Question

1. the pattern in this table continues. determine the expression that relates the number of triangles to the figure number.

1. which line is the graph of ( x + 5 = 0 )?

Explanation:

Question 6

Step1: Test option a ($2f$)

For \( f = 1 \), \( 2\times1 = 2 \) (matches \( t = 2 \)). For \( f = 2 \), \( 2\times2 = 4 \) (matches \( t = 4 \)). For \( f = 3 \), \( 2\times3 = 6 \) (matches \( t = 6 \)). For \( f = 4 \), \( 2\times4 = 8 \) (matches \( t = 8 \)). For \( f = 5 \), \( 2\times5 = 10 \) (matches \( t = 10 \)).

Step2: Test option b ($2 + t$)

This relates \( t \) to itself, not \( f \), so invalid.

Step3: Test option c ($2t$)

For \( f = 1, t = 2 \), \( 2\times2 = 4
eq1 \), invalid.

Step4: Test option d ($2 + f$)

For \( f = 1 \), \( 2 + 1 = 3
eq2 \), invalid.

The equation \( x + 5 = 0 \) simplifies to \( x = -5 \). A line with \( x = -5 \) is vertical (constant \( x \)-value). From the graph, Line S has \( x = -5 \) (since it's at \( x = -5 \) across all \( y \)-values). Line R is \( x = 5 \), Line P is horizontal, Line Q is horizontal.

Answer:

a. \( 2f \)

Question 7