Answer:f(x)=x2−6x−9 f ( x ) = x 2 - 6 x - 9. Replace f(x) f ( x ) with y y . y=x2−6x−9 y = x 2 - 6 x - 9. Interchange the variables. x=y2−6y−9 x = y 2 - 6 y - 9.
Step-by-step explanation:
Answer:
35 students
Step-by-step explanation:
If there are 4 girls, then there are 3 boys
You will multiply both by 5 to get 20
So 3×5 is 15
20+15 = 35
Answer:
-3/2
Step-by-step explanation:
Answer:
x =
y + 20
[Given]
4x - 6y = 20
[Add 6y to both sides of the equation]
4x = 6y + 20
[Divide both sides of the equation by 4]
x =
y + 20
[Simplify
, both 6 and 4 are divisible by 2]
x =
y + 20
Answer:
![x=-0.3](https://tex.z-dn.net/?f=x%3D-0.3)
![x=-11.7](https://tex.z-dn.net/?f=x%3D-11.7)
Step-by-step explanation:
![4x^2+24x+13=2x^2+6\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\4x^2+24x+13-6=2x^2+6-6\\Simplify\\4x^2+24x+7=2x^2\\\mathrm{Subtract\:}2x^2\mathrm{\:from\:both\:sides}\\4x^2+24x+7-2x^2=2x^2-2x^2\\Simplify\\2x^2+24x+7=0\\\mathrm{Solve\:with\:the\:quadratic\:formula}\\Quadratic\:Equation\:Formula\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=4x%5E2%2B24x%2B13%3D2x%5E2%2B6%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D6%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C4x%5E2%2B24x%2B13-6%3D2x%5E2%2B6-6%5C%5CSimplify%5C%5C4x%5E2%2B24x%2B7%3D2x%5E2%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D2x%5E2%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C4x%5E2%2B24x%2B7-2x%5E2%3D2x%5E2-2x%5E2%5C%5CSimplify%5C%5C2x%5E2%2B24x%2B7%3D0%5C%5C%5Cmathrm%7BSolve%5C%3Awith%5C%3Athe%5C%3Aquadratic%5C%3Aformula%7D%5C%5CQuadratic%5C%3AEquation%5C%3AFormula%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%5Cx_%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=24,\:c=7:\quad x_{1,\:2}=\frac{-24\pm \sqrt{24^2-4\cdot \:2\cdot \:7}}{2\cdot \:2}\\x=\frac{-24+\sqrt{24^2-4\cdot \:2\cdot \:7}}{2\cdot \:2}:\quad \frac{-12+\sqrt{130}}{2}\\x=\frac{-24-\sqrt{24^2-4\cdot \:2\cdot \:7}}{2\cdot \:2}:\quad -\frac{12+\sqrt{130}}{2}\\The\:solutions\:to\:the\:quadratic\:equation\:are:\\x=\frac{-12+\sqrt{130}}{2},\:x=-\frac{12+\sqrt{130}}{2}\\\\quad x=-0.29912\ ,\:x=-11.70087](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7D%5Cquad%20a%3D2%2C%5C%3Ab%3D24%2C%5C%3Ac%3D7%3A%5Cquad%20x_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-24%5Cpm%20%5Csqrt%7B24%5E2-4%5Ccdot%20%5C%3A2%5Ccdot%20%5C%3A7%7D%7D%7B2%5Ccdot%20%5C%3A2%7D%5C%5Cx%3D%5Cfrac%7B-24%2B%5Csqrt%7B24%5E2-4%5Ccdot%20%5C%3A2%5Ccdot%20%5C%3A7%7D%7D%7B2%5Ccdot%20%5C%3A2%7D%3A%5Cquad%20%5Cfrac%7B-12%2B%5Csqrt%7B130%7D%7D%7B2%7D%5C%5Cx%3D%5Cfrac%7B-24-%5Csqrt%7B24%5E2-4%5Ccdot%20%5C%3A2%5Ccdot%20%5C%3A7%7D%7D%7B2%5Ccdot%20%5C%3A2%7D%3A%5Cquad%20-%5Cfrac%7B12%2B%5Csqrt%7B130%7D%7D%7B2%7D%5C%5CThe%5C%3Asolutions%5C%3Ato%5C%3Athe%5C%3Aquadratic%5C%3Aequation%5C%3Aare%3A%5C%5Cx%3D%5Cfrac%7B-12%2B%5Csqrt%7B130%7D%7D%7B2%7D%2C%5C%3Ax%3D-%5Cfrac%7B12%2B%5Csqrt%7B130%7D%7D%7B2%7D%5C%5C%5C%5Cquad%20x%3D-0.29912%5C%20%2C%5C%3Ax%3D-11.70087)