<h3>
Answers: C and D</h3>
Why? Because they are mirrors of each other. In other words, one table has its x and y row swapped compared to the other table.
The input x = -120 leads to the output y = 627 in table C. Then in table D, we have the input x = 627 to go the output y = -120. Refer to the first column of each table mentioned. The same applies for the other columns as well. The inverse table undoes everything the original table does.
Answer: The quotient is (x-2).
Step-by-step explanation:
Since we have given that
![f(x)=(x^3+3x^2-4x-12)\\\\and\\\\g(x)=x^2+5x+6\\\\So,\ \frac{\left(x^3+3x^2-4x-12\right)}{\left(x^2+5x+6\right)}](https://tex.z-dn.net/?f=f%28x%29%3D%28x%5E3%2B3x%5E2-4x-12%29%5C%5C%5C%5Cand%5C%5C%5C%5Cg%28x%29%3Dx%5E2%2B5x%2B6%5C%5C%5C%5CSo%2C%5C%20%5Cfrac%7B%5Cleft%28x%5E3%2B3x%5E2-4x-12%5Cright%29%7D%7B%5Cleft%28x%5E2%2B5x%2B6%5Cright%29%7D)
Now, we have to find the quotient of the above expression.
So, here we go:
![Factorise\ (x^3+3x^2-4x-12)\\\\=\left(x^3+3x^2\right)+\left(-4x-12\right)\\\\=-4\left(x+3\right)+x^2\left(x+3\right)\\\\=\left(x+3\right)\left(x^2-4\right)](https://tex.z-dn.net/?f=Factorise%5C%20%28x%5E3%2B3x%5E2-4x-12%29%5C%5C%5C%5C%3D%5Cleft%28x%5E3%2B3x%5E2%5Cright%29%2B%5Cleft%28-4x-12%5Cright%29%5C%5C%5C%5C%3D-4%5Cleft%28x%2B3%5Cright%29%2Bx%5E2%5Cleft%28x%2B3%5Cright%29%5C%5C%5C%5C%3D%5Cleft%28x%2B3%5Cright%29%5Cleft%28x%5E2-4%5Cright%29)
Now, we will divide the above simplest form with g(x):
![\frac{\left(x+3\right)\left(x^2-4\right)}{\left(x+2\right)\left(x+3\right)}\\\\=\frac{x^2-4}{x+2}\\\\=\frac{\left(x+2\right)\left(x-2\right)}{x+2}\ using\ (a^2-b^2)=(a+b)(a-b)\\\\=x-2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cleft%28x%2B3%5Cright%29%5Cleft%28x%5E2-4%5Cright%29%7D%7B%5Cleft%28x%2B2%5Cright%29%5Cleft%28x%2B3%5Cright%29%7D%5C%5C%5C%5C%3D%5Cfrac%7Bx%5E2-4%7D%7Bx%2B2%7D%5C%5C%5C%5C%3D%5Cfrac%7B%5Cleft%28x%2B2%5Cright%29%5Cleft%28x-2%5Cright%29%7D%7Bx%2B2%7D%5C%20using%5C%20%28a%5E2-b%5E2%29%3D%28a%2Bb%29%28a-b%29%5C%5C%5C%5C%3Dx-2)
Hence, the quotient is (x-2).
Answer:
z = 156
Step-by-step explanation:
y² = 65²-25² = 4225 - 625 = 3600
(x+25)²-65² = z²
x²+50x+625-4225 = z²
x²+50x-3600 = z² ....(1)
x²+60² = z²
x²+3600 = z² ....(2)
(1)-(2): 50x - 7200 = 0
50x = 7200
x = 144
check: x² + y² = z² 144² + 60² = 24336 = z² z = 156
(25+144)²-65² = z² = 28561 - 4225 = 24336 z = 156
Answer:6
Step-by-step explanation:
1.add all the numbers up 48+75+80+61=264
2. The amount of the numbers all together by how much numbers there are and there is 4 numbers so do 264/4 which is 66