Two students were testing the parachute designs they made for an egg-drop project. Both students dropped their eggs from a height of 10 feet. One design made the egg fall at a rate 5 feet per second, and the other design made the egg fall at a rate of 3 feet per second. If x represents the time in seconds that the egg falls and y represents the height of the egg, which system of equations represents the situation described?(1 point)

Question

Responses

{y=10+5xy=10+3x
enlarged left brace start layout first row y equals 10 plus 5 x second row y equals 10 plus 3 x end layout

{y=−5xy=−3x
enlarged left brace start layout first row y equals negative 5 x second row y equals negative 3 x end layout

{y=10−5xy=10−3x
enlarged left brace start layout first row y equals 10 minus 5 x second row y equals 10 minus 3 x end layout

{y=5x−10y=3x −10
enlarged left brace start layout first row y equals 5 x minus 10 second row y equals 3 x minus 10 end layout
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Answer 1

To represent the situation, we need to set up equations based on the height of the egg over time for both parachute designs.

Given:

• The height from which both eggs are dropped is 10 feet.
• The rate of descent for the first design is 5 feet per second, and for the second design, it is 3 feet per second.

The height \(y\) decreases as time \(x\) increases. We can think of the height of the egg at time \(x\) as starting from 10 feet and decreasing with time at the given rates.

For the first design (5 feet/second):

• The equation would be: \(y = 10 - 5x\)

For the second design (3 feet/second):

• The equation would be: \(y = 10 - 3x\)

Thus, the system of equations representing the situation is:

\[ \begin{align*} y &= 10 - 5x \ y &= 10 - 3x \end{align*} \]

So the correct answer is:

{y=10−5xy=10−3x}