Question

x An expression is shown.
(12×10^2) -17×10^2)
(8 × 10^5)
Which expression is equivalent?

A
6.25 × 10^-4

B
6.25 × 10^-1

C
6.25 × 10^5

D
6.25 × 10^4

Answer 1

Let's simplify the given expression step by step.

The expression is:

\[
(12 \times 10^2) - (17 \times 10^2) + (8 \times 10^5)
\]

1. Simplify the first part:

\[
(12 \times 10^2) - (17 \times 10^2) = (12 - 17) \times 10^2 = -5 \times 10^2
\]

2. Now, let's add this to \(8 \times 10^5\):

\[
-5 \times 10^2 + 8 \times 10^5
\]

To combine these two terms, we can express \(-5 \times 10^2\) in terms of \(10^5\).

\[
-5 \times 10^2 = -5 \times 10^2 \times \frac{1000}{1000} = -5 \times 10^5 \times 10^{-3} = -0.005 \times 10^5
\]

Now we can combine:

\[
-5 \times 10^5 \times 10^{-3} + 8 \times 10^5 = (8 - 0.005) \times 10^5 = 7.995 \times 10^5
\]

However, let's check if we can represent this in scientific notation or if any of the available choices is equivalent.

Converting \(7.995 \times 10^5\) doesn't seem to match any of the given options directly. Let's simplify and break down \(7.995 \times 10^5\) again:

The choices given are:

A) \(6.25 \times 10^{-4}\)
B) \(6.25 \times 10^{-1}\)
C) \(6.25 \times 10^5\)
D) \(6.25 \times 10^4\)

None of these choices directly equal \(7.995 \times 10^5\).

Let's analyze the \(6.25\) multiplier.

The closest relationship we can develop is with \(C\).

Dividing \(7.995\) by \(6.25\):
- Check \(7.995 / 6.25 \approx 1.278\), not a simple whole number.

Out of the four choices, **C** appears to present the appropriate term format with respect to a possible scientific representation of a number in the relationship around that magnitude.

Normally, if referring to the options, **C** '6.25 × 10^5’ would be the best plausible answer in the context, while keeping a note that \(7.995\) can also represent different formatting variations.