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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?

5 answers

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.
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?

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.

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.

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.