Ask a New Question
Menu

Consider the expression (16−12)2+5(8+22)53−(1+4)2 . What is the simplified numerator?(1 point) Responses 76 76 42+60 4 squared plus 60 100 100 54

7 answers

To solve the expression \((16 - 12)^2 + 5(8 + 22) \cdot 53 - (1 + 4)^2\), we will break it down step by step.

  1. Calculate \((16 - 12)^2\): \[ 16 - 12 = 4 \quad \Rightarrow \quad (4)^2 = 16 \]

  2. Calculate \(8 + 22\): \[ 8 + 22 = 30 \]

  3. Now calculate \(5 \cdot (8 + 22) \cdot 53\) (which is \(5 \cdot 30 \cdot 53\)): \[ 5 \cdot 30 = 150 \] Now multiply by \(53\): \[ 150 \cdot 53 = 7950 \]

  4. Calculate \((1 + 4)^2\): \[ 1 + 4 = 5 \quad \Rightarrow \quad (5)^2 = 25 \]

  5. Now, combine all parts: \[ \text{Numerator} = 16 + 7950 - 25 \]

    Calculate \(16 - 25\): \[ 16 - 25 = -9 \]

    Now add \(7950\): \[ -9 + 7950 = 7941 \]

So, the simplified numerator is \(7941\).

None of the provided options (76, 42 + 60, 4 squared plus 60, 100, 54) appear to match this result. The correct simplified numerator we calculated is 7941.

which one is it

I apologize for any confusion. Let's summarize the calculations and identify if any of the provided options might match incorrectly or if there's a mistake in the calculation.

Let's reiterate the calculations clearly step by step:

  1. Calculate \((16 - 12)^2\): \[ (16 - 12)^2 = 4^2 = 16 \]

  2. Calculate \(5(8 + 22) \cdot 53\):

    • First calculate \(8 + 22\): \[ 8 + 22 = 30 \]
    • Now calculate \(5 \cdot 30\): \[ 5 \cdot 30 = 150 \]
    • Finally, multiply by \(53\): \[ 150 \cdot 53 = 7950 \]

  3. Calculate \((1 + 4)^2\): \[ (1 + 4)^2 = 5^2 = 25 \]

  4. Combine these values: \[ 16 + 7950 - 25 \]

    • First, combine \(16 - 25\): \[ 16 - 25 = -9 \]
    • Then add \(7950\): \[ -9 + 7950 = 7941 \]

So the simplified numerator is \(7941\), and it does not match any of the provided options directly.

However, let's consider the given answer choices again:

  • \(76\)
  • \(42 + 60\) (which is \(102\))
  • \(4^2 + 60\) (which is \(16 + 60 = 76\))
  • \(100\)
  • \(54\)

None of these match the result \(7941\).

It seems like there could be an error in the choices provided. Based on my calculations, the correct result is indeed 7941. Please verify if the options given are accurately reflecting the problem statement or if there was a miscommunication regarding the expression.

76, 4^2+60, 100, 54 Which one is the answer

Let’s simplify the relevant expressions connected to the provided options to find out which one is correct or matches the calculations we previously performed.

  1. For \(76\): This does not require simplification as it is a numeral.

  2. For \(4^2 + 60\): \[ 4^2 = 16 \quad \Rightarrow \quad 4^2 + 60 = 16 + 60 = 76 \]

  3. For \(100\): This is simply the number itself.

  4. For \(54\): This is simply the number itself.

Conclusion:

From these calculations:

  • \(76\) is the same as \(4^2 + 60\).
  • Therefore, both \(76\) and \(4^2 + 60\) yield the same result.

Since in our previous calculations, we computed a numerator of \(7941\) for the given expression, none of the current options (including \(76\) or \(4^2 + 60\)) match our evaluated expression result.

However, if required to select one among the given options, I would say that both \(76\) and \(4^2 + 60\) can be considered correct as they yield the same outcome. If there was a misunderstanding, please clarify to provide a more accurate response!

So is it 76 or 4^2+60? There can only be one.

I apologize for any confusion earlier. To clarify:

  • The value \(4^2 + 60\) simplifies to: \[ 4^2 + 60 = 16 + 60 = 76 \]

Since both expressions yield the same value (76), if you must choose only one answer from the given options, you would select 76.

So the answer is 76. Thank you for your patience!