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
garik1379 [7]
3 years ago
11

The lengths of a rectangular garden, the inner rectangle, is 9ft more than its width. For the garden. Let x = width, x + 9 = len

gth. It is surrounded by a brick walkway 4ft wide. Suppose the total area of the walkway is 400ft^2.
a. Write a polynomial to represent the length of PQ

b. What are the dimensions of the garden?

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
5 0

Answer:

PQ = x + 13

The dimension of the garden is 52.5ft by 43.5ft

Step-by-step explanation:

Given

The shape above

Required

Determine PQ

Determine dimension of the garden

Calculating Length PQ

Represent the length of the inner rectangle as L

Represent the width of the inner rectangle as W

W = x

L = x + 9

The distance between the inner rectangle and the outer triangle is 4ft

This implies that;

PQ = L + 4

Substitute x + 9 for L

PQ = x + 9 + 4

PQ = x + 13

Also;

QR = W + 4

Substitute x for W

QR = x + 4

Calculating The Dimension of The Garden

First, we need to determine the Area of the inner rectangle

Area_1 = L * W

Recall that  W = x and L = x + 9

So;

Area_1 = x * (x + 9)

For the bigger rectangle

Area_2 = PQ * QR

Recall that  PQ = x + 13 and QR = x + 4

So;

Area_2 = (x + 13)(x + 4)

Given that the Area of the walkway is 400ft^2

This implies that

Area_2 = Area_1 + 400

Substitute Area_1 = x * (x + 9) and Area_2 = (x + 13)(x + 4)

(x + 13)(x + 4) = x * (x + 9) +  400

Open All Brackets

x^2 + 13x + 4x + 52 = x^2 + 9x +  400

x^2 + 17x + 52 = x^2 + 9x +  400

Collect Like Terms

x^2 - x^2 + 17x - 9x =  400- 52

8x = 348

Divide both sides by 8

\frac{8x}{8} = \frac{348}{8}

x = \frac{348}{8}

x =43.5

Since the dimensions of the garden is W = x and L = x + 9

<em>Substitute 43.5 for x in both cases</em>

L = 43.5 + 9 = 52.5

W = 43.5

<em>Hence, the dimension of the garden is 52.5ft by 43.5ft</em>

You might be interested in
What is -5 to the 4 power in expanded form
Kruka [31]
-5 to the 4th power in expanded form would be -5 x -5 x -5 x -5.  This is equal to positive 625.
8 0
3 years ago
Read 2 more answers
100 POINTS!<br> help please <br><br> which is the graph of f(x) = 3 square root x/4
AnnyKZ [126]

your answer

hope it will work for you

5 0
3 years ago
George is throwing a party for his son's 9th birthday he orders for sandwiches to the party if each person will eat 2/3 of a san
ddd [48]

Answer:

George can feed 6 people.

Step-by-step explanation:

Given:

Number of sandwiches = 4

Each person eats two-third of a sandwich.

Therefore, number of persons eating 4 sandwich is given as:

\textrm{Number of persons} =\frac{\textrm{Total sandwiches eaten}}{\textrm{Total sandwiches eaten by 1 person}}

Therefore,

\textrm{Number of persons} = \frac{4}{\frac{2}{3}}\\\\\textrm{Number of persons} =4\times \frac{3}{2}=6

7 0
3 years ago
Emir is standing in a treehouse and looking down at a swingset in the yard next door. The angle of depression from Emir's eyelin
boyakko [2]
<h3>Answer:  24 feet  (Choice D)</h3>

=============================================

Explanation:

Refer to the diagram below. The goal is to find x, which is the horizontal distance from the base of the tree to the swing set.

Focus on triangle BCD.

The angle B is roughly 30.26 degrees, and this is the angle of depression. This is the amount of degrees Emir must look down (when starting at the horizontal) to spot the swing set.

We know that he's 14 ft off the ground, which explains why AB = CD = 14.

The goal is to find BC = AD = x.

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

Again, keep your focus on triangle BCD.

We'll use the tangent ratio to say

tan(angle) = opposite/adjacent

tan(B) = CD/BC

tan(30.26) = 14/x

x*tan(30.26) = 14

x = 14/tan(30.26)

x = 23.9965714046732

That value is approximate. Make sure your calculator is in degree mode.

That value rounds to 24 feet when rounding to the nearest whole foot.

6 0
3 years ago
What is the y-coordinate of the solution for the system of equations? x−y=−11 y+7=−2x
ICE Princess25 [194]

Answer:

y= 5

Step-by-step explanation:

Given the system of equations:

x-y=-11

y+7=-2x

In order to find the y coordinate of the solution we must first find the solution to this system of equations. We first start by solving one of the given equations and then substitute the answer of that into the second equation and further solve to get the final answers.

x=y=-11

y+7=-2x

y+7=-2x

+ -7

y = -2x - 7

x - y = -11

y = -2x-7

x-(-2x-7)=-11

x--2x=x+2x=3x

3x+7=-11

-7

-11+-7=-18

3x=-18

\div3

-18\div3=-6

x=-6

y=-2x-7

y=(-2)(-6)-7

-2\times-6=12-7=5

y=5

Hope this helps.

7 0
2 years ago
Other questions:
  • Write the degree of polynomials how do you find the degree?
    7·2 answers
  • -8c2+-c2+5c–7+-10c2+2
    13·1 answer
  • What is the answer to this question? x/5 - 13 = 20
    7·2 answers
  • -3 7/10 divided by 2 1/4<br><br> Please simplify the answer.
    13·1 answer
  • Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 5x + 12), [−3, 1]
    8·1 answer
  • Can someone help me out with this question please :)
    14·1 answer
  • What is the linear function equation represented by the graph?
    8·2 answers
  • WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!! EASY IM J
    5·2 answers
  • Complete the table below
    14·1 answer
  • What is the slope of a line perpendicular to
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!