Answer:
y - 3 = ⁵/₂(x - 2) {the point-slope form of the equation}
y = ⁵/₂x - 2 {the slope-intercept form of the equation}
5x - 2y = 4 {the standard form of the equation}
Step-by-step explanation:
The point-slope form of equation is: y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope.
m = ⁵/₂
(2, 3) ⇒ x₀ = 2, y₀ = 3
So, the point-slope form of the equation:
y - 3 = ⁵/₂(x - 2)
Therefore:
y - 3 = ⁵/₂x - 5 {add 3 to both sides}
y = ⁵/₂x - 2 ← the slope-intercept form of the equation
-⁵/₂x + y = - 2 {multiply both sides by (-2)}
5x - 2y = 4 ← the standard form of the equation
Answer:
a) reflection across the x-axis, shift 8 units left
b) vertical stretch of 2, reflection across the y-axis, shift up 1
Step-by-step explanation:
The negative sign outside the square root represents a reflection across the x-axis, and the +8 inside represents a shift 8 to the left
The 2 outside the square root represents a vertical stretch of 2, and the negative sign inside the square root represents a reflection across the y-axis. The +1 at the end represents a shift up 1
Answer:
8(cos(π) +i·sin(π))
Step-by-step explanation:
The number in parentheses has a magnitude of ...
√(1^2 +(√3)^2) = √4 = 2
Then the cube of that number will have a magnitude of 8, eliminating the 2nd and 4th choices
The angle of the number in parentheses is ...
arctan(-√3/1) = -π/3
Then 3 times that angle will be -π, also π.
The number of interest has a magnitude of 8 and an angle of π, so is written in the desired form as ...
8(cos(π) +i·sin(π)) . . . . . matches the 3rd choice
To redraw the graph so the change in wins between the three seasons does not seem so great we use a bigger scale.
In the gragh that is shown, the scale used is 1 grid unit to represent 1 goal, if we may change the scale to something like 1 grid unit to represent 2 goals or 1 grid unit to represent 3 goal, then the change in wins between the three seasons will not seem so great
I checked my answer on a graph and the line turned out to be horizontal. When the line is horizontal it is called a zero slope line. There is no slope.
