Answer:
[-3, ∞)
Step-by-step explanation:
There are many ways to find the range but I will use the method I find the easiest.
First, find the derivative of the function.
f(x) = x² - 10x + 22
f'(x) = 2x - 10
Once you find the derivative, set the derivative equal to 0.
2x - 10 = 0
Solve for x.
2x = 10
x = 5
Great, you have the x value but we need the y value. To find it, plug the x value of 5 back into the original equation.
f(x) = x² - 10x + 22
f(5) = 5² - 10(5) + 22
= 25 - 50 +22
= -3
Since the function is that of a parabola, the value of x is the vertex and the y values continue going up to ∞.
This means the range is : [-3, ∞)
Another easy way is just graphing the function and then looking at the range. (I attached a graph of the function below).
Hope this helped!
Answer:
D
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
To calculate m use the slope formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (3, 6) and (x₂, y₂ ) = (8, 4)
m =
= -
, hence
y = -
x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (8, 4), then
4 = -
+ c ⇒ c = 4 +
= 
y = -
x +
← equation of line
Answer:
d
Step-by-step explanation:
cannot be a or c cause it has a negative sign in front of it causing it to reflect over y axis. Cannot be B cause it doesn't have two coefficients with X. I also graphed it.
Answer:
18.6 months
Step-by-step explanation:
Given that :
Best fit line from scatterplot :
y=-12.05x +224.26
x = Number of month
y = charge on battery
Number of months a typical battery uses before being dead completely :
When battery is dead completely ; charge =0, y = 0
y = -12.05x + 224.26
0 = - 12.05x + 224.26
12.05x = 224.26
x = 224.26 / 12.05
x = 18.610788
Hence, 18.6 months before battery is completely dead.
im pretty sure it's the first option.