explain how to use the missing pieces strategy to compare two fractions include a diagram with your explanation

Mathematics

1 answer:

ivolga24 [154]3 years ago

4 0

T-14 for t=27 evaluate each expression for the value given

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

6 0

3 years ago

The width of a rectangle is 4 feet and the diagonal length of he rectangle is 13 feet what is the measurement is the closest to

AURORKA [14]

Answer:

The length is APPROXIMATELY equal to 12.4.

Step-by-step explanation:

Use the converse of the Pythagorean Theorem ( $a^{2}$ + $b^{2}$ = $c^{2}$ [where "c" is both the longest side and the hypotenuse]) since a rectangle's diagonals will always cut it into two right triangles: