Question

Marco planted a tree that was 54 inches tall several years ago. The tree has grown at a rate of approximately 1.5 inches per year. Marco uses this equation to calculate the tree’s height,
h.


What does the x
represent in this equation?

Answer 1

Rational numbers a and c are plotted on the number line.

The number line shows point A is 6 units to the left of 0 and point C is 2 units to the right of 0.

Based on the number line, which statement is true?

Answer 2

A.
The value of a-c
is positive.

B.
The value of -a-c
is positive.

C.
The value of c-a
is negative.

D.
The value of -c-a
is negative.

Answer 3

In the context of the equation that Marco uses to calculate the tree's height \( h \), the variable \( x \) typically represents the number of years since the tree was planted.

Given that the tree was initially 54 inches tall and grows at a rate of approximately 1.5 inches per year, the equation for the tree’s height over time could be expressed as:

\[
h = 54 + 1.5x
\]

In this equation:
- \( h \) is the height of the tree in inches.
- \( 54 \) is the initial height of the tree.
- \( 1.5 \) is the growth rate in inches per year.
- \( x \) is the number of years since the tree was planted.

Answer 4

Based on the information you've provided:

- Point A is 6 units to the left of 0, which means that point A represents the rational number \(-6\).
- Point C is 2 units to the right of 0, which means that point C represents the rational number \(2\).

With this information, we can make a few comparisons regarding their values:

1. \( A < 0 \) (since \( A = -6 \))
2. \( C > 0 \) (since \( C = 2 \))
3. \( A < C \) (since \(-6 < 2\))

Thus, the true statement based on the placement of points A and C on the number line would be that point A is less than point C:

**-6 < 2** or **A < C**.

Answer 5

Let's analyze the options based on the values we have determined for \( a \) and \( c \):

- \( a = -6 \) (point A)
- \( c = 2 \) (point C)

Now we'll evaluate each of the statements one by one.

**A. The value of \( a - c \) is positive.**

\[
a - c = -6 - 2 = -8
\]

This is negative, so **A is false**.

---

**B. The value of \( -a - c \) is positive.**

\[
-a - c = -(-6) - 2 = 6 - 2 = 4
\]

This is positive, so **B is true**.

---

**C. The value of \( c - a \) is negative.**

\[
c - a = 2 - (-6) = 2 + 6 = 8
\]

This is positive, so **C is false**.

---

**D. The value of \( -c - a \) is negative.**

\[
-c - a = -2 - (-6) = -2 + 6 = 4
\]

This is positive, so **D is false**.

---

Based on the evaluations, the only true statement is **B: The value of \(-a - c\) is positive.**