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solmaris [256]
3 years ago
5

Jack, Jill, and Ron share a 2-bedroom apartment. Rent is represented by R. The water bill is $20 per person. The electric bill i

s $250 a month. Jill will be picking up the water bill for everyone as well as half of the electric. Ron will be paying the other half of the electric bill as well as his third of the rent. Jack will be paying Jill's portion of the rent as well as his own. 
Match each person with the appropriate algebraic expression.-abcd -abcd 185-abcd -abcd Jill's paymentJack's paymentRon's paymentNo Match
Mathematics
1 answer:
erastovalidia [21]3 years ago
4 0
Jack: 2R/3
Jill: 3 • 20 + 0.5 • 250 = 185
Ron: R/3 + 125

hope that helps

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For the function g(x)=3-8(1/4)^2-x
Reika [66]

Using function concepts, it is found that:

  • a) The y-intercept is y = 2.5.
  • b) The horizontal asymptote is x = 3.
  • c) The function is decreasing.
  • d) The domain is (-\infty,\infty) and the range is (-\infty,3).
  • e) The graph is given at the end of the answer.

------------------------------------

The given function is:

g(x) = 3 - 8\left(\frac{1}{4}\right)^{2-x}

------------------------------------

Question a:

The y-intercept is g(0), thus:

g(0) = 3 - 8\left(\frac{1}{4}\right)^{2-0} = 3 - 8\left(\frac{1}{4}\right)^{2} = 3 - \frac{8}{16} = 3 - 0.5 = 2.5

The y-intercept is y = 2.5.

------------------------------------

Question b:

The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.

\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2+\infty} = 3 - 8\left(\frac{1}{4}\right)^{\infty} = 3 - 8\frac{1^{\infty}}{4^{\infty}} = 3 -0 = 3

--------------------------------------------------

\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2-\infty} = 3 - 8\left(\frac{1}{4}\right)^{-\infty} = 3 - 8\times 4^{\infty} = 3 - \infty = -\infty

Thus, the horizontal asymptote is x = 3.

--------------------------------------------------

Question c:

The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.

--------------------------------------------------

Question d:

  • Exponential function has no restrictions in the domain, so it is all real values, that is (-\infty,\infty).
  • From the limits in item c, the range is: (-\infty,3)

--------------------------------------------------

The sketching of the graph is given appended at the end of this answer.

A similar problem is given at brainly.com/question/16533631

8 0
2 years ago
6.) The line that passes through point (-2,3) and (6,y) has a slope of. What is the value of “y,?
WITCHER [35]
What is the slope? We need the slope to find y
7 0
3 years ago
PLZ HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!During a 4-month-long drought, the water level in a lake changed
Dafna1 [17]

Answer:

-78

Step-by-step explanation:

4 Months is -312 so dividing by 4 will give the decrease of one month:

-312 ÷ 4 = -78

3 0
3 years ago
On a test of 80 problems, Bill got 75% of the problems correct. How many question did he get correct?​
Pavel [41]

Answer: 60

Step-by-step explanation:

75% of 80 is 60.

Multiply 80 by .75 to get the answer.

6 0
3 years ago
A mother invests $7000 in a bank account at the time of her daughter's birth. The interest is 18) compounded quarterly at a rate
Alex

well, from birth to your twentieth birthday that'll just be 20 years, so

~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &20 \end{cases} \\\\\\ A=7000\left(1+\frac{0.08}{4}\right)^{4\cdot 20}\implies A=7000(1.02)^{80}\implies A\approx 34128.07

5 0
2 years ago
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