards that arent 3 and 4 cards that are. that means that odds are:
12:1 of not drawing 3
2) fallow same logic. its just opposite.
1:12
3) same logic. but there are only 2 black 7 cards which means that odds are:
50:2 or
25:1
4) opposite of previous.
1:25
The triangles formed by the path of the ball and the wall in the given diagram are similar triangles.
<h3>Correct Response;</h3>
The point on the wall she should aim is; <u>A. 7.8 feet away from point B</u>
<h3 /><h3>Method by which the above value is obtained;</h3>
The possible diagram in the question is attached
Let <em>x</em> represent the distance from point <em>B</em> where the ball lands.
ΔCDE is similar to ΔABE, by Angle-Angle similarity postulate.
By trigonometric ratio, the tangent of the angles ∠CDE and ∠BAE are;
![tan(\angle CDE) = \mathbf{\dfrac{20 - x}{25}}](https://tex.z-dn.net/?f=tan%28%5Cangle%20CDE%29%20%3D%20%5Cmathbf%7B%5Cdfrac%7B20%20-%20x%7D%7B25%7D%7D)
![tan(\angle BAE) = \mathbf{ \dfrac{x}{16}}](https://tex.z-dn.net/?f=tan%28%5Cangle%20BAE%29%20%3D%20%5Cmathbf%7B%20%5Cdfrac%7Bx%7D%7B16%7D%7D)
tan(∠CDE) = tan(∠BAE)
Therefore;
![\dfrac{20 - x}{25} = \dfrac{x}{16}](https://tex.z-dn.net/?f=%5Cdfrac%7B20%20-%20x%7D%7B25%7D%20%3D%20%5Cdfrac%7Bx%7D%7B16%7D)
Which gives;
16 × (20 - x) = 25·x
320 = 41·x
x = 320 ÷ 41 ≈ 7.8
The point on the wall she should aim if she's standing at point <em>A</em> is therefore;
- <u>A, 7.8 feet away from point </u><u><em>B</em></u>
Learn more about trigonometric ratios here:
brainly.com/question/4326804