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MrMuchimi
2 years ago
9

Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula?

Quadratic formula: x =
Mathematics
2 answers:
finlep [7]2 years ago
9 0

Answer:

x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)} shows correct substitution of the values a, b, and c  from the given quadratic equation  -3x^2-2x+6=0  into quadratic formula.

Step-by-step explanation:

Given: The quadratic equation -3x^2-2x+6=0

We have to show the correct substitution of the values a, b, and c from the given quadratic equation  -3x^2-2x+6=0  into quadratic formula.

The standard form of quadratic equation is ax^2+bx+c=0 then the solution of quadratic equation using quadratic formula is given as x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac} }{2a}

Consider the given  quadratic equation -3x^2-2x+6=0

Comparing with general  quadratic equation, we have

a = -3 , b = -2 , c = 6

Substitute in quadratic formula, we get,

x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}

Simplify, we have,

x_{1,2}=\frac{2\pm\sqrt{76} }{-6}

Thus, x_{1}=\frac{2+\sqrt{76} }{-6} and x_{2}=\frac{2-\sqrt{76} }{-6}

Simplify, we get,

x_1=-\frac{1+\sqrt{19}}{3},\:x_2=\frac{\sqrt{19}-1}{3}

Thus, x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)} shows correct substitution of the values a, b, and c  from the given quadratic equation  -3x^2-2x+6=0  into quadratic formula.

balandron [24]2 years ago
5 0
          ____________
2 +- <span>√-2^2 - 4(-3)(6) )
------------------------------
              2(-3)</span>
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Kevin and Marcus were comparing their ages. The same of their ages was at least 9 years but was at most 24 years. If Kevin is 6
saul85 [17]

<em><u>The inequality that represent age of marcus is:</u></em>

24\geq 6+m\geq 9

<em><u>The possible values for age of Marcus is:</u></em>

m = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18

<em><u>Solution:</u></em>

Given that,

The sum of ages of Kevin and Marcus was at least 9 years but was at most 24 years

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24\geq \text{ sum of ages } \geq 9

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Sum of ages = kevin age + marcus age

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24\geq 6+m\geq 9

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\mathrm{If}\:a\ge \:u\ge \:b\:\mathrm{then}\:a\ge \:u\quad \mathrm{and}\quad \:u\ge \:b\\\\24\ge \:6+m\quad \mathrm{and}\quad \:6+m\ge \:9\\\\Solve\ them\ separately

24\ge \:6+m\\\\\mathrm{Switch\:sides}\\\\6+m\le \:24\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\6+m-6\le \:24-6\\\\\mathrm{Simplify}\\\\m\le \:18

Now solve another inequality

6+m\ge \:9\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\6+m-6\ge \:9-6\\\\\mathrm{Simplify}\\\\m\ge \:3\\\\\mathrm{Combine\:the\:intervals}\\\\m\le \:18\quad \mathrm{and}\quad \:m\ge \:3\\\\\mathrm{Merge\:Overlapping\:Intervals}\\\\3\le \:m\le \:18

24\ge \:6+m\ge \:9\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:3\le \:m\le \:18\:\\ \:\mathrm{Interval\:Notation:}&\:\left[3,\:18\right]\end{bmatrix}

<em><u>Thus possible values for age of Marcus is:</u></em>

m = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18

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