Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Select the correct answer.

Two hot air balloons are flying above a park. One balloon started at a height of 3,000 feet above the ground and is decreasing in height at a rate of 40 feet per minute. The second balloon is rising at a rate of 50 feet per minute after beginning from a height of 1,200 feet above the ground.

Given that [tex]\( h \)[/tex] is the height of the balloons after [tex]\( m \)[/tex] minutes, determine which system of equations represents this situation.

A.
[tex]\[ h = 3,000 - 40m \][/tex]
[tex]\[ h = 1,200 + 50m \][/tex]

B.
[tex]\[ \begin{array}{l}
h = 3,000 + 40m \\
h = 1,200 - 50m
\end{array} \][/tex]

C.
[tex]\[ m = 3,000 - 40h \][/tex]
[tex]\[ m = 1,200 + 50h \][/tex]

D.
[tex]\[ \begin{array}{l}
h = 3,000m - 40 \\
h = 1,200m + 50
\end{array} \][/tex]

Sagot :

GinnyAnswer
Let's break down the given situation into a system of linear equations based on the heights of two hot air balloons over time:

1. First Balloon:
- Starts at a height of 3,000 feet
- Decreases in height at a rate of 40 feet per minute

Therefore, if [tex]\( h \)[/tex] represents the height of the first balloon after [tex]\( m \)[/tex] minutes, the equation for the first balloon can be written as:
[tex]\[ h = 3000 - 40m \][/tex]

2. Second Balloon:
- Starts at a height of 1,200 feet
- Increases in height at a rate of 50 feet per minute

Therefore, if [tex]\( h \)[/tex] represents the height of the second balloon after [tex]\( m \)[/tex] minutes, the equation for the second balloon can be written as:
[tex]\[ h = 1200 + 50m \][/tex]

Given these two equations, we form a system of equations to represent the situation:

[tex]\[ \begin{array}{l} h = 3000 - 40m \\ h = 1200 + 50m \\ \end{array} \][/tex]

Therefore, the correct answer is:

A.
[tex]\[ \begin{array}{l} h = 3000 - 40 m \\ h = 1200 + 50 m \\ \end{array} \][/tex]
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.