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1 year ago

Help me answer as soon as possible, thank you!A and B only

Mathematics

1 answer:

MArishka [77]1 year ago

3 0

Answer:

(a)4

(b)7

Explanation:

Given f(x) and g(x) defined below:

$\begin{gathered} f(x)=\{(3,2),(5,1),(7,4),(9,3),(11,5)\} \\ g(x)=\{(1,3),(2,5),(3,7),(4,9),(5,11)\} \end{gathered}$

(a) f(g(3))

$\begin{gathered} g(3)=7 \\ f\lbrack g(3)\rbrack=f(7)=4 \\ \implies f\lbrack g(3)\rbrack=4 \end{gathered}$

The value of f(g(3)) is 4.

(b) (g o f)(9)

$\begin{gathered} (g\circ f)(9)=g\lbrack f(9)\rbrack \\ f(9)=3 \\ g\lbrack f(9)\rbrack=g(3)=7 \\ \implies(g\circ f)(9)=7 \end{gathered}$

The value of (g o f)(9) is 7.

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What is the equation of the line that represents the horizontal asymptote of the function f(x)=25,000(1+0.025)^(x)?

posledela

Answer:

The answer is below

Step-by-step explanation:

The horizontal asymptote of a function f(x) is gotten by finding the limit as x ⇒ ∞ or x ⇒ -∞. If the limit gives you a finite value, then your asymptote is at that point.

$\lim_{x \to \infty} f(x)=A\\\\or\\\\ \lim_{x \to -\infty} f(x)=A\\\\where\ A\ is\ a\ finite\ value.\\\\Given\ that \ f(x) =25000(1+0.025)^x\\\\ \lim_{x \to \infty} f(x)= \lim_{x \to \infty} [25000(1+0.025)^x]= \lim_{x \to \infty} [25000(1.025)^x]\\=25000 \lim_{x \to \infty} [(1.025)^x]=25000(\infty)=\infty\\\\ \lim_{x \to -\infty} f(x)= \lim_{x \to -\infty} [25000(1+0.025)^x]= \lim_{x \to -\infty} [25000(1.025)^x]\\=25000 \lim_{x \to -\infty} [(1.025)^x]=25000(0)=0\\\\$

$Since\ \lim_{x \to -\infty} f(x)=0\ is\ a\ finite\ value,hence:\\\\Hence\ the\ horizontal\ asymtotes\ is\ at\ y=0$

5 0

3 years ago

Which statements about the graphs of functions g(x) = 4x and f(x) = x are true? Select all that apply.

Makovka662 [10]

Answer:

Step-by-step explanation:

5 0

3 years ago

a woman has $28,000. part is invested for one year in a certificate of deposit paying 7% interest, and the remaining amount in c

alexira [117]

Answer:

Amount invested at 7% = 16000

Amount invested at 9% = 12000

Step-by-step explanation:

Let x be the amount invested at 7% and y be the amount invested at 9%.

Since the total amount invested is $28000, therefore, we can set up the first equation as:

$x+y=28000$

Secondly, we are give that sum of two investments is $2200. Therefore, we can write the second equation as:

$0.07x+0.09y=2200$

Now we need to solve these two equations to get the values of x and y.

First of all, we multiply the second equation with 100 in order to get rid of decimal values.

$(0.07x+0.09y)*100=2200*100\\7x+9y=220000$

Let us use substitution method here. First of all we will solve for y from first equation and plug that into second equation.

$y=28000-x$

$7x+9(28000-x)=220000\\7x+252000-9x=220000\\-2x=-32000\\x=16000$

Therefore, amount invested at 7% is $16000 and amount invested at 9% is 28000-16000=$12000.

7 0

3 years ago

Which expression is equivalent to (7^3)^−2?

Verdich [7]

Use the exponent property regarding a power to power. When you have a power to power, you multiply both powers. In this case, you will get 7^-6. That is equivalent to the first option. I hope this helped, though it is a bit late xD.

8 0

3 years ago

Can somebody help me asap.

ehidna [41]

Answer:

Step-by-step explanation:

1) m∠1 +m∠2 + m∠3 = m∠LAM (Angle addition postulate)

2) m∠1 + m∠2 + m∠3 = 180 (def. of straight angle)

3) y║z (Given)

4) ∠1 ≅ ∠5 (alternate interior angles theorem)

5) ∠3 ≅ ∠6 (alternate interior angles theorem)

6) Since m∠1 + m∠2 + m∠3 = 180

m∠5 + m∠2 + m∠6 = 180

Hence proved.

7 0

3 years ago