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

Question

Responses

2.9×10^4
2.9
×
10
4
ft.
2.9 times 10 superscript 4 baseline ft.

29,000 ft.
29,000 ft.

2.9×10^3
2.9
×
10
3
ft.
2.9 times 10 cubed ft.

1.1×10^3
1.1
×
10
3
ft.

Answer 1

To find the height of Mt. Everest, we start with the height of Denali, which is approximately 20,000 ft (or \(2.0 \times 10^4\) ft). Since Mt. Everest is about \(9 \times 10^3\) ft higher than Denali, we need to add this to Denali's height:

\[ \text{Height of Mt. Everest} = \text{Height of Denali} + \text{Height increase} \] \[ \text{Height of Mt. Everest} = 20,000 , \text{ft} + 9,000 , \text{ft} \] In scientific notation, this is: \[ \text{Height of Mt. Everest} = 2.0 \times 10^4 , \text{ft} + 9.0 \times 10^3 , \text{ft} \]

We can convert \(9,000\) ft into scientific notation: \[ 9,000 , \text{ft} = 9.0 \times 10^3 , \text{ft} \]

Now, we rewrite \(20,000\) ft in terms of powers of ten: \[ 2.0 \times 10^4 , \text{ft} + 0.9 \times 10^4 , \text{ft} = (2.0 + 0.9) \times 10^4 = 2.9 \times 10^4, \text{ft} \]

Thus, the height of Mt. Everest is approximately: \[ \boxed{2.9 \times 10^4} , \text{ft} \]