Question

1. which ordered pair represents the result of reflecting point d over the y-axis?

options:
a ( (-6, -5) )
b ( (5,6) )
c ( (5, -6) )
d ( (6,5) )
(image of coordinate plane with point d)

1. simplify the expression ( \frac{14^{11}}{14^8} ). write the expression with positive exponents.
2. plot all the points from the table in the coordinate plane.

point	coordinates
b	( (0, 2) )
c	( (1, 7) )
d	( (6, 0) )

(image of coordinate plane for plotting)

Explanation:

Question 4

Step1: Find coordinates of D

From the graph, point D has coordinates \((-6, 5)\) (assuming the grid and position; x=-6, y=5).

Step2: Reflect over y - axis

The rule for reflecting a point \((x,y)\) over the y - axis is \((x,y)\to(-x,y)\). So for \((-6,5)\), the reflection is \((6,5)\).

Step1: Use exponent rule

When dividing exponents with the same base \(a^m\div a^n=a^{m - n}\), here \(a = 14\), \(m = 11\), \(n = 6\).
So \(\frac{14^{11}}{14^{6}}=14^{11 - 6}\)

Step2: Calculate the exponent

\(11-6 = 5\), so \(14^{11-6}=14^{5}\)

Step1: Plot point A

For point A \((3,5)\), move 3 units to the right on the x - axis and 5 units up on the y - axis and mark the point.

Step2: Plot point B

For point B \((0,2)\), stay at \(x = 0\) (origin on x - axis) and move 2 units up on the y - axis and mark the point.

Step3: Plot point C

For point C \((1,7)\), move 1 unit to the right on the x - axis and 7 units up on the y - axis and mark the point.

Step4: Plot point D

For point D \((6,0)\), move 6 units to the right on the x - axis and stay at \(y = 0\) (x - axis) and mark the point.

Answer:

D. \((6,5)\)

Question 5