Answer:
![\mathrm{Therefore,\:the\:final\:solutions\:for\:}y=9-x,\:y=2x^2+4x+6\mathrm{\:are\:}](https://tex.z-dn.net/?f=%5Cmathrm%7BTherefore%2C%5C%3Athe%5C%3Afinal%5C%3Asolutions%5C%3Afor%5C%3A%7Dy%3D9-x%2C%5C%3Ay%3D2x%5E2%2B4x%2B6%5Cmathrm%7B%5C%3Aare%5C%3A%7D)
![\begin{pmatrix}x=\frac{1}{2},\:&y=\frac{17}{2}\\ x=-3,\:&y=12\end{pmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bpmatrix%7Dx%3D%5Cfrac%7B1%7D%7B2%7D%2C%5C%3A%26y%3D%5Cfrac%7B17%7D%7B2%7D%5C%5C%20x%3D-3%2C%5C%3A%26y%3D12%5Cend%7Bpmatrix%7D)
Step-by-step explanation:
Given the simultaneous equations
![y=9-x](https://tex.z-dn.net/?f=y%3D9-x)
![y\:=\:2x^2\:+\:4x\:+\:6](https://tex.z-dn.net/?f=y%5C%3A%3D%5C%3A2x%5E2%5C%3A%2B%5C%3A4x%5C%3A%2B%5C%3A6)
Subtract the equations
![y=9-x](https://tex.z-dn.net/?f=y%3D9-x)
![-](https://tex.z-dn.net/?f=-)
![\underline{y=2x^2+4x+6}](https://tex.z-dn.net/?f=%5Cunderline%7By%3D2x%5E2%2B4x%2B6%7D)
![y-y=9-x-\left(2x^2+4x+6\right)](https://tex.z-dn.net/?f=y-y%3D9-x-%5Cleft%282x%5E2%2B4x%2B6%5Cright%29)
![\mathrm{Refine}](https://tex.z-dn.net/?f=%5Cmathrm%7BRefine%7D)
![x\left(2x+5\right)=3](https://tex.z-dn.net/?f=x%5Cleft%282x%2B5%5Cright%29%3D3)
![\mathrm{Solve\:}\:x\left(2x+5\right)=3](https://tex.z-dn.net/?f=%5Cmathrm%7BSolve%5C%3A%7D%5C%3Ax%5Cleft%282x%2B5%5Cright%29%3D3)
∵ ![\mathrm{Expand\:}x\left(2x+5\right):\quad 2x^2+5x](https://tex.z-dn.net/?f=%5Cmathrm%7BExpand%5C%3A%7Dx%5Cleft%282x%2B5%5Cright%29%3A%5Cquad%202x%5E2%2B5x)
![\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubtract%5C%3A%7D3%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D)
![2x^2+5x-3=3-3](https://tex.z-dn.net/?f=2x%5E2%2B5x-3%3D3-3)
![\mathrm{Solve\:with\:the\:quadratic\:formula}](https://tex.z-dn.net/?f=%5Cmathrm%7BSolve%5C%3Awith%5C%3Athe%5C%3Aquadratic%5C%3Aformula%7D)
![\mathrm{Quadratic\:Equation\:Formula:}](https://tex.z-dn.net/?f=%5Cmathrm%7BQuadratic%5C%3AEquation%5C%3AFormula%3A%7D)
![\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3Aa%5C%3Aquadratic%5C%3Aequation%5C%3Aof%5C%3Athe%5C%3Aform%5C%3A%7Dax%5E2%2Bbx%2Bc%3D0%5Cmathrm%7B%5C%3Athe%5C%3Asolutions%5C%3Aare%5C%3A%7D)
![x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
![\mathrm{For\:}\quad a=2,\:b=5,\:c=-3:\quad x_{1,\:2}=\frac{-5\pm \sqrt{5^2-4\cdot \:2\left(-3\right)}}{2\cdot \:2}v\\](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7D%5Cquad%20a%3D2%2C%5C%3Ab%3D5%2C%5C%3Ac%3D-3%3A%5Cquad%20x_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-5%5Cpm%20%5Csqrt%7B5%5E2-4%5Ccdot%20%5C%3A2%5Cleft%28-3%5Cright%29%7D%7D%7B2%5Ccdot%20%5C%3A2%7Dv%5C%5C)
![x=\frac{-5+\sqrt{5^2-4\cdot \:2\left(-3\right)}}{2\cdot \:2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-5%2B%5Csqrt%7B5%5E2-4%5Ccdot%20%5C%3A2%5Cleft%28-3%5Cright%29%7D%7D%7B2%5Ccdot%20%5C%3A2%7D)
![=\frac{-5+\sqrt{5^2+4\cdot \:2\cdot \:3}}{2\cdot \:2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-5%2B%5Csqrt%7B5%5E2%2B4%5Ccdot%20%5C%3A2%5Ccdot%20%5C%3A3%7D%7D%7B2%5Ccdot%20%5C%3A2%7D)
![=\frac{-5+\sqrt{49}}{2\cdot \:2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-5%2B%5Csqrt%7B49%7D%7D%7B2%5Ccdot%20%5C%3A2%7D)
![=\frac{-5+\sqrt{49}}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-5%2B%5Csqrt%7B49%7D%7D%7B4%7D)
![=\frac{-5+7}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-5%2B7%7D%7B4%7D)
![=\frac{2}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2%7D%7B4%7D)
![=\frac{1}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7D)
Similarly,
![x=\frac{-5-\sqrt{5^2-4\cdot \:2\left(-3\right)}}{2\cdot \:2}:\quad -3](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-5-%5Csqrt%7B5%5E2-4%5Ccdot%20%5C%3A2%5Cleft%28-3%5Cright%29%7D%7D%7B2%5Ccdot%20%5C%3A2%7D%3A%5Cquad%20-3)
![\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}](https://tex.z-dn.net/?f=%5Cmathrm%7BThe%5C%3Asolutions%5C%3Ato%5C%3Athe%5C%3Aquadratic%5C%3Aequation%5C%3Aare%3A%7D)
![x=\frac{1}{2},\:x=-3](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B2%7D%2C%5C%3Ax%3D-3)
![\mathrm{Plug\:the\:solutions\:}x=\frac{1}{2},\:x=-3\mathrm{\:into\:}y=9-x](https://tex.z-dn.net/?f=%5Cmathrm%7BPlug%5C%3Athe%5C%3Asolutions%5C%3A%7Dx%3D%5Cfrac%7B1%7D%7B2%7D%2C%5C%3Ax%3D-3%5Cmathrm%7B%5C%3Ainto%5C%3A%7Dy%3D9-x)
![\mathrm{For\:}y=9-x\mathrm{,\:subsitute\:}x\mathrm{\:with\:}\frac{1}{2}:\quad y=\frac{17}{2}](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7Dy%3D9-x%5Cmathrm%7B%2C%5C%3Asubsitute%5C%3A%7Dx%5Cmathrm%7B%5C%3Awith%5C%3A%7D%5Cfrac%7B1%7D%7B2%7D%3A%5Cquad%20y%3D%5Cfrac%7B17%7D%7B2%7D)
![\mathrm{For\:}y=9-x\mathrm{,\:subsitute\:}x\mathrm{\:with\:}-3:\quad y=12](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7Dy%3D9-x%5Cmathrm%7B%2C%5C%3Asubsitute%5C%3A%7Dx%5Cmathrm%7B%5C%3Awith%5C%3A%7D-3%3A%5Cquad%20y%3D12)
![\mathrm{Therefore,\:the\:final\:solutions\:for\:}y=9-x,\:y=2x^2+4x+6\mathrm{\:are\:}](https://tex.z-dn.net/?f=%5Cmathrm%7BTherefore%2C%5C%3Athe%5C%3Afinal%5C%3Asolutions%5C%3Afor%5C%3A%7Dy%3D9-x%2C%5C%3Ay%3D2x%5E2%2B4x%2B6%5Cmathrm%7B%5C%3Aare%5C%3A%7D)
![\begin{pmatrix}x=\frac{1}{2},\:&y=\frac{17}{2}\\ x=-3,\:&y=12\end{pmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bpmatrix%7Dx%3D%5Cfrac%7B1%7D%7B2%7D%2C%5C%3A%26y%3D%5Cfrac%7B17%7D%7B2%7D%5C%5C%20x%3D-3%2C%5C%3A%26y%3D12%5Cend%7Bpmatrix%7D)
Answer:
D
Step-by-step explanation:
The square root of 64 = 8 and the square root of -289 is 17i, and they are subtracting.
No it’s 5/24 he’s or she is wrong
Answer:
4√2 units (Answer C).
Step-by-step explanation:
Going from the seat at (-4,6) to the one at (0,10), x increases by 4 units and y increases by 4 units. We need to use the distance formula to determine how far apart these seats are.
d = √(change in x)^2 + (change in y)^2 ).
That works out to:
d = √(4^2 + 4^2) = √(32) = 4√2 units (Answer C).
Slope (3) y intercept (0,-2)