Question

they connect through recycling energy and matter. now, how does this cycle help keep carbon dioxide and oxygen balanced in our atmosphere?

Explanation:

This question is about the balance of carbon dioxide and oxygen in the atmosphere, likely related to the carbon - oxygen cycle (involving photosynthesis and respiration). Photosynthesis by plants takes in $\ce{CO_2}$ and releases $\ce{O_2}$, while respiration by organisms (including plants and animals) takes in $\ce{O_2}$ and releases $\ce{CO_2}$. These two processes are interdependent and work together to maintain the balance of these two gases in the atmosphere. For example, plants during photosynthesis use carbon dioxide and water (in the presence of light energy) to produce glucose and oxygen ($\ce{6CO_2 + 6H_2O \xrightarrow[chlorophyll]{light} C_6H_{12}O_6 + 6O_2}$). Organisms then use the oxygen in respiration, where glucose and oxygen are converted into carbon dioxide, water, and energy ($\ce{C_6H_{12}O_6 + 6O_2
ightarrow 6CO_2 + 6H_2O + energy}$). This cycle of photosynthesis and respiration ensures that the amount of carbon dioxide and oxygen in the atmosphere remains relatively stable.

Answer:

The carbon - oxygen cycle (involving photosynthesis and respiration) maintains the balance. Photosynthesis (by plants) absorbs $\ce{CO_2}$ and releases $\ce{O_2}$ ($\ce{6CO_2 + 6H_2O \xrightarrow[chlorophyll]{light} C_6H_{12}O_6 + 6O_2}$), while respiration (by organisms) absorbs $\ce{O_2}$ and releases $\ce{CO_2}$ ($\ce{C_6H_{12}O_6 + 6O_2
ightarrow 6CO_2 + 6H_2O + energy}$). These two processes are complementary, keeping the levels of $\ce{CO_2}$ and $\ce{O_2}$ in the atmosphere balanced.