Answer:
(45,35)
Step-by-step explanation:
1 - Stack the equations on top of each other
3x - 4y = -5
4x + 4y = 40
2 - We can eliminate by subtracting the bottom equation from the top equation
3x - 4y = -5
- 4x - 4y = 40
3 - The y's cancel out, leaving us with...
3x = -5
- 4x = 40
4 - Continue simplifying
-1x = -45
5 - We can switch the -1x with -x to make things simple
-x = -45
6 - Positize (make it positive) the statement
x = 45
7 - Halfway there! Substitute the x value into one of the equations
(3 * 45) - 4y = -5
8 - Solve
135 - 4y = -5
Minus 135 on both sides
-4y = -140
Divide by -4 on both sides
y = 35
9 - Here is your answer!!
x = 45
y = 35
(45,35)
A)120 cubic centimeters :)
Answer:
The second option
Step-by-step explanation:
Please find attached the complete question in the attached image
the proportion of students that like the silver calculator is 0.4 while the proportion of students that like the black calculator is 0.6. More students like the black calculator
the proportion of students that prefer the black model 77 calculator is 0.3 while the proportion of students that prefer the silver model 55 is 0.25. More students prefer the black model 77 calculator
the proportion of students that prefer the model 66 calculator is 0.15 while the proportion of students that prefer the model 55 calculator is 0.35. More students prefer the model 55
the fewest student prefer the silver model 66 calculator because it has the lowest proportion
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)
For this case we must find the value of n of the following equation:
![n + \frac {1} {5} n = 24](https://tex.z-dn.net/?f=n%20%2B%20%5Cfrac%20%7B1%7D%20%7B5%7D%20n%20%3D%2024)
Taking common factor "n" from the left side of the equation we have:
![n (1+ \frac {1} {5}) = 24\\n \frac {6} {5} = 24](https://tex.z-dn.net/?f=n%20%281%2B%20%5Cfrac%20%7B1%7D%20%7B5%7D%29%20%3D%2024%5C%5Cn%20%5Cfrac%20%7B6%7D%20%7B5%7D%20%3D%2024)
Multiplying by 5 on both sides of the equation:
![6n = 120](https://tex.z-dn.net/?f=6n%20%3D%20120)
Dividing between 6 on both sides of the equation:
![n = 20](https://tex.z-dn.net/?f=n%20%3D%2020)
Thus, the value of n is 20.
Answer:
![n = 20](https://tex.z-dn.net/?f=n%20%3D%2020)