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
stira [4]
3 years ago
9

Sergei buys a rectangular rug for his living room. He measures the diagonal of the rug to be 18 feet. The length of the rug is 3

feet longer than the width.
What are the approximate dimensions of the rug? Round each dimension to the nearest tenth of a foot.

10.4 feet by 7.4 feet
11.1 feet by 8.1 feet
13.4 feet by 10.4 feet
14.1 feet by 11.1 feet
Mathematics
2 answers:
Novosadov [1.4K]3 years ago
7 0

Answer:

D. 14.1 feet by 11.1 feet.

Step-by-step explanation:

Let w be the width of the rug.

We have been given that the length of the rug is 3 feet longer than the width. So the length of the rug would be w+3.

We have been given that the measure of the diagonal of the rug to be 18 feet. To find the width of rug we will use Pythagoras theorem as rug is rectangular.

w^2+(w+3)^2=18^2

w^2+w^2+6w+9=324

2w^2+6w+9=324

2w^2+6w+9-324=0

2w^2+6w-315=0

We will use quadratic formula to solve for w.

w=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

w=\frac{-6\pm \sqrt{6^2-4*2*-315}}{2*2}

w=\frac{-6\pm \sqrt{36+2520}}{4}

w=\frac{-6\pm \sqrt{2556}}{4}

w=\frac{-6}{4}\pm \frac{\sqrt{2556}}{4}

w=\frac{-6}{4}\pm \frac{50.55689863}{4}

Since the width cannot be negative, so width of the rug would be:

w=\frac{-6}{4}+\frac{50.55689863}{4}

w=-1.5+12.639224659

w=11.139224\approx 11.1

Therefore, the width of rug would be 11.1 feet.

Since length of rug is 3 feet longer than width, so width of the rug would be 11.1+3=14.1,

Therefore, the option D is the correct choice.

ivanzaharov [21]3 years ago
3 0

14.1 feet by 11.1 feet is the correct one

You might be interested in
The amazon rainforest covered 6.42 million square kilometers in 1994. In 2014, it covered 50/59 as much. Which is closest to the
USPshnik [31]

the answer is b, just divide 50 by 59 and multiply that sum to 6.4

3 0
3 years ago
Read 2 more answers
What is 119 over 8 in its simplest form?
ivolga24 [154]
119/8 is already in simplest form. However, if you attempt to change it to a mixed number the correct answer would be 14 7/8 (7 over 8).

Hope I helped!
3 0
3 years ago
Use 1/2ab sin C formula pls
Harman [31]

Step-by-step explanation:

area =  \frac{1}{2} a.b \sin(C)  \\ from \:cosine \: rule \\  {c}^{2}  =  {a}^{2}  +  {b}^{2}  - 2a.b \cos(C)  \\ 36 = 144 + 81 - (2 \times 12 \times 9) \cos(C)  \\ 189 = 216 \cos(C)  \\  \cos(C)  = 0.875 \\ C =  \cos {}^{ - 1} (0.875) \\ C = 28.96 \degree \\ area =  \frac{1}{2}  \times 144 \times 9 \times  \sin(28.96 \degree)  \\ area = 313.8 \: sq \: units

3 0
3 years ago
Solve for x in simplest form.<br> 2=1/2(7x-4)
Sladkaya [172]

Answer:1.1428 is the answer

Step-by-step explanation: Distribute using (Pemdas) 2nd find x alone and divide by 4

6 0
3 years ago
Please help! Thank you so much!!!
docker41 [41]

Answer:

m : the slope of the line.

( x, y ) : any point on the line.

( x1, y1 ) : a given point on the line.

8 0
2 years ago
Other questions:
  • Adison earned $25 mowing her neighbor's lawn. Then she loaned her friend $18, and got $50 from her grandmother for her birthday.
    10·1 answer
  • A realtor sold a house for $75,000 and earned a commission of $4500. Which proportion could be used to find the amount of commis
    10·1 answer
  • 3(у - 3) - 2(у 4) = 4​
    13·2 answers
  • What is the volume of a rectangular prism with a length of 5 ft, width of 6 ft and a height of 4.5 ft ?
    5·1 answer
  • The sun of three numbers is 19. The sum of twice the first number, 5 times the second number, and 6 times the third number is 77
    13·1 answer
  • (50 Points)
    5·1 answer
  • A conference will take place in a large hotel meeting room. The organizers of the conference have created a drawing for how to a
    9·1 answer
  • Part A: Explain why the x-coordinates of the points where the graphs of the equations y = ^2−x and y = ^4x + 3 intersect are the
    10·1 answer
  • A ​30-inch board is to be cut into three pieces so that the second piece is 4 times as long as the first piece and the third pie
    10·1 answer
  • 2. Every December, Tagaytay City Science National High School is sponsoring a
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!