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
Klio2033 [76]
3 years ago
13

Khianna is trying to help her neighbor Mrs. Johnson design and estimate the cost of a new square patio to be made from 16 inch s

quare pavers. The pavers are sold in boxes of 12 and cost $99.99

Mathematics
1 answer:
Gnoma [55]3 years ago
5 0

Part I: Scale Drawing

<span>Decide on a scale factor to represent the distance covered by the patio. Then, use the space below to design Mrs. Johnson’s patio to be a square that is at least 8 feet on each side.</span>

 a) Scale Factor: 1 in/ 2 ft 

Use a straightedge and a ruler to draw to scale a design for Mrs. Johnson’s patio

b) see the picture attached

Mrs. Johnson’s patio to be a square that is 10 ft x 10 ft

<span><span>c) What are the dimensions of Mrs. Johnson’s patio? </span>
</span>the dimensions of Mrs. Johnson’s patio are 10 ft x 10 ft

<span><span>d) Calculate the area of Mrs. Johnson’s patio.  Show all work.  
</span> </span>
area of the square=b²
where b is the length side of the square
b=10 ft
so
Area=10²-----> area =100 ft²

<span><span>e) How many pavers will be needed?  Show all work. </span>
</span>
we know that
1 paver is 16 in x 16 in dimensions
convert to ft
1 ft----------->12 in
x ft-----------> 16 in
x=16/12-----> x=4/3 ft
so
1 paver is (4/3) ft x (4/3) ft dimensions

area of one paver=(4/3)²----> 16/9 ft²

if one paver has an area of----------------> 16/9 ft²
x pavers----------------------->  100 ft²
x=100/(16/9)------> x=100*9/16-----> x=56.25 pavers

if one box --------------> 12 pavers
x box---------> 56.25 pavers
x=56.25/12-----> x=4.68 box-------> x=5 boxes
5 boxes of pavers will be needed 

<span><span>f) What will it cost to build the patio?  Show all work. 
 </span> </span>
the cost of one box is--------> $99.99
5 boxes-----------> x
x=5*$99.99------>x=$499.95

the cost to build the patio is $499.95

Part II: Bigger Design

<span>There is a saying that bigger is better, so why not double the dimensions of Mrs. Johnson’s patio to make the side measurement twice as big? Mrs. Johnson and I think that it would better meet her needs.  After seeing the original estimation, she thinks that she could afford to double the size. I explained that making the patio twice as big would mean twice the cost. Mrs. Johnson says, “Let’s do it!”</span>

 

<span>a) What would be the new dimensions of Mrs. Johnson’s patio?
</span>the new  dimensions of Mrs. Johnson’s patio are 20 ft x 20 ft

<span>b) Calculate the new area of Mrs. Johnson’s patio.  Show all work.
</span>area of the square=b²
where b is the length side of the square
b=20 ft
so 
Area=20²-----> area =400 ft²<span>  
</span>
<span><span>c) How many pavers will be needed for the new design?  Show all work.
</span> </span>
1 paver is (4/3) ft x (4/3) ft dimensions

area of one paver=(4/3)²----> 16/9 ft²

if one paver has an area of----------------> 16/9 ft²
x pavers----------------------->  400 ft²
x=400/(16/9)------> x=400*9/16-----> x=225 pavers

if one box --------------> 12 pavers
x box---------> 225 pavers
x=225/12-----> x=18.75 box-------> x=19 boxes
19 boxes of pavers will be needed 

<span>d) What will it cost to build the bigger patio?  Show all work. 
</span>the cost of one box is--------> $99.99
19 boxes-----------> x
x=19*$99.99------>x=$1899.81
the cost to build the bigger patio is $1899.81

<span><span>e) Is Khianna right?  Will doubling the size of the patio, double the cost?</span>
</span>
<span>Khianna is wrong to double the dimensions the cost quadruples</span>

You might be interested in
Check image giving brainliest to first correct answer
Snowcat [4.5K]

Answer:

<em>7</em>

Step-by-step explanation:

<em>S</em><em>o</em><em>:</em><em>a</em><em>=</em><em>3</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em>b</em><em>=</em><em>(</em><em>-</em><em>2</em><em>)</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>c</em><em>=</em><em>2</em>

<em>S</em><em>u</em><em>b</em><em>s</em><em>t</em><em>i</em><em>t</em><em>u</em><em>t</em><em>e</em><em> </em><em>t</em><em>h</em><em>e</em><em> </em><em>n</em><em>u</em><em>m</em><em>b</em><em>e</em><em>r</em><em>s</em><em> </em><em>i</em><em>n</em><em>t</em><em>o</em><em> </em><em>e</em><em>a</em><em>c</em><em>h</em><em> </em><em>letters</em>

<em> </em><em>s</em><em>o</em><em> </em><em>a</em><em> </em><em>i</em><em>s</em><em> </em><em>r</em><em>e</em><em>p</em><em>r</em><em>e</em><em>s</em><em>e</em><em>n</em><em>t</em><em>e</em><em>d</em><em> </em><em>b</em><em>y</em><em> </em><em>3</em><em>,</em><em>c</em><em> </em><em>b</em><em>y</em><em> </em><em>2</em><em> </em><em>a</em><em>n</em><em>d</em><em> </em><em>b</em><em> </em><em>-</em><em>2</em>

<em> </em><em>t</em><em>h</em><em>e</em><em>r</em><em>e</em><em>f</em><em>o</em><em>r</em><em>e</em><em> </em><em>g</em><em>i</em><em>v</em><em>i</em><em>n</em><em>g</em><em> </em><em>u</em><em>s</em><em>:</em><em> </em><em> </em><em> </em><em> </em><em>2</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>3</em><em>+</em><em>(</em><em>-</em><em>2</em><em>)</em><em>=</em><em>9</em><em>+</em><em>(</em><em>-</em><em>2</em><em>)</em><em>=</em><em>7</em>

7 0
2 years ago
Come on plz tell me someone is awake
VladimirAG [237]

Answer:

I am

Step-by-step explanation:

1500

4 0
3 years ago
Read 2 more answers
13 If CDEF is a rhombus, find m FED.
Tatiana [17]

Answer:

36

Step-by-step explanation:

8x-20=5x+1

-5       -5

3x=-20+1

+20 +20

3x=21

3  3

x=7

8(7)-20

FED=36

8 0
2 years ago
The sum of two numbers is 110.The larger number is 2 less than 7 times the smaller.Find the Large number
natima [27]

Answer:

The larger number is 96.

Step-by-step explanation:

let \: the \: two \: numbers \: be \: a \: and \: b \\ a + b = 110 \\ let \: a \: be \: the \: larger \: number \\ a = 7b - 2 \\ we \: can \: get \: the \: value \: of \: b \: by \: substituting \: the \: value \: above \: for \: a \: in \: eq \: 1 \\ 7b - 2 + b = 110 \\ 8b - 2 = 110 \\ 8b = 110 + 2 \\ 8b = 112 \\ b = \frac{112}{8}  \\b = 14\\ calculate \:the \: value \: of \: a \: using \: the \: equation \: above \\ a + b = 110 \\ a = 110 - 14 \\ a = 96 \\ hence \: the \: large \: number \: is \: 96

8 0
2 years ago
State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.
never [62]

Answer:

Triangles ABC and MNO are similar by SSS

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional

In this problem

If this problem the corresponding sides are

AB and MN

BC and NO

AC and MO

Verify if the corresponding sides are proportional

\frac{AB}{MN}=\frac{BC}{NO}=\frac{AC}{MO}

substitute the given values

\frac{5}{7.5}=\frac{5}{7.5}=\frac{8}{12}

0.67=0.67=0.67 ----- is true

so

When two triangles have corresponding sides with identical ratios , the triangles are similar by SSS Similarity

therefore

Triangles ABC and MNO are similar by SSS

8 0
3 years ago
Other questions:
  • Find the area of the triangle. Round your answer to the nearest thousandths. <br><br> A=1/2 bh
    10·1 answer
  • A figure is translated horizontally 4 units. Which drawling shows a correct translation?
    13·1 answer
  • Find the slope of the line that passes through the points (5, 8) and (9, 4).
    13·1 answer
  • Explain how you would graph the line containing a slope of –1/5 that goes through the point (1,–4).
    9·2 answers
  • At your school, the building is 20 feet tall, a tree's height is 252 inches, and the flagpole is 6 yards high. Which of the thre
    9·1 answer
  • Myles doesn't want to spend more than $11,000 per month on gate keepers. He hires 12 gate keepers who work an
    14·1 answer
  • Point R divides in the ratio 1 : 3. If the x-coordinate of R is -1 and the x-coordinate of P is -3, what is the x-coordinate of
    8·1 answer
  • Which of the following describes a positive correlation?
    6·1 answer
  • The lengths of the sides of a rectangle are in a ratio of 4:7. If the length is 31.5 in, find the width, perimeter, and area of
    14·1 answer
  • HELP PLEEEASE DUE TODAY ALL MY POINTS<br><br> if ΔABC and ΔXYZ are similar which must be true
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!