How can I solve this equation 5x^2-2x-6=-2x^2+9x

1 answer:

wel3 years ago

3 0

Add 2x^2 to both sides
7x^2-2x-6=9x

Subtract 9x from both sides
7x^2-11x-6=0

Factor by using slip and slide
x^2-11x-42
(x-14)(x+3)
(x-14/7)(x+3/7)
(x-2)(7x+3)

Then use the Zero Product Property to find roots
x-2=0
x=2

7x+3=0
7x=-3
x=-3/7

Final answer: x=-3/7, x=2

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$\\(i)\\
\text{We know that the average rate of change of a function f(x) on inerval [a,b] is}\\
\\
f_{avg}=\frac{f(b)-f(a)}{b-a}\\
\\
\text{so using this the average rate of chang of g for x on interval }[3,7] \text{ is}\\
\\
g_{avg}=\frac{g(7)-g(3)}{7-3}\\
\\
=\frac{4-1}{4}\\
\\
=\frac{3}{4}\\
\\
\text{so average rate of change of g on interval [3,7] is }\frac{3}{4}$

$\\(ii)\\ \text{Average rate of chang of f for x on interval }[3,7] \text{ is}\\
\\
f_{avg}=\frac{f(7)-f(3)}{7-3}\\
\\
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\\
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\\
\text{so average rate of change of g on interval [3,7] is }\frac{-5}{4}$

$\\(iii)\\
\text{Since g(4)=5, so we have}\\
\\
f(g(4))=f(5)\\
\\
\text{since the value of f is 1 at x=5. so }\\
\\
f(g(4))=f(5)=1\\
\\
\text{hence we have, }f(g(4))=$ 1

$\\(iv)\\
\text{Since f(3)=5, so we have}\\
\\
g(f(3))=g(5)\\
\\
\text{since the value of g is 2 at x=5. so }\\
\\
g(f(3))=g(5)=2\\
\\
\text{hence we have, }g(f(3))=$ 2

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