Answer:
see below
Step-by-step explanation:
Part A
We can shift f(x) to the left or we can shift f(x) up to make it become g(x)
Part B
y = f(x + k) k > 0 moves it left
Using the point ( 2,8) for f(x) and ( 0,8) for g(x)
k is 2 units
g(x) = f(x+2)
y = f(x) + k k > 0 moves it up
Using the point ( 0,-2) for f(x) and ( 0,8) for g(x)
The difference between -2 and 8 is 10
k = 10
g(x) = f(x) + 10
Part C
for the shift to the left g(x) = f(x+2)
for the shift up g(x) = f(x) + 10
The first is C and the second is D
Answer:
D) 27
Step-by-step explanation:
It's a rectangle so the opposite sides are congruent to each other.
<em />
<em>Long Side:</em>
6x + 6 = 42
subtract 6 from both sides:
6x = 36
divide both sides by 6:
x = 6
<em />
<em>Short Side:</em>
5y + 5 = 30
subtract 5 from both sides:
5y = 25
divide both sides by 5:
y = 5
<em />
<em>The Equation:</em>
2x + 3y
substitute in the values:
2(6) + 3(5)
do the multiplication:
12 + 15
add the values together:
27
In order to calculate standard deviation, apply the standard deviation formula, which is given in the attached file. In this formula, we are finding the square root of the sum of the square of given values less their mean value (the sum of the given numbers divided to their amount) divided to N-1, where N is the amount of the given numbers. When we calculate the mean, it is 42.7 and the standard deviation is 10.02275