Answer:
Step-by-step explanation:
<u>The absolute value function is:</u>
<u>Step 1. Function is vertically stretched by a factor of 3:</u>
<u>Step 2. Shifted two units left:</u>
<u>Step 3. Shifted 5 units down:</u>
<em>See attached</em>
<em>Steps are </em><em>Black → Blue → Green → Red</em>
Answer:
Step-by-step explanation:
First, to figure out the equation of a line you must find the slope then plug in the coordinates.
In order to find the slope of the equation, you know that it is perpendicular to the equation y = -3x + 7.
Perpendicular slopes are basically reciprocals with opposite signs; you flip the number and give it the opposite symbol.
For example, the perpendicular slope of 2 would -1/2, because flipping the fraction 2/1 is 1/2 and the opposite sign of + would be -.
Therefore, the perpendicular slope of -3 would be 1/3, be 3/1 flipped upside down is 1/3 and the opposite sign of - is +.
Then you plug in the slope into the equation of a line along with the coordinate.
A line is y = mx + b
Since you found the slope, m = 1/3
They also give you the coordinate (3,5), meaning when x = 3, the y =5.
You plug everything into the equation to solve for b:
5 = (1/3)(3) + b
b = 5 - (1/3 * 3) = 5 - 1 = 4
Since you have values for m and b, the equation can now be constructed as
y = 1/3x + 4
Answer:
The nth term of the geometric sequence 7, 14, 28, ... is:
Step-by-step explanation:
Given the geometric sequence
7, 14, 28, ...
We know that a geometric sequence has a constant ratio 'r' and is defined by
where a₁ is the first term and r is the common ratio
Computing the ratios of all the adjacent terms
The ratio of all the adjacent terms is the same and equal to
now substituting r = 2 and a₁ = 7 in the nth term
Therefore, the nth term of the geometric sequence 7, 14, 28, ... is: