Denali, which is about 20,000 ft. above sea level, is the highest mountain in the United States. Mt. Everest, the highest mountain on earth, is about 9×10^3

Question

ft. higher than Denali. About how high is Mt. Everest? The answer should be in scientific notation.(1 point)
Responses

1.1×103
ft.
1 point 1 times 10 cubed ft. - no response given

2.9×104
ft.
2 point 9 times 10 to the 4th power ft. - no response given

29,000 ft.

Answer 1

To find the height of Mt. Everest, we start from the height of Denali, which is about 20,000 ft, and add the additional height of 9,000 ft (since Mt. Everest is about \( 9 \times 10^3 \) ft higher than Denali).

1. Convert the height of Denali to scientific notation: \[ 20,000 \text{ ft} = 2.0 \times 10^4 \text{ ft} \]

2. Convert the additional height to scientific notation: \[ 9,000 \text{ ft} = 9.0 \times 10^3 \text{ ft} \]

3. Now, we add the two heights together: \[ \text{Total height} = 2.0 \times 10^4 \text{ ft} + 9.0 \times 10^3 \text{ ft} \] We can express \( 9.0 \times 10^3 \text{ ft} \) in terms of \( 10^4 \): \[ 9.0 \times 10^3 = 0.9 \times 10^4 \]

4. Now add: \[ 2.0 \times 10^4 + 0.9 \times 10^4 = (2.0 + 0.9) \times 10^4 = 2.9 \times 10^4 \text{ ft} \]

Therefore, the height of Mt. Everest is approximately \( 2.9 \times 10^4 \) ft.

The correct response from your options is: 2.9×10^4 ft.