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DaniilM [7]
3 years ago
15

[15 POINTS] FIND THE LENGTH OF SIDE AB IN THE TRIANGLE SHOWN

Mathematics
1 answer:
cupoosta [38]3 years ago
7 0
Using Pythagoras theorem, we have
AC^2=AB^2+BC^2
(9)^2=AB^2+(7)^2
81=AB^2+49
81-49=AB^2
32=AB^2
√32=AB
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Write the function in standard form<br><br> f(x) = -4 (x - 6)^2 + 15
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Answer:

  f(x) = -4x^2 +48x -129

Step-by-step explanation:

It usually works well to compute the square first. That is, simplify according to the order of operations.

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  f(x) = -4x^2 +48x -144 +15

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7 0
2 years ago
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Find the number of ways of arranging the numbers
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First of all, note that all integers are either 0,1, or 2 modulo 3 (if you're not familiar with this terminology, it means that every integer is either a multiple of 3, or it is 1 or 2 away from a multiple of 3).

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\begin{array}{c|c}x&x\mod 3\\0&0\\1&1\\2&2\\3&0\\4&1\\5&2\\6&0\\7&1\\8&2\\9&0\end{array}

In order to make sure that the sum of any three adjacent numbers is divisible by 3, we have to make sure that any group of 3 three adjacent numbers contains a 0, a 1 and a 2. This is possible only if we arrange our 9 numbers in 3 groups of 3 numbers containing 0,1 and 2 exactly once, repeating always the same pattern.

For example, we could arrange our numbers following the pattern

0,1,2,0,1,2,0,1,2

or

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We have 3!=6 possible patterns. Suppose for example that we choose the pattern

0,1,2,0,1,2,0,1,2

One possible way of following this pattern would be the arrangement

3,1,2,6,4,5,9,7,8

In fact, we substituted every '0' with a multiple of 3 (3, 6 or 9), every '1' with a number 1 away from a multiple of 3 (1, 4 or 7) and every '2' with a number 2 away from a multiple of 3 (2, 5 or 8).

This means that, once we fix a patter, we have 3 choices for the first 3 slots, 2 choices for the next 3 slots, and the final slot will be fixed. So, we have

3\cdot 3\cdot 3\cdot 2 \cdot 2 \cdot 2 = 216

possible ways of following a fixed pattern. Since the number of patterns was 6, we have

216\cdot 6 = 1296

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3 years ago
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2 years ago
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PilotLPTM [1.2K]

Answer:

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