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Nastasia [14]
2 years ago
9

The sum of an unknown and eight is twenty. What is the unknown?​

Mathematics
2 answers:
gregori [183]2 years ago
7 0

Answer:

12

Step-by-step explanation:

We can transform this into an equation in which the unknown will be represented by x. The word "sum" shows us that we are using addition, and we already know that we are adding 8 to the unknown (or x) and the answer to the equation is 20. Lets put this into a number equation now.

x+8=20

Now we just undo the equation. We have to subtract 8 from both sides.

x+8(-8)=20(-8)

x=12

The answer is 12. :) have a good day!

Zarrin [17]2 years ago
4 0

indicates subtraction

20 - 8 = 12

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PLEASE HELPPP
MAXImum [283]
The complete question is

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>

6 0
3 years ago
Read 2 more answers
The values (11.1, 4) and (x, 15) are from an inverse variation. Find the missing value and round to the nearest
Murrr4er [49]
12 this is because my number for sports is 12 and i just need to answer a ? for point thanks have a good day
3 0
3 years ago
A reindeer can run 96 miles in 3 hours at this rate how far can a reindeer run in 1hour explain
jekas [21]
This is how you do it: you put mile 96 over 3 and if u wanna know how many it will run in 1 hour. You cross multiply so you multiply 96 times1 and you get 96 but now you have to divide it by 3. If you do that you'll get the answer which is 32. There are other ways to do it but I just think it's way easier this way
6 0
3 years ago
Paul spelled 6 out of 16 words correctly on his spelling test. What fraction of the words did he misspell?
olya-2409 [2.1K]

Answer:

5/8 are spelled incorrectly

Step-by-step explanation:

There are 16 words

He spelled 6 correctly

That means he spelled 16-6 = 10 incorrectly

The fraction spelled incorrectly is wrong/total

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Simplify by dividing the top and bottom by 2

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5 0
3 years ago
Read 2 more answers
F(x)=2x^2 -5 , simplify f(x+h)/h , where h≠0
7nadin3 [17]

Answer:

\huge\boxed{\dfrac{f(x+h)}{h}=\dfrac{2x^2+4xh+2h^2-5}{h}}

\huge\boxed{\dfrac{f(x+h)}{h}=\dfrac{2x^2-5}{h}+4x+2h}

Step-by-step explanation:

f(x)=2x^2-5\\\\\dfrac{f(x+h)}{h}=\dfrac{2(x+h)^2-5}{h}=\dfrac{2(x^2+2xh+h^2)-5}{h}\\\\\dfrac{f(x+h)}{h}=\dfrac{2x^2+4xh+2h^2-5}{h}\\\\h\neq0

4 0
2 years ago
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