We would need to know how many are in each box to figure this out.
<u>Answer:</u>
or ![f(7)=-1.67](https://tex.z-dn.net/?f=f%287%29%3D-1.67)
<u>Step-by-step explanation:</u>
We are given the following function of x and we are to find the value of
:
![f ( x ) = \frac { 3 } { x + 2 } - \sqrt { x - 3 }](https://tex.z-dn.net/?f=%20f%20%28%20x%20%29%20%3D%20%5Cfrac%20%7B%203%20%7D%20%7B%20x%20%2B%202%20%7D%20-%20%5Csqrt%20%7B%20x%20-%203%20%7D%20)
Substituting the given value (7) in the above function to get:
![f(x)=\frac{3}{x+2}-\sqrt{x-3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B3%7D%7Bx%2B2%7D-%5Csqrt%7Bx-3%7D)
![f ( 7 )= \ frac{3}{7+2}-\sqrt{7-3}](https://tex.z-dn.net/?f=%20f%20%28%207%20%29%3D%20%5C%20frac%7B3%7D%7B7%2B2%7D-%5Csqrt%7B7-3%7D)
![f(7) = \frac { 3 } { 9 } - \sqrt { 4 }](https://tex.z-dn.net/?f=%20f%287%29%20%3D%20%5Cfrac%20%7B%203%20%7D%20%7B%209%20%7D%20-%20%5Csqrt%20%7B%204%20%7D%20)
![f(7)=\frac{1}{3}-2](https://tex.z-dn.net/?f=f%287%29%3D%5Cfrac%7B1%7D%7B3%7D-2)
![f(7)=\frac{1}{3}-\frac{6}{3}](https://tex.z-dn.net/?f=f%287%29%3D%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B6%7D%7B3%7D)
or ![f(7)=-1.67](https://tex.z-dn.net/?f=f%287%29%3D-1.67)
Answer:
-4.5
Step-by-step explanation:
![6x+5.5=3x-8\\](https://tex.z-dn.net/?f=6x%2B5.5%3D3x-8%5C%5C)
![6x-3x=-8-5.5](https://tex.z-dn.net/?f=6x-3x%3D-8-5.5)
![3x=-13.5](https://tex.z-dn.net/?f=3x%3D-13.5)
![x=\frac{-13.5}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-13.5%7D%7B3%7D)
![x=-4.5](https://tex.z-dn.net/?f=x%3D-4.5)
Consider a right triangle in which one of the angles
satisfies
![\sin\theta=\dfrac35\implies\theta=\sin^{-1}\dfrac35](https://tex.z-dn.net/?f=%5Csin%5Ctheta%3D%5Cdfrac35%5Cimplies%5Ctheta%3D%5Csin%5E%7B-1%7D%5Cdfrac35)
That is, the side opposite
occurs in a ratio of 3 to 5 with the hypotenuse. The side adjacent to
then occurs in a ratio of 4 to 5 with the hypotenuse. In other words,
![\cos\theta=\dfrac45](https://tex.z-dn.net/?f=%5Ccos%5Ctheta%3D%5Cdfrac45)
because
![\sin^2\theta+\cos^2\theta=\dfrac9{25}+\dfrac{16}{25}=1](https://tex.z-dn.net/?f=%5Csin%5E2%5Ctheta%2B%5Ccos%5E2%5Ctheta%3D%5Cdfrac9%7B25%7D%2B%5Cdfrac%7B16%7D%7B25%7D%3D1)
Then in this triangle,
![\cot\theta=\cot\left(\sin^{-1}\dfrac35\right)=\dfrac{\cos\theta}{\sin\theta}=\dfrac{\frac45}{\frac35}=\dfrac43](https://tex.z-dn.net/?f=%5Ccot%5Ctheta%3D%5Ccot%5Cleft%28%5Csin%5E%7B-1%7D%5Cdfrac35%5Cright%29%3D%5Cdfrac%7B%5Ccos%5Ctheta%7D%7B%5Csin%5Ctheta%7D%3D%5Cdfrac%7B%5Cfrac45%7D%7B%5Cfrac35%7D%3D%5Cdfrac43)
Lets start with the chain of 3's:
18 = 3 + 3 + 3 + 3 + 3 + 3
But, we know that
3 + 3 = 2 + 2 + 2
Sol, let's replace 3 + 3 by 2 + 2 + 2 one by one.
Hence, the possible ways of combinations are listed below:
18 = 3 + 3 + 3 + 3 + 2 + 2 + 2 (1)
18 = 3 + 3 + 2 + 2 + 2 + 2 + 2 + 2 (2)
Therefore, there are two combinations of 2- and 3- point shots that could total 18 points.