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The rule for the input and output values that are represented in the flow diagram below. B) output = u + 6

Mathematics

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2 parts
1.4

output = input + 6\text{output = input + 6}

1.5

3x - x

Step-by-step solution

6 steps

Here are the solutions to your questions:

Part 1.4· 3 steps

  1. Observe the input and output values from the flow diagram.

    Input values: {−9,−7,−5,−3,−1,1,3,5}\{-9, -7, -5, -3, -1, 1, 3, 5\}
    Output values: {−3,−1,1,3,5,7,9,11}\{-3, -1, 1, 3, 5, 7, 9, 11\}

  2. Determine the relationship between each input and its corresponding output.

    Let's test the difference between output and input for a few pairs:
    For input −9-9, output is −3-3: −3−(−9)=−3+9=6-3 - (-9) = -3 + 9 = 6
    For input −7-7, output is −1-1: −1−(−7)=−1+7=6-1 - (-7) = -1 + 7 = 6
    For input 1, output is 7: 7−1=67 - 1 = 6
    For input 5, output is 11: 11−5=611 - 5 = 6

  3. Formulate the rule.

    Since the difference is consistently 6, the rule is to add 6 to the input to get the output.
    If the input is represented by xx and the output by yy, the rule is y=x+6y = x + 6.

    The rule is output = input + 6\boxed{\text{output = input + 6}}.

Part 1.53x - x

  1. Identify the unknown number.

    Let the unknown number be represented by a variable, for example, xx.

  2. Translate "the product of 3 and that same number".

    The product of 3 and xx is 3×x3 \times x, which can be written as 3x3x.

  3. Translate "Subtract a number from the product of 3 and that same number".

    This means we subtract the number (xx) from the product (3x3x).
    So, the expression is 3x−x3x - x.

    The correct algebraic expression is 3x−x\boxed{3x - x}.

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