When you receive Plant A, it is 4 cm tall and grows at a constant rate of 2 cm per month. When you receive Plant C, it is 8 cm tall and grows at a constant rate of 2 cm per month.

Question

Lines a and c are parallel. Will Plants A and C ever be the same height?
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Yes

No

Answer 1

To determine if Plants A and C will ever be the same height, we can set up equations based on their initial heights and growth rates.

Let's denote:

• \( h_A(t) \) as the height of Plant A after \( t \) months,
• \( h_C(t) \) as the height of Plant C after \( t \) months.

For Plant A:

• Initial height = 4 cm
• Growth rate = 2 cm/month

Thus, the height of Plant A after \( t \) months can be expressed as: \[ h_A(t) = 4 + 2t \]

For Plant C:

• Initial height = 8 cm
• Growth rate = 2 cm/month

Thus, the height of Plant C after \( t \) months can be expressed as: \[ h_C(t) = 8 + 2t \]

To find out if and when the heights are the same, we need to set \( h_A(t) = h_C(t) \): \[ 4 + 2t = 8 + 2t \]

Now, if we simplify this: Subtract \( 2t \) from both sides: \[ 4 = 8 \]

This statement is false, meaning that there is no value of \( t \) that makes the heights of Plant A and Plant C equal.

Since both plants grow at the same rate but Plant C starts at a greater height, they will never be the same height.

Therefore, the answer is No.