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2 years ago

HELP TIMED! Piece Wise functions

Mathematics

1 answer:

BigorU [14]2 years ago

6 0

Answer:

Last Option: (-∞, 4) U (4, ∞)

Step-by-step explanation:

Domain is the set of x-values that can be inputted into function f(x).

We see that our x-values span all numbers except x = -4. Therefore, it is not included in our domain:

(-∞, 4) U (4, ∞)

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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

A store owner will order iPads for local schools. The relationship between x, the number of boxes he will order, and y, the numb

wolverine [178]

Answer:

y, ‎y = ‎15x.

Step-by-step explanation:

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2 years ago

if you take out a loan that cost $130.50 over 9 years and interest rate of 10% how much total was the loan for

Tom [10]

130.50x9x.010= 11.75

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3 years ago

I NEED THIS ANSWER A S A P

borishaifa [10]

Answer:

Step-by-step explanation:

if wrong then pls contact me in the comment section

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2 years ago

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Factor the expression. 4d + 12 Enter your answers in the boxes.

Dmitry_Shevchenko [17]

4d + 12 = 4(d + 3)
Basically, you just need to determine what 4d and 12 have in common. In this case, they both divide evenly by 4. Therefore 4 (d + 3) = 4d + 12 according to the distributive property.

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3 years ago

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