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
12345 [234]
3 years ago
13

Tonya has a rectangular rug with an area of 21 square feet. The rug is 4 feet longer than it is wide. Create an equation that ca

n be used to determine the length and the width of the rug. Tonya adds a 1.5-foot boarder all the way around the rug. What is the area of the enlarged rug? Show all work.
Mathematics
1 answer:
marissa [1.9K]3 years ago
7 0

a) The equations to determine the length and the width of the rug are

l = 4 + w and l × w = 21

b) The enlarged rug's area =  60 square feet

Step-by-step explanation:

Step 1 :

Let l be the length and w represent the width of the rectangular rug

Given the area  = 21 square feet.

So l × w = 21

Also given, the length is 4 feet longer than the width .

So we have

l = 4 + w

Step 2 :

Using the above 2 equations we have

(4+w)w = 21

w² + 4 w - 21 = 0

(w+7)(w-3) = 0

=> w = -7 or w = 3

Since w is the width of the rug, we take the positive value w = 3 as the width

So w = 3 feet

So

l = 4 + w = 4 +3 = 7 feet

Step 3 :

When a 1.5 foot border is added all the way round the rug, the length and  width are increased by 3 feet (1.5 feet on both sides)  the rug's enlarged  length and the rug's enlarged width is

l = 7 + 3 = 10

w = 3 + 3 = 6

The enlarged rug's area = 10 × 6 = 60 square feet

Step 4 :

Answer :

The equations to determine the length and the width of the rug are

l = 4 + w and l × w = 21

The enlarged rug's area =  60 square feet

You might be interested in
If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5),
nikklg [1K]

Step-by-step explanation:

<u>Step 1:  Solve using the first point</u>

<em>(2, 28)</em>

28 = a(2)^3 + b(2)^2 + c(2) + d

28 = 8a + 4b + 2c + d

<u>Step 2:  Solve using the second point</u>

<em>(-1, -5)</em>

-5 = a(-1)^3 + b(-1)^2 + c(-1) + d

-5 = -a + b - c + d

<u>Step 3:  Solve using the third point</u>

<em>(4, 220)</em>

220 = a(4)^3 + b(4)^2 + c(4) + d

220 = 64a + 16b + 4c + d

<u>Step 4:  Solve using the fourth point</u>

<em>(-2, -20)</em>

-20 = a(-2)^3 + b(-2)^2 + c(-2) + d

-20 = -8a + 4b - 2c + d

<u>Step 5:  Combine the first and fourth equations</u>

<u />28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d

8 = 8b + 2d

8 - 8b = 8b - 8b + 2d

(8 -8b)/2 = 2d/2

4 - 4b = d

<u>Step 6:  Solve for c in the second equation</u>

-5 + 5 = -a + b - c + d + 5

0 + c = -a + b - c + c + d + 5

c = -a + b + d + 5

<u>Step 7:  Substitute d with the stuff we got in step 5</u>

c = -a + b + (4 - 4b) + 5

c = -a + b + 4 - 4b + 5

c = -a - 3b + 9

<u>Step 8:  Substitute d and c into the first equation</u>

<u />28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)

28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b

28 - 22 = 6a - 6b + 22 - 22

6 / 6 = (6a - 6b) / 6

1 + b = a - b + b

1 + b = a

<u>Step 9:  Substitute a, b, and c into the third equation</u>

220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)

220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b

220 - 100 = 60b + 100 - 100

120 / 60 = 60b / 60

2 = b

<u>Step 10:  Find a using b = 2</u>

a = b + 1

a = (2) + 1

a = 3

<u>Step 11:  Find c using a = 3 and b = 2</u>

c = -a - 3b + 9

c = -(3) - 3(2) + 9

c = -3 - 6 + 9

c = 0

<u>Step 12:  Find d using b = 2</u>

d = 4 - 4b

d = 4 - 4(2)

d = 4 - 8

d = -4

Answer:  a = 3, b = 2, c = 0,d = -4

6 0
3 years ago
Read 2 more answers
Explain intersecting, perpendicular, and parallel
inessss [21]
Intersecting is where two lines cross at any angle.
Perpendicular means two lines cross at exactly a 90-degree angle
Parallel indicates that the two lines have the same slope and never cross.
5 0
3 years ago
Read 2 more answers
PLEASE HELP ME ASAP!!!!!
zheka24 [161]

Answer:

Can you show me the pattern?

6 0
3 years ago
Read 2 more answers
HURRY WILL GIVE BRAINLIEST
chubhunter [2.5K]
If you separate the triangles, you'll notice that both are literally the same triangle because all angles are the same.
8 0
3 years ago
Read 2 more answers
A tennis ball is in a cylindrical container. The ball has a radius of 5 inches and the cylinder has a height of 8 inches. How mu
Nostrana [21]

Answer:

104.7 in^3

Step-by-step explanation:

Step one:

given data

The ball has a radius of 5 inches and

the cylinder has a height of 8 inches

Step two:

The volume of the cylinder

v= \pi r^2 h

substitute our data

v= 3.142*5^2*8\\\\v=628.4in^3

The volume of the ball

v=4/3 \pi r^3

substitute our data

v= 4/3 *3.142*5^3\\\\v= 523.7 in^3

The space will have a volume of

=628.4-523.7

=104.7 in^3

7 0
3 years ago
Other questions:
  • You buy a deluxe box of 45 ornaments for your tree for $15 when you get home and open the box you realize that 10 of the ornamen
    8·1 answer
  • The width of a rectangular box is 4 times its length, and its height is 6in more than its length. The volume of the box is 102in
    8·1 answer
  • What is the volume of the triangular prism?
    11·2 answers
  • The table of values represents the function g(x) and the graph shows the function f(x).
    13·1 answer
  • A basket of 8 red beads 6 yellow beads and 6 green beads a bead will be drawn from the basket and replaced 150 times. What is a
    6·1 answer
  • What’s 2x4+10-17•2067
    8·2 answers
  • a washer and dryer costs $951 combined. The washer costs $51 more than the dryer. what is the cost of the dryer?​
    12·2 answers
  • Type "me"if you're religion is Christian.​
    5·2 answers
  • Is x = -12 a solution of x^2 +10x+25=49?
    13·1 answer
  • Which equation is correct?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!