PLEASE HELPPP
2 answers:
The complete question is
</span> <span>e) How many pavers will be needed? Show all work.
</span> <span>f) What will it cost to build the patio? Show all work.
</span>
</span> <span>b) Calculate the new area of Mrs. Johnson’s patio. Show all work.
</span> <span>c) How many pavers will be needed for the new design? Show all work.
</span> <span>d) What will it cost to build the bigger patio? Show all work.
</span> <span>e) Is Khianna right? Will doubling the size of the patio, double the cost?
</span>
ANSWERS
Part I: Scale Drawing
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.
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
c) What are the dimensions of Mrs. Johnson’s patio? the dimensions of Mrs. Johnson’s patio are 10 ft x 10 ft
d) Calculate the area of Mrs. Johnson’s patio. Show all work.
area of the square=b²
where
b is the length side of the square
b=10 ft
so
Area=10²-----> area of Mrs. Johnson’s patio=100 ft²
e) How many pavers will be needed? Show all work.
we know that
1 paver is 16 in x 16 in dimensions
convert in 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
f) What will it cost to build the patio? Show all work.
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
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!”
a) What would be the new dimensions of Mrs. Johnson’s patio?
the new dimensions of Mrs. Johnson’s patio are 20 ft x 20 ft
b) Calculate the new area of Mrs. Johnson’s patio. Show all work.
area of the square=b²
where
b is the length side of the square
b=20 ft
so
Area=20²-----> new area of Mrs. Johnson’s patio=400 ft²
c) How many pavers will be needed for the new design? Show all work.
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
d) What will it cost to build the bigger patio? Show all work.
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
e) Is Khianna right? Will doubling the size of the patio, double the cost?
Khianna is wrong, <span>doubling the dimensions, the area quadruples, therefore also costs quadruple</span>
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 square pavers. The pavers are sold in boxes of 12 and cost $99.99
Part I: Scale Drawing
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.
a) Scale Factor: ____________________________
b) Use a straightedge and a ruler to draw to scale a design for Mrs. Johnson’s patio:
c) What are the dimensions of Mrs. Johnson’s patio?
<span>d) Calculate the area of Mrs. Johnson’s patio. Show all work.</span> <span>e) How many pavers will be needed? Show all work.
</span> <span>f) What will it cost to build the patio? Show all work.
</span>
Part II: Bigger Design
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>a) What would be the new dimensions of Mrs. Johnson’s patio?</span> <span>b) Calculate the new area of Mrs. Johnson’s patio. Show all work.
</span> <span>c) How many pavers will be needed for the new design? Show all work.
</span> <span>d) What will it cost to build the bigger patio? Show all work.
</span> <span>e) Is Khianna right? Will doubling the size of the patio, double the cost?
</span>
ANSWERS
Part I: Scale Drawing
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.
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
c) What are the dimensions of Mrs. Johnson’s patio? the dimensions of Mrs. Johnson’s patio are 10 ft x 10 ft
d) Calculate the area of Mrs. Johnson’s patio. Show all work.
area of the square=b²
where
b is the length side of the square
b=10 ft
so
Area=10²-----> area of Mrs. Johnson’s patio=100 ft²
e) How many pavers will be needed? Show all work.
we know that
1 paver is 16 in x 16 in dimensions
convert in 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
f) What will it cost to build the patio? Show all work.
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
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!”
a) What would be the new dimensions of Mrs. Johnson’s patio?
the new dimensions of Mrs. Johnson’s patio are 20 ft x 20 ft
b) Calculate the new area of Mrs. Johnson’s patio. Show all work.
area of the square=b²
where
b is the length side of the square
b=20 ft
so
Area=20²-----> new area of Mrs. Johnson’s patio=400 ft²
c) How many pavers will be needed for the new design? Show all work.
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
d) What will it cost to build the bigger patio? Show all work.
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
e) Is Khianna right? Will doubling the size of the patio, double the cost?
Khianna is wrong, <span>doubling the dimensions, the area quadruples, therefore also costs quadruple</span>
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<h2>Answer:</h2>
Shown below
<h2>Step-by-step explanation:</h2>First of all, we have the following points:
To plot these points, we need to graph a coordinate grid. Recall that a coordinate grid is composed of two perpendicular lines, that we call the axes and are labeled like number lines. The horizontal axis is called the x-axis while the vertical axis is called the y-axis, and these two axes intersect at a point called the origin. Next, let's plot each point as follows:
<h2>PART 1. Plot the points on your own coordinates grid and connect in alphabetical order. </h2><h2></h2>
Point a:
Let's stand at the origin and then move three units to the left and three units up. The resulting point is shown in the firs figure below.
Point b:
Let's stand at the origin and then move two units to the right and three units up. The resulting point is shown in the firs figure below.
Point c:
Let's stand at the origin and then move five units to the right and two units down. The resulting point is shown in the firs figure below.
Point d:
Let's stand at the origin and then move three units to down. The resulting point is shown in the firs figure below.
Point e:
Let's stand at the origin and then move three units to the left and two units down. The resulting point is shown in the firs figure below.
Next, let's connect connect the points in alphabetical order, so that the line are connected from a to b, from b to c, from c to d, from d to e and from e to a again. So the resulting graph is shown in the second figure. As you can see, this is an irregular pentagon.
<h2>PART 2. Decompose figure ABCDE into rectangles and triangles.</h2>Every pentagon can be divided up into three triangles. Hence, from the third figure. the triangles are:
ΔABE
ΔBDE
ΔBCD
Since a rectangle is a quadrilateral whose angles are all right angles, then there is no chance to obtain a rectangle from ABCDE. To obtain a rectangle, we'd need other points and this is not what the problem asks.