Solve the inequality: |2x−16| ≤0

Mathematics

1 answer:

ahrayia [7]3 years ago

6 0

Answer:

$x\leq 8$

Step-by-step explanation:

Work is attached!

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If 4f(x)+f(5-x)=x2<br><br> What is f(x)?

aksik [14]

We are given that $4f(x)+f(5-x)=x^2$ .

Substitute x with 5-x, then the above equation becomes:

$4f(5-x)+f(5-(5-x))=(5-x)^2$ , that is

$4f(5-x)+f(x)=(5-x)^2$

So, we have the following system of equations:

i) $4f(x)+f(5-x)=x^2$
ii) $4f(5-x)+f(x)=(5-x)^2$

multiply the first equation by -4, so that we eliminate f(5-x)'s

i) $-16f(x)-4f(5-x)=-4x^2$
ii) $4f(5-x)+f(x)=(5-x)^2$

adding the 2 equations side by side we have:

$-15f(x)=-4x^2+(5-x)^2$

expanding the binomial, and collecting same terms we have:

$-15f(x)=-4x^2+(25-10x+x^2)$

$-15f(x)=-3x^2-10x+25$

dividing by -5:

$3f(x)=\frac{3}{5}x^2+2x-5$

dividing by 3:

$\displaystyle{f(x)= \frac{1}{5}x^2+ \frac{2}{3}x-\frac{5}{3}$

Answer: $\displaystyle{f(x)= \frac{1}{5}x^2+ \frac{2}{3}x-\frac{5}{3}$

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3 years ago

If f(x) = -2x2 + x – 5, what is f(3)?

exis [7]

F(3)=2x2-3-5

= 4-3-5

=1-5

=-4

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3 years ago

Draw a pair of opposite rays

pav-90 [236]