Which of the following expressions is equal to 1930+43(10−7⋅40)?(1 point) Responses 5 5 193+43(10−7⋅4) 193 plus Start Fraction 4 over 3 End Fraction left parenthesis 10 minus 7 times 4 right parenthesis 403 Start Fraction 40 over 3 End Fraction 193+43(10−7⋅1)

Answer 1

To simplify the expression \( 1930 + 43(10 - 7 \cdot 40) \), let's break it down step by step.

First, calculate \( 7 \cdot 40 \):

\[ 7 \cdot 40 = 280 \]

Now substitute this back into the expression:

\[ 1930 + 43(10 - 280) \]

Next, calculate \( 10 - 280 \):

\[ 10 - 280 = -270 \]

Now substitute this back into the expression:

\[ 1930 + 43(-270) \]

Now calculate \( 43 \cdot -270 \):

\[ 43 \cdot -270 = -11610 \]

Now substitute this back into the expression:

\[ 1930 - 11610 \]

Finally, compute \( 1930 - 11610 \):

\[ 1930 - 11610 = -9670 \]

Now we need to check which of the provided expressions is equal to \(-9670\).

Let's evaluate the provided options step-by-step:

1. Option 1: \( 193 + 43(10 - 7 \cdot 4) \)

   • Calculate \( 7 \cdot 4 = 28 \)
   • Therefore, \( 10 - 28 = -18 \)
   • Now compute \( 43(-18) = -774 \)
   • Thus, \( 193 - 774 = -581 \)

2. Option 2: \( 193 + \frac{4}{3}(10 - 7 \cdot 40) \)

   • Already computed \( 10 - 280 = -270 \)
   • Now compute \( \frac{4}{3}(-270) = -360 \)
   • Therefore, \( 193 - 360 = -167 \)

3. Option 3: \( 403 \cdot \frac{40}{3} \)

   • Compute \( \frac{40}{3} \approx 13.33 \)
   • Therefore, \( 403 \cdot 13.33 \approx 5366.33 \)

4. Option 4: \( 193 + 43(10 - 7 \cdot 1) \)

   • Calculate \( 7 \cdot 1 = 7 \)
   • Thus, \( 10 - 7 = 3 \)
   • Compute \( 43 \cdot 3 = 129 \)
   • Therefore, \( 193 + 129 = 322 \)

None of the above options equal \(-9670\).

Therefore, none of the given responses are equal to the original expression \( 1930 + 43(10 - 7 \cdot 40) = -9670 \).