Answer:
the awnswer is a = 7 + c
Step-by-step explanation:
Let the numbers be x and y. Then xy = -30 and x+y = -3.
Solve xy = -30 for y: y = -30/x
subst. -30/x for y in x+y= -3: x - 30/x = -3
Multiply all 3 terms by x: x^2 - 30 = -3x, so x^2 + 3x - 10 = 0
Solve this quadratic equation for x. x: {-5, 2}
If x = -5, then x+y = -3 becomes -5 + y = -3, and y = 2.
You should check to determine whether x=2 is also correct. If it is, what is the corresponding y value?
6x² + 48x + 96
6(x² + 8x + 16)
6(x + 4)(x + 4) is your polynomial fully factored so I'm guessing the binomial you're looking for is (x + 4).
Answer:
554,555
Step-by-step explanation:
Find the equation of the inverse.
![y = {2}^{x + 5} - 6](https://tex.z-dn.net/?f=y%20%3D%20%20%7B2%7D%5E%7Bx%20%2B%205%7D%20%20-%206)
we have
![y=\mleft\{2\mright\}^{\mleft\{x+5\mright\}}-6](https://tex.z-dn.net/?f=y%3D%5Cmleft%5C%7B2%5Cmright%5C%7D%5E%7B%5Cmleft%5C%7Bx%2B5%5Cmright%5C%7D%7D-6)
step 1
Exchange the variables
x for y and y for x
![x=\{2\}^{\{y+5\}}-6](https://tex.z-dn.net/?f=x%3D%5C%7B2%5C%7D%5E%7B%5C%7By%2B5%5C%7D%7D-6)
step 2
Isolate the variable y
![(x+6)=2^{(y+5)}](https://tex.z-dn.net/?f=%28x%2B6%29%3D2%5E%7B%28y%2B5%29%7D)
apply log both sides
![\begin{gathered} \log (x+6)=(y+5)\cdot\log (2) \\ y+5=\frac{\log (x+6)}{\log (2)} \\ \\ y=\frac{\log(x+6)}{\log(2)}-5 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Clog%20%28x%2B6%29%3D%28y%2B5%29%5Ccdot%5Clog%20%282%29%20%5C%5C%20y%2B5%3D%5Cfrac%7B%5Clog%20%28x%2B6%29%7D%7B%5Clog%20%282%29%7D%20%5C%5C%20%20%5C%5C%20y%3D%5Cfrac%7B%5Clog%28x%2B6%29%7D%7B%5Clog%282%29%7D-5%20%5Cend%7Bgathered%7D)
step 3
Let
![f^{(-1)}(x)=y](https://tex.z-dn.net/?f=f%5E%7B%28-1%29%7D%28x%29%3Dy)
therefore
the inverse function is