Answer:
C
Step-by-step explanation:
We have the equation:
![x^2-6x=10](https://tex.z-dn.net/?f=x%5E2-6x%3D10)
We can subtract 10 from both sides:
![x^2-6x-10=0](https://tex.z-dn.net/?f=x%5E2-6x-10%3D0)
Since this equation isn't factorable, we can use the quadratic formula:
![\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
In this case, <em>a</em> = 1, <em>b</em> = -6, and <em>c</em> = -10.
Substitute:
![\displaystyle x=\frac{-(-6)\pm\sqrt{(-6)^2-4(1)(-10)}}{2(1)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-%28-6%29%5Cpm%5Csqrt%7B%28-6%29%5E2-4%281%29%28-10%29%7D%7D%7B2%281%29%7D)
Simplify:
![\displaystyle x=\frac{6\pm\sqrt{76}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B6%5Cpm%5Csqrt%7B76%7D%7D%7B2%7D)
Note that:
![\sqrt{76}=\sqrt{4\cdot 19}=2\sqrt{19}](https://tex.z-dn.net/?f=%5Csqrt%7B76%7D%3D%5Csqrt%7B4%5Ccdot%2019%7D%3D2%5Csqrt%7B19%7D)
Hence:
![\displaystyle x=\frac{6\pm2\sqrt{19}}{2}=3\pm\sqrt{19}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B6%5Cpm2%5Csqrt%7B19%7D%7D%7B2%7D%3D3%5Cpm%5Csqrt%7B19%7D)
Therefore, our answer is C.
The cost is dependent on the number of games played so
Cost: dependent
Number of games: independent
Answer: There are 41 blocks in all.
Step-by-step explanation:
Given: Number of red blocks = 4
Number of Yellow blocks = red blocks + 15
= 4+15= 19
Number of blue blocks = red blocks +14 = 4+14=18
Total blocks = red blocks + yellow blocks + blue blocks
= 4+19+18 =41
Hence, there are 41 blocks in all.