1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
BaLLatris [955]
3 years ago
5

The length of a banquet table is 4 feet longer than 6 times its width. If the perimeter is 78 feet, what are the dimensions of t

he table?
Mathematics
1 answer:
harina [27]3 years ago
7 0
Hello,
2(l+w)=78
Divided 2 from both side
2(l+w)/2=78/2
l+w=39 feet

l=6w+4
Replace l with 6w+4

6w+4+w=39
7w+4=39
Subtract 4 from both side
7w=35
Divided 7 from both side
w=5 feet
l=6w+4
l=6(5)+4
l=30+4
l=34 feet. As a result, the length of the rectangle is 34 feet and the width of rectangle is 5 feet. Hope it help!
You might be interested in
How do you solve this limit of a function math problem? ​
hram777 [196]

If you know that

e=\displaystyle\lim_{x\to\pm\infty}\left(1+\frac1x\right)^x

then it's possible to rewrite the given limit so that it resembles the one above. Then the limit itself would be some expression involving e.

For starters, we have

\dfrac{3x-1}{3x+3}=\dfrac{3x+3-4}{3x+3}=1-\dfrac4{3x+3}=1-\dfrac1{\frac34(x+1)}

Let y=\dfrac34(x+1). Then as x\to\infty, we also have y\to\infty, and

2x-1=2\left(\dfrac43y-1\right)=\dfrac83y-2

So in terms of y, the limit is equivalent to

\displaystyle\lim_{y\to\infty}\left(1-\frac1y\right)^{\frac83y-2}

Now use some of the properties of limits: the above is the same as

\displaystyle\left(\lim_{y\to\infty}\left(1-\frac1y\right)^{-2}\right)\left(\lim_{y\to\infty}\left(1-\frac1y\right)^y\right)^{8/3}

The first limit is trivial; \dfrac1y\to0, so its value is 1. The second limit comes out to

\displaystyle\lim_{y\to\infty}\left(1-\frac1y\right)^y=e^{-1}

To see why this is the case, replace y=-z, so that z\to-\infty as y\to\infty, and

\displaystyle\lim_{z\to-\infty}\left(1+\frac1z\right)^{-z}=\frac1{\lim\limits_{z\to-\infty}\left(1+\frac1z\right)^z}=\frac1e

Then the limit we're talking about has a value of

\left(e^{-1}\right)^{8/3}=\boxed{e^{-8/3}}

# # #

Another way to do this without knowing the definition of e as given above is to take apply exponentials and logarithms, but you need to know about L'Hopital's rule. In particular, write

\left(\dfrac{3x-1}{3x+3}\right)^{2x-1}=\exp\left(\ln\left(\frac{3x-1}{3x+3}\right)^{2x-1}\right)=\exp\left((2x-1)\ln\frac{3x-1}{3x+3}\right)

(where the notation means \exp(x)=e^x, just to get everything on one line).

Recall that

\displaystyle\lim_{x\to c}f(g(x))=f\left(\lim_{x\to c}g(x)\right)

if f is continuous at x=c. \exp(x) is continuous everywhere, so we have

\displaystyle\lim_{x\to\infty}\left(\frac{3x-1}{3x+3}\right)^{2x-1}=\exp\left(\lim_{x\to\infty}(2x-1)\ln\frac{3x-1}{3x+3}\right)

For the remaining limit, write

\displaystyle\lim_{x\to\infty}(2x-1)\ln\frac{3x-1}{3x+3}=\lim_{x\to\infty}\frac{\ln\frac{3x-1}{3x+3}}{\frac1{2x-1}}

Now as x\to\infty, both the numerator and denominator approach 0, so we can try L'Hopital's rule. If the limit exists, it's equal to

\displaystyle\lim_{x\to\infty}\frac{\frac{\mathrm d}{\mathrm dx}\left[\ln\frac{3x-1}{3x+3}\right]}{\frac{\mathrm d}{\mathrm dx}\left[\frac1{2x-1}\right]}=\lim_{x\to\infty}\frac{\frac4{(x+1)(3x-1)}}{-\frac2{(2x-1)^2}}=-2\lim_{x\to\infty}\frac{(2x-1)^2}{(x+1)(3x-1)}=-\frac83

and our original limit comes out to the same value as before, \exp\left(-\frac83\right)=\boxed{e^{-8/3}}.

3 0
3 years ago
How many times greater is one gallon than one quart. PLS MY BRAIN IS ABOUT TO EXPLODE IM TO TIRED FOR PRACTICE.
gavmur [86]
A gallon is 4 times greater than a quart
3 0
2 years ago
Read 2 more answers
What is 20 plus 2 /6
Leya [2.2K]
Answer:
20 1/3
Explanation:
4 0
3 years ago
Mrs. Cazares went shopping for candy for her students. She bought 6 bags of candy. She had a coupon for $6 off her purchase. If
Umnica [9.8K]

Answer:

7

Step-by-step explanation:

hope you have a great day!

3 0
3 years ago
Read 2 more answers
on one day, 4 plumbers and 5 helpers earned $182. On another day, working the same number of hours and at the same rate of pay,
Elanso [62]
I hope this helps you



4plumbers +5helpers =182

5plumbers +6helpers =224



-24plumbers -30helpers =1092


25plumbers+30helpers =1120



1plumbers =28


4.28+5helpers =182



5helpers =70


1helpers=14
7 0
3 years ago
Other questions:
  • What is the solution to the following equation?
    6·2 answers
  • Sue had 4 cos of sugar. she had to make 2 batches of brownies that needs 10/16 cup of sugar she also had to make 4 batches of su
    5·1 answer
  • I got 4.9 and 40 i dont know if im right
    14·1 answer
  • Express as decimal numerals 3 946/1000
    5·2 answers
  • the ratio of one side of abc to the corresponding side of similar def is 5:8. if the perimeter of def is 96 inches, what is the
    15·1 answer
  • Given the expression below if p=-3/2 which is thr smallest subset containing the value of the expression.
    11·1 answer
  • Casey earned $220 selling baked goods. Her expenses were $2.50 per baked good. Which equation can be used to find b, the number
    9·2 answers
  • Value of the digit 3 for 2136 is​
    12·2 answers
  • The daily listening audience of an AM radio station is four times as large as that of its FM sister station. If 105,000 people l
    10·1 answer
  • Three integers have a mean of 7, a median of 6 and a range of 13.<br><br> Find the three integers.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!