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3 years ago

What are the steps to solve, 510=x+.21x-.19x

Mathematics

1 answer:

PtichkaEL [24]3 years ago

4 0

Answer:

500

Step-by-step explanation:

510=x+.21x-.19x

510=(1+.21-.19)X

510=1.02X

X=510/1.02

X=500

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. If α and β are the roots of

Lostsunrise [7]

Answer:

$18x^2+85x+18 = 0$

Step-by-step explanation:

Given Equation is

=> $2x^2+7x-9=0$

Comparing it with $ax^2+bx+c = 0$ , we get

=> a = 2, b = 7 and c = -9

So,

Sum of roots = α+β = $-\frac{b}{a}$

α+β = -7/2

Product of roots = αβ = c/a

αβ = -9/2

Now, Finding the equation whose roots are:

α/β ,β/α

Sum of Roots = $\frac{\alpha }{\beta } + \frac{\beta }{\alpha }$

Sum of Roots = $\frac{\alpha^2+\beta^2 }{\alpha \beta }$

Sum of Roots = $\frac{(\alpha+\beta )^2-2\alpha\beta }{\alpha\beta }$

Sum of roots = $(\frac{-7}{2} )^2-2(\frac{-9}{2} ) / \frac{-9}{2}$

Sum of roots = $\frac{49}{4} + 9 /\frac{-9}{2}$

Sum of Roots = $\frac{49+36}{4} / \frac{-9}{2}$

Sum of roots = $\frac{85}{4} * \frac{2}{-9}$

Sum of roots = S = $-\frac{85}{18}$

Product of Roots = $\frac{\alpha }{\beta } \frac{\beta }{\alpha }$

Product of Roots = P = 1

The Quadratic Equation is:

=> $x^2-Sx+P = 0$

=> $x^2 - (-\frac{85}{18} )x+1 = 0$

=> $x^2 + \frac{85}{18}x + 1 = 0$

=> $18x^2+85x+18 = 0$

This is the required quadratic equation.

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