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guajiro [1.7K]
3 years ago
11

Nicole simplifies 2^a*2^5/2^b to 2^(a-b+5). Which two properties of exponents did she use while simplifying the expression?

Mathematics
1 answer:
emmainna [20.7K]3 years ago
5 0

Answer:

D.

Step-by-step explanation:

2^a*2^5/2^b = 2^(a+5)/2^b. using power of a product property.

then

2^(a+5)/2^b= 2^(a+5)*2^-b. Using Negative Exponent property.

Again we can use power of a product property and we get 2^(a+5)*2^-b=2^(a-b+5)

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Answer:

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Step-by-step explanation:

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3 years ago
Use substitution to solve the system of equations.<br> -1=2x-y<br> 8x-4y=-4
sineoko [7]

Answer:

x=-1/2+y/2

Step-by-step explanation:

6 0
3 years ago
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
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Area=20²-----> area =400 ft²<span>  
</span>
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</span> </span>
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if one paver has an area of----------------> 16/9 ft²
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x=400/(16/9)------> x=400*9/16-----> x=225 pavers

if one box --------------> 12 pavers
x box---------> 225 pavers
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<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
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<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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4 0
3 years ago
Use F = (9/5)C + 32 to convert 100°C to Fahrenheit
pshichka [43]

\huge\fbox{Answer ☘}

\bold\blue{°F = ( \frac{9}{5} )°C \: + 32 }\\\\ °F = ( \frac{9}{5} )100° \:  +  \: 32 \\\\ °F = 9(20)° + 32 \\\\ °F= 180 + 32 \\\\ \bold{°F = 212°}

hope helpful~

5 0
3 years ago
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