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ankoles [38]
3 years ago
10

3. Look for a pattern to determine the next two numbers in the list. Show your work. (5 points)

Mathematics
1 answer:
EleoNora [17]3 years ago
3 0

Answer:

The sequence is subtracting 12 each time. The next two numbers would be 152, and 140

Step-by-step explanation:

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I feel like it’s B but I’m not sure
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What is the quotient of 2/3 divided by 4 in simples form
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Step-by-step explanation:

Quotient of 2/3 divided by 4

= (2/3) / 4

= 2/12

= 1/6.

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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
Gnoma [55]

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>

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3 years ago
Which of the following equations have infinitely many solutions?
Svetllana [295]

Answer:

Choice A

Step-by-step explanation:

In each case, each equation has an equation of a line in y = mx + b form equaling another equation of a line in y = mx + b form. If the two sides are equal, it is the same equation, there are infinitely many solutions. If the sides are different, then if the slopes are different, the lines intersect at one point, and there is exactly 1 solution. If the slopes are equal, the lines are parallel, and there is no solution.

(Choice A) -10x-10=-10x-10

In Choice A, both sides of the equation are equal, so there are infinitely many solutions.

(Choice B) 10x-10=-10x+10

(Choice C) 10x-10=-10x-10

(Choice D) -10x-10=-10x+10

In choices B through D, the two sides are not equal, so there is either 1 solution (B and C since they have different slopes) or no solution (D since the slopes are equal).

3 0
3 years ago
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