Multiples : these are what we get after multiplying a number by an integer (not a decimal or fraction)
Example : 6 * 1 = 6......6 * 2 = 12.....6 * 3 = 18......so 6,12, and 18 are multiples of 6.
factors : these are what we multiply by to get a number
Example : 1 * 6 = 6.....so 1 and 6 are factors of 6....2 * 3 = 6 ...so 2 and 3 are also factors of 6
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problem 1 : Look at ur clues...each number is less then or equal to 12....this right here eliminates D because of the 15. The greatest common factor of the 2 numbers is 2....and this eliminates B because if it has a factor of 2, it has to be an even number. So that leaves us with :
A. 6 and 10
C. 10 and 12
last clue....they have a least common multiple of 60...this means that ur 2 numbers cant have any other common multiples until 60.
6 * 10......both are multiples of 60...however, they are also both multiples of 30...so 60 is not the least common multiple of 6 and 10, it is 30.
Therefore, ur answer is C. 10 and 12....with the LCM of 60, LCF of 2 and < or = to 12
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problem 2 : GCF (greatest common factor) of 42 and 84
factors of 42 : 1,2,3,6,7,14,21,42
factors of 84 : 1,2,3,4,6,7,12,14,21,28,42,84
therefore, the GCF of these 2 numbers is 42
Since polar coordinates are made up in this way
we need to solve for r and then find the angle. In our rectangular coordinate given,
and 
We will use this fact to first find the angle then r, which might seem backwards but I am going to do it in this order. The formula to find the angle measure uses the tangent identity
.
Filling in our y and x from the rectangular coordinate we have
or
.
The tangent identity is the side opposite the reference angle (theta) over the side adjacent to it. Since in our rectangular coordinate both x and y are negative, we will be in QIII where x and y are negative. The side across from the reference angle is the square root of 3, which should tell us at this point in our math careers that the reference angle is a 60 degree angle. But in the third quadrant, the angle is 180+60 which is 240 degrees. Converting that to radians we get 
. That's our angle. In order to solve for r now, we will need the cosine of that angle. In our 30-60-90 right triangle we can solve for the length of the missing side which is the hypotenuse. If our Pythagorean triple is
and x = -4, then the length of the hypotenuse is 2(-4) which is -8 but since a hypotenuse is never negative, it's just 8. That's also the value for r! That means that the polar coordinates that are the same as the rectangular ones we were given are
first choice above.
By direct calculation, we will see that the full price of each necktie is $29.
<h3>
How to find the complete price of each necktie?</h3>
Let's say that the full price of each necktie is f.
We know that Will each necktie costed $8 less than the full price, so he paid:
(f - $8) for each one.
Knowing that he bought 7 and paid a total of $147, we know that he paid:
$147/7 = $21
Then we need to solve:
(f - $8) = $21
Solving for f, we have:
f = $21 + $8 = $29.
So the full price of each necktie is $29.
If you want to learn more about algebra, you can read:
brainly.com/question/4344214
Answer:
Number of carnations = 6
Step-by-step explanation:
Let the number of carnations school band buys from florist be x.
Cost of each carnation = $0.50
Total cost for x number of carnations = $0.50x
Also , delivery cost = $15
So, total cost on buying x number of carnations from florist = 0.50x + 15
Now,
School band sells carnations at a price of $3 each.
Total revenue they get get after selling x number of carnations = $3x
We need to find that , when will the cost of the carnations be equal to the revenue from selling them.
i.e 3x = 0.50x + 15
or 3x - 0.50x = 15
or 2.50x = 15
or x = 
or x = 6
so on selling 6 carnations cost of carnation reach to the point where it is equal to revenue
