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This system of linear inequalities can be used to find the possible heights, in inches, of Darius, d, and his brother William, w.

d ≥ 36

w < 68

d ≤ 4 + 2w

Which statements must be true about their heights? Select three options.

Darius is at least 36 inches tall.
Darius is at most 36 inches tall.
William’s height is less than 68 inches.
William’s height is at least 68 inches.
Darius is less than 4 inches taller than twice William’s height.
Darius is no more than 4 inches taller than twice William’s height.

Sagot :

Sethartiolamarceloidn

Answer:

Let's analyze each statement based on the given system of linear inequalities:

1. \( d \ge 36 \) – Darius is at least 36 inches tall.

2. \( w < 68 \) – William’s height is less than 68 inches.

3. \( d \le 4 + 2w \) – Darius is no more than 4 inches taller than twice William’s height.

Given these inequalities, the statements that must be true are:

1. **Darius is at least 36 inches tall.**

- This is directly stated by the inequality \( d \ge 36 \).

2. **William’s height is less than 68 inches.**

- This is directly stated by the inequality \( w < 68 \).

3. **Darius is no more than 4 inches taller than twice William’s height.**

- This is directly stated by the inequality \( d \le 4 + 2w \).

Thus, the correct options are:

- Darius is at least 36 inches tall.

- William’s height is less than 68 inches.

- Darius is no more than 4 inches taller than twice William’s height.

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