let's recall the remainder theorem.
we know that (x-1) is a factor, that means x -1 = 0 or x = 1.
since we know that (x-1) is a factor, then dividing the polynomial by it will give us a remainder of 0, which correlates with saying that f(1) = 0, in this case, so we can simply plug in "1" as the argument, knowing it gives 0.
![f(x)=3x^3+kx-11\\\\[-0.35em]~\dotfill\\\\\stackrel{0}{f(1)}=3(1)^3+k(1)-11\implies \stackrel{f(1)}{0}=3+k-11\implies 0=-8+k\implies 8=k](https://tex.z-dn.net/?f=f%28x%29%3D3x%5E3%2Bkx-11%5C%5C%5C%5C%5B-0.35em%5D~%5Cdotfill%5C%5C%5C%5C%5Cstackrel%7B0%7D%7Bf%281%29%7D%3D3%281%29%5E3%2Bk%281%29-11%5Cimplies%20%5Cstackrel%7Bf%281%29%7D%7B0%7D%3D3%2Bk-11%5Cimplies%200%3D-8%2Bk%5Cimplies%208%3Dk)
Answer:
The x-intercept is 2.
Step-by-step explanation:
![2 \sqrt[3]{x - 10} + 4 = 0](https://tex.z-dn.net/?f=2%20%5Csqrt%5B3%5D%7Bx%20-%2010%7D%20%20%2B%204%20%3D%200)
![2 \sqrt[3]{x - 10} = - 4](https://tex.z-dn.net/?f=2%20%5Csqrt%5B3%5D%7Bx%20-%2010%7D%20%20%3D%20%20-%204)
![\sqrt[3]{x - 10 } = - 2](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7Bx%20-%2010%20%7D%20%20%3D%20%20-%202)
Answer:
First the mode. Since 5 popped up the most, 5 is the mode.
Next is the median. I crossed 1 dot from each side until it shows the last dot, and 5 was the last one.
After that the range. 9-2=7
Finally the worst, the mean... 2+2+3+3+3+4+5+5+5+5+5+6+6+6+8+9+9+9+9
=104/19=5.47
SO, Mode=5 Median=5 Range=7, and the mean is 5.47 (rounded nearest hundred)
Answer:
225 adult tickets
Step-by-step explanation:
S: no. of students
A: no. of adults
S = A + 54
S + A = 504
A + A + 54 = 504
2A = 450
A = 225
S = 225 + 54
S = 279
Answer:
x = -7
Step-by-step explanation:
5x+8=3x-6
Subtract 3x from each side
5x-3x+8=3x-3x-6
2x+8 = -6
Subtract 8 from each side
2x+8-8 = -6-8
2x = -14
Divide by 2
2x/2 = -14/2
x = -7
