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3 years ago

Let f(x) = 16 - x^2, g(x) = 4 - x. Find (fg)(x) and its domain.

Mathematics

1 answer:

timofeeve [1]3 years ago

5 0

Answer:

(fg)(x) = x^3-4x^2-16x+64, D: All Real Numbers

Step-by-step explanation:

(fg)(x) = f(x) x g(x)

= 16-x^2(4-x)

=64-16x-4x+x^3

(fg)(x) = x^3-4x^2-16x+64

Domain is all real numbers because you can substitute any real number for x and the function would still work.

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3 4/7 minus 2 1/5 by rounding to the nearest half

mylen [45]

Answer:

$1 \frac{13}{35}$

Step-by-step explanation:

$3 \frac{4}{7} - 2 \frac{1}{5}$

you can solve for the fractions first, but you have to give them a common denominator

$\frac{20}{35}- \frac{7}{35}$

$= \frac{13}{35}$ which is in simplest form

then solve for the whole numbers

3-2=1

therefore, the answer is $1 \frac{13}{35}$

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3 years ago

I like a girl how do i tell her ?

ZanzabumX [31]

Answer:

Step-by-step explanation:

Just truely be open about your feelings, don't try and sugarcoat it, or leave things out, just be honest with her and tell her straight up, politely of course.

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2 years ago

Read 2 more answers

What is the fourth term in the binomial expansion (a+b)^6)

Dafna11 [192]

Answer:

$20a^3b^3$

Step-by-step explanation:

<u>Binomial Series</u>

$(a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n$

<u>Factorial</u> is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Example: 4! = 4 × 3 × 2 × 1

Therefore, the fourth term in the binomial expansion (a + b)⁶ is:

$\implies \dfrac{n!}{3!(n-3)!}a^{n-3}b^3$

$\implies \dfrac{6!}{3!(6-3)!}a^{6-3}b^3$

$\implies \dfrac{6!}{3!3!}a^{3}b^3$

$\implies \left(\dfrac{6 \times 5 \times 4 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}{3 \times 2 \times 1 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}\right)a^{3}b^3$

$\implies \left(\dfrac{120}{6}\right)a^{3}b^3$

$\implies 20a^3b^3$

7 0

2 years ago

PLS SOMEONE HELP PLSSS

Sav [38]

Answer:

x=17

Step-by-step explanation:

ok so since lines PR and RQ are congruent (we know because of the lines on them), that means angles P and Q are also equal.

now we can set up the equation to find x like this:

29+29+(8x-14)=180 (180 because the three angles of a triangle always equal 180)

x=17

8 0

3 years ago

Lucia is making invisibility potions. Each potion requires 2 eyes of newt. How many invisibility potions can Lucia make with 16

____ [38]

Lucia can make 8 invisibility potions total!
she has 16 newt eyes overall and only two are required for one option
sooo
she can make 8 potions.

hope this helps!

4 0

3 years ago