Help? A set of pens sells for $5.25 and costs $1.80 to make. Forty percent of the profit (the difference between the purchase pr
2 answers:
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Answer:
46
Step-by-step explanation:
Let represent a number with
in the ten's position and
is the one's position.
This means actually has value of
.
We are given the sum of those digits of is 10; this means
.
It says if 18 is added to the number , then the result is
.
So has value
and
has value
.
We are given then:
Subtract on both sides:
Simplify:
Subtract on both sides:
Divide both sides by 9:
Rearrange by commutative property:
So the system of equations we want to solve is:
-------------------------Add equations together (this will eliminate the variable and allow you to go ahead and solve for
:
Divide both sides by 2:
Simplify:
If and
, then
.
since 4+6=10.
So the original number is (46).
18 more than 46 is 18+46=(64) which is what we wanted.
We also have the sum of 4 and 6 is 10 as well.
Problem 5
<h3>Answer: 6i</h3>------------------
Explanation:
We have these four identities
- i^0 = 1
- i^1 = i
- i^2 = -1
- i^3 = -i
Notice how computing i^4 leads us back to 1. So i^4 = i^0. The pattern repeats every 4 terms. So we divide the exponent by 4 and look at the remainder. We ignore the quotient entirely. We can see that 28/4 = 7 remainder 0. Meaning that i^28 = i^0 = 1.
We can think of it like this if you wanted
i^28 = (i^4)^7 = 1^7 = 1
Then the sqrt(-36) becomes 6i
So overall, we end up with the final answer of 6i
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Problem 6
<h3>Answer: -3i</h3>------------------
Explanation:
We'll use the ideas mentioned in problem 5
46/4 = 11 remainder 2
i^46 = i^2 = -1
sqrt(-9) = 3i
The two outside negative signs cancel out, but there's still a negative from -1 we found earlier. So we end up with -3i
In other words, here is one way you could write out the steps
=============================================
Problem 7
<h3>Answer: -1</h3>------------------
Work Shown:
i^10 = i^2 because 10/4 = 2 remainder 2
i^19 = i^3 because 19/4 = 4 remainder 3
i^7 = i^3 because 7/4 = 1 remainder 3
Again, all we care about are the remainders.
=============================================
Problem 8
<h3>Answer: -1 + i</h3>------------------
Work Shown:
i^22*i^6 = i^(22+6) = i^28
Earlier in problem 5, we found that i^28 = i^0 = 1
So,