Answer:
2
Step-by-step explanation:
We can put this into an equation:
10/x=5
first, we multiply x on both sides:
10=5x
and then we divide by 5 on both:
2=x
so the answer is 2
Answer:
(4x^2 +9)(4x^2-9) =0
Step-by-step explanation:
16x^4 - 18 = 0
Rewriting
(4x^2)^2 - 9^2 =0
We notice that this is the difference of squares
a^2 - b^2 = (a-b)(a+b)
(4x^2 -9)(4x^2+9) =0
A combination is an unordered arrangement of r distinct objects in a set of n objects. To find the number of permutations, we use the following equation:
n!/((n-r)!r!)
In this case, there could be 0, 1, 2, 3, 4, or all 5 cards discarded. There is only one possible combination each for 0 or 5 cards being discarded (either none of them or all of them). We will be the above equation to find the number of combination s for 1, 2, 3, and 4 discarded cards.
5!/((5-1)!1!) = 5!/(4!*1!) = (5*4*3*2*1)/(4*3*2*1*1) = 5
5!/((5-2)!2!) = 5!/(3!2!) = (5*4*3*2*1)/(3*2*1*2*1) = 10
5!/((5-3)!3!) = 5!/(2!3!) = (5*4*3*2*1)/(2*1*3*2*1) = 10
5!/((5-4)!4!) = 5!/(1!4!) = (5*4*3*2*1)/(1*4*3*2*1) = 5
Notice that discarding 1 or discarding 4 have the same number of combinations, as do discarding 2 or 3. This is being they are inverses of each other. That is, if we discard 2 cards there will be 3 left, or if we discard 3 there will be 2 left.
Now we add together the combinations
1 + 5 + 10 + 10 + 5 + 1 = 32 choices combinations to discard.
The answer is 32.
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Note: There is also an equation for permutations which is:
n!/(n-r)!
Notice it is very similar to combinations. The only difference is that a permutation is an ORDERED arrangement while a combination is UNORDERED.
We used combinations rather than permutations because the order of the cards does not matter in this case. For example, we could discard the ace of spades followed by the jack of diamonds, or we could discard the jack or diamonds followed by the ace of spades. These two instances are the same combination of cards but a different permutation. We do not care about the order.
I hope this helps! If you have any questions, let me know :)
Answer: The greatest number of playlist Katherine can make =8
Each of playlist will have 4 pop songs and 9 rock songs.
Step-by-step explanation:
Given: The number of pop songs Katherine has= 32
The number of rock songs Katherine has= 72
If she want to make playlist such that in each playlist there is equal number of pop and rock songs, we need to find the GCF(greatest common factor) of 32 and 72.
We know that 
We can see the GCF(32,72)=
Hence, the greatest number of playlist Katherine can make =8
The number of pop songs= 
the number of rock songs=
Each of playlist will have 4 pop songs and 9 rock songs.
Answer:
The statement is true
Step-by-step explanation:
Multiples of 4 (until 40): 4 , 8 , 12 , 16 , 20 , 24 , 28 , 32 , 36 , 40
All of these are even numbers
