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kicyunya [14]
3 years ago
15

Draw a factor tree the prime factorization of 45 and 90 in the space provided below

Mathematics
1 answer:
Ann [662]3 years ago
3 0
45                                        90 
 /  \                                       /  \
5  9                                     45  2
   /  \                                   /  \
  3   3                                5   9 
 5x3x3                                   / \  
                                          3    3
                                        2x5x3x3
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Give a combinatorial proof that the cardinality of the power set of a finite set A is 2^|A|
juin [17]

There are \dbinom{|A|}k ways of building a subset of k elements from A, so the total number of subsets you can build is

\displaystyle\sum_{k=0}^{|A|}\binom{|A|}k

Recalling the binomial theorem, the above sum is equal to

\displaystyle\sum_{k=0}^{|A|}\binom{|A|}k1^k1^{|A|-k}=(1+1)^{|A|}=2^{|A|}

as required.

3 0
4 years ago
What's the slope of a line that passes through (-8,-16) and (18,5)?​
frosja888 [35]

Answer:

C. 21/26

Step-by-step explanation:

Slope Formula: m = \frac{y2-y1}{x2-x1}

Plug in our coordinates:

m = (5 + 16)/(18 + 8)

m = 21/26

4 0
4 years ago
Read 2 more answers
How many solutions does the equation 4x+3-1=2(2x+2)-2x have explain your reasoning
Ostrovityanka [42]

Anwser: X=1

4x+3-1=2(2x+2)-2x

4x+2=4x+4-2x

4x+2=2x+4

-2 -2x

2x=2

X=1

8 0
3 years ago
Kayla ate one-eighth of a pizza. Joe ate two-eight of a pizza. How much total pizza did they eat
WITCHER [35]

Answer:

3/8

Step-by-step explanation:

6 0
3 years ago
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Solve the system of linear equations by elimination. 3x+3=3y and 2x−6y=2
Drupady [299]
3x + 3 = 3y         < -- make this 3x - 3y = -3
2x - 6y = 2

multiply by 2 on the first equation
6x - 6y = -6
2x - 6y = 2           
subtract them

4x = -8
x = -2


substitute x = -2 into any of the equation
2x - 6y = 2
2(-2) - 6y = 2
-4 - 6y = 2
-6y = 6
y = -1

So the answer is 
(-2 , -1)
6 0
4 years ago
Read 2 more answers
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