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kotegsom [21]
3 years ago
12

How is the graph of y = (x + 1)^2- 5 transformed from the graph of y=x^2?

Mathematics
1 answer:
Ainat [17]3 years ago
8 0

\text{Hi there! :D}

\boxed{\text{There is a horizontal shift of 1 unit left and 5 units down.}}

\text{Recall that the transformations form of a quadratic function is:}\\\\y = \pm a(b(x-h))+k \text{ where:}\\\\a = \text{ vertical stretch/compression}\\\\b = \text{ horizontal stretch/compression}\\\\h = \text{ shift left/right}\\\\k = \text{ shift up/down}\\\\\text{Therefore, in this instance:}\\\\h = -1\\\\k = -5, \text{ so:}\\\\\text{There is a horizontal shift of 1 unit left and 5 units down.}

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Find the number of ways of arranging the numbers
Doss [256]

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).

So, we can think of our numbers as

\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

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

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

possible arrangements.

7 0
3 years ago
Read 2 more answers
107 = 7 - 2(7b - 1) what does b equal?
topjm [15]

107 = 7 -2 (7b - 1)

First, distribute -2 to all terms within the parenthesis

-2(7b - 1) = -14b + 2

107 = 7 -14b + 2

Combine like terms

107 = -14b (+7 + 2)

107 = -14b + 9

Isolate the b. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

Subtract 9 from both sides

107 (-9) = -14b + 9 (-9)

107 - 9 = -14b

98 = -14b

Isolate the b. Divide -14 from both sides

(98)/-14 = (-14b)/-14

98/-14 = b

b = −7

-7 is your answer

hope this helps

5 0
3 years ago
Which equation is represented by the line
Rainbow [258]
The correct choice is the third one. Y=2/3x
8 0
3 years ago
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frez [133]

Answer:

I THINK MAYBE C hope this helps

Step-by-step explanation:

4 0
3 years ago
Which expression is equivalent to
noname [10]

Answer:

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Step-by-step explanation:

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√m^4 = m^2

√n^6 = n^3

Put it all together and you get 15/25 m^2 n^3

Simplify 15/25 to 3/5

4 0
3 years ago
Read 2 more answers
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