The solutions are (2.1925, 5.1925) and (-3.1925, -0.1925)
<em><u>Solution:</u></em>
Given that,
![y = x + 3 ------- eqn 1\\\\y = x^2 + 2x - 4 ----- eqn 2](https://tex.z-dn.net/?f=y%20%3D%20x%20%2B%203%20-------%20eqn%201%5C%5C%5C%5Cy%20%3D%20x%5E2%20%2B%202x%20-%204%20%20-----%20eqn%202)
<em><u>We have to substitute eqn 1 in eqn 2</u></em>
![x + 3 = x^2 + 2x - 4](https://tex.z-dn.net/?f=x%20%2B%203%20%3D%20x%5E2%20%2B%202x%20-%204)
![\mathrm{Switch\:sides}\\\\x^2+2x-4=x+3\\\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\\\x^2+2x-4-3=x+3-3\\\\\mathrm{Simplify}\\\\x^2+2x-7=x\\\\\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}\\\\x^2+2x-7-x=x-x\\\\\mathrm{Simplify}\\\\x^2+x-7=0](https://tex.z-dn.net/?f=%5Cmathrm%7BSwitch%5C%3Asides%7D%5C%5C%5C%5Cx%5E2%2B2x-4%3Dx%2B3%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D3%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5Cx%5E2%2B2x-4-3%3Dx%2B3-3%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5Cx%5E2%2B2x-7%3Dx%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7Dx%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5Cx%5E2%2B2x-7-x%3Dx-x%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5Cx%5E2%2Bx-7%3D0)
![\mathrm{Solve\:with\:the\:quadratic\:formula}\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=1,\:c=-7\\\\x =\frac{-1\pm \sqrt{1^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSolve%5C%3Awith%5C%3Athe%5C%3Aquadratic%5C%3Aformula%7D%5C%5C%5C%5C%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%5C%5C%5C%5Cx%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5C%5C%5C%5Cmathrm%7BFor%5C%3A%7D%5Cquad%20a%3D1%2C%5C%3Ab%3D1%2C%5C%3Ac%3D-7%5C%5C%5C%5Cx%20%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B1%5E2-4%5Ccdot%20%5C%3A1%5Cleft%28-7%5Cright%29%7D%7D%7B2%5Ccdot%20%5C%3A1%7D)
![x = \frac{-1 \pm \sqrt{ 1 + 28}}{2}\\\\x = \frac{ -1 \pm \sqrt{29}}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-1%20%5Cpm%20%5Csqrt%7B%201%20%2B%2028%7D%7D%7B2%7D%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B%20-1%20%5Cpm%20%5Csqrt%7B29%7D%7D%7B2%7D)
![x = \frac{ -1 \pm 5.385 }{2}\\\\We\ have\ two\ solutions\\\\x = \frac{ -1 + 5.385 }{2}\\\\x = 2.1925](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B%20-1%20%5Cpm%205.385%20%7D%7B2%7D%5C%5C%5C%5CWe%5C%20have%5C%20two%5C%20solutions%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B%20-1%20%2B%205.385%20%7D%7B2%7D%5C%5C%5C%5Cx%20%3D%202.1925)
![Also\\\\x = \frac{ -1 - 5.385 }{2}\\\\x = -3.1925](https://tex.z-dn.net/?f=Also%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B%20-1%20-%205.385%20%7D%7B2%7D%5C%5C%5C%5Cx%20%3D%20-3.1925)
Substitute x = 2.1925 in eqn 1
y = 2.1925 + 3
y = 5.1925
Substitute x = -3.1925 in eqn 1
y = -3.1925 + 3
y = -0.1925
Thus the solutions are (2.1925, 5.1925) and (-3.1925, -0.1925)
Answer: c
Step-by-step explanation:
The upper comment is correct
y=x+5
Step-by-step explanation:
The opposite of y is x axis
Answer:
Commission is $45.00
Weekly salary was $150.00 + $45.00
She earned $195.00 for her paycheck
Step-by-step explanation: