<h3>
Answer: 30</h3>
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Explanation:
Method 1)
The short way to find this answer is to multiply the values together to get 6*15 = 90, then divide by the GCF 3 getting 90/3 = 30 as the LCM.
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Method 2)
The longer way is to list the prime factorizations of each value
6 = 2*3
15 = 3*5
The unique factors are: 2, 3, 5
The most that each unique factor happens is one time.
Those unique factors multiply out to 2*3*5 = 30
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Method 3)
Another way is to list out the multiples of 6 and 15
multiples of 6 = {6, 12, 18, 24, 30, 36, 42, 48, ...}
multiples of 15 = {15, 30, 45, 60, 75, 90, 105, ...}
We see that 30 is the smallest value in both sets, so 30 is the LCM.
Answer:
The answer is 40a+14c
Step-by-step explanation:
Step 1: Open the brackets
7a-9c+12a+33c+21a-10c
Step 2: Group all the like terms
Like terms are terms with similar variables, for example;
(7a, 12a, 21a) are all like terms since they have a common variable (a)
(-9c, 33c,-10c) are also like terms since they have a common variable (c)
Step 2: Solve
(7a+12a+21a)+(33c-10c-9c)=40a+14c
The answer is 40a+14c
Let x be the number of members in Daniel's tennis team.
The amount made = $582.85
Expenses (food and drinks) = $64
Balance remaining for sharing = 582.85 - 64 = $518.85
Amount received by each player = (amount made - Expenses)/Number of members = 518.85/x
Answer:
Volume = 128
Surface area = 179.2
Step-by-step explanation:
The figure appears to be a square pyramid
The volume of a pyramid can be calculated using the formula : a²(h/3)
where a = base length and h = height
Here the base length appears to be 8 and the height appears to be 6
So we have V = a²(h/3) and a = 8 and h = 6
==> plug in values
V = 8²(6/3)
==> evaluate exponent
V = 64(6/3)
==> divide 6 by 3
V = 64(2)
==> multiply 64 and 2
V = 128
Formula for surface area of a square pyramid is SA = a² + 2al
where a = base length and l = slant height
Looking at the pyramid the slant height appears to be 7.2 and the base length is 8
so we have SA = a² + 2al and a = 8 and l = 7.2
==> plug in values
SA = 8² + 2(8)(7.2)
==> evaluate exponent
SA = 64 + 2(8)(7.2)
==> multiply 2, 8 and 7.2
SA = 64 + 115.2
==> add 64 and 115.2
SA = 179.2
The trains are 275 km apart when both are at their first stop
<em><u>Solution:</u></em>
The tracks make an angle of 130°, with the station as a vertex
Therefore, from given figure in question,
Angle at station = 130 degree
Let "c" be the point at station
The first train travels 100 km and makes its first stop at point A
Distance between A and station c = 100 km
Let a = 100 km
The second train travels 200 km and makes it first stop at point B
Distance between B and station c = 200 km
Let b = 200 km
We have to find the value of "d"
We can use the law of cosine
The square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.
From given figure in question,
Side opposite "d" to 130 degree is equal to sum of square of other sides a and b minus twice the product of those sides and the cosine of the angle between them which is 130 degrees
Therefore,
Thus trains are 275 km apart when both are at their first stop