Answer:
![x=4](https://tex.z-dn.net/?f=x%3D4)
Step-by-step explanation:
Given
, start by squaring both sides to work towards isolating
:
![\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5C%5Cleft%28%5Csqrt%7Bx%2B12%7D-%5Csqrt%7B2x%2B1%7D%5Cright%29%5E2%3D%5Cleft%281%5Cright%29%5E2)
Recall
and
:
![\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5C%5Cleft%28%5Csqrt%7Bx%2B12%7D-%5Csqrt%7B2x%2B1%7D%5Cright%29%5E2%3D%5Cleft%281%5Cright%29%5E2%5C%5C%5Cimplies%20x%2B12-2%5Csqrt%7B%28x%2B12%29%282x%2B1%29%7D%2B2x%2B1%3D1)
Isolate the radical:
![\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5Cx%2B12-2%5Csqrt%7B%28x%2B12%29%282x%2B1%29%7D%2B2x%2B1%3D1%5C%5C%5Cimplies%20-2%5Csqrt%7B%28x%2B12%29%282x%2B1%29%7D%3D-3x-12%5C%5C%5Cimplies%20%5Csqrt%7B%28x%2B12%29%282x%2B1%29%7D%3D%5Cfrac%7B-3x-12%7D%7B-2%7D)
Square both sides:
![\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5C%28x%2B12%29%282x%2B1%29%3D%5Cleft%28%5Cfrac%7B-3x-12%7D%7B-2%7D%5Cright%29%5E2)
Expand using FOIL and
:
![\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36](https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5C2x%5E2%2B25x%2B12%3D%5Cfrac%7B9%7D%7B4%7Dx%5E2%2B18x%2B36)
Move everything to one side to get a quadratic:
![\displaystyle-\frac{1}{4}x^2+7x-24=0](https://tex.z-dn.net/?f=%5Cdisplaystyle-%5Cfrac%7B1%7D%7B4%7Dx%5E2%2B7x-24%3D0)
Solving using the quadratic formula:
A quadratic in
has real solutions
. In
, assign values:
![\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5C%5Ca%3D-%5Cfrac%7B1%7D%7B4%7D%5C%5Cb%3D7%5C%5Cc%3D-24)
Solving yields:
![\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5Cx%3D%5Cfrac%7B-7%5Cpm%20%5Csqrt%7B7%5E2-4%5Cleft%28-%5Cfrac%7B1%7D%7B4%7D%5Cright%29%5Cleft%28-24%5Cright%29%7D%7D%7B2%5Cleft%28-%5Cfrac%7B1%7D%7B4%7D%5Cright%29%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B-7%5Cpm%20%5Csqrt%7B25%7D%7D%7B-%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C%5C%5C%5Cbegin%7Bcases%7Dx%3D%5Cfrac%7B-7%2B5%7D%7B-0.5%7D%3D%5Cfrac%7B-2%7D%7B-0.5%7D%3D%5Cboxed%7B4%7D%5C%5Cx%3D%5Cfrac%7B-7-5%7D%7B-0.5%7D%3D%5Cfrac%7B-12%7D%7B-0.5%7D%3D24%20%5C%3A%28%5Ctext%7BExtraneous%7D%29%5Cend%7Bcases%7D)
Only
works when plugged in the original equation. Therefore,
is extraneous and the only solution is ![\boxed{x=4}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%3D4%7D)
Table B could represent Relationship B
Time (weeks) 3 4 6 9
Plant growth (in.) 0.9 1.2 1.8 2.7
The correct answer between all
the choices given is the second choice or letter B. I am hoping that this
answer has satisfied your query and it will be able to help you in your
endeavor, and if you would like, feel free to ask another question.
Answer:
I think it is add 11 both sides? If it is wrong i am sooooo sorry
Step-by-step explanation:
Add 3 on both sides of the equation
3x=0
divide 3 on both sides of the equation
x=0
Answer:
54 pounds
Step-by-step explanation:
To find out how much flour is needed to make 9 cakes, we first need to find out how much much flour is needed to make 1 cake. For that, we need to divide 6 by 36. That will give you 6. Now that we know how much flour is needed to make 1 cake, we will just have to multiply 6 by 9 to find out how much flour is needed to make 9 cakes. That will give you 54 pounds, which is your final answer.