Think of the equation of a linear function:
Recall y = mx + b for vertical shifts, we just add or subtract from 'b' and that will move the line up or down accordingly.. However, for horizontal shifts, we will need to add or subtract from 'x'. Note that the slope or 'm' stays the same for each type of shift.
Now that we know how the shifts occur, we might consider a different form of the equation for a linear function: y = a(x - h) + k here the 'a' is just our slope, 'k' is our original y intercept, and 'h' will represent the amount of horizontal shift.
So to get the desired transformations of a horizontal shift to the left of 8 and a vertical shift of down 3 from our original function y = x, we can make the following changes: y = (x + 8) - 3 Now you might be confused with how we got the 'x + 8'.. Let's consider values of 'h'. For positive values of h, the result will be a shift to the right and for negative values of h the result will be a shift to the left. So since we want a shift to the left we need to use a '-8' and when we substitute that into our new form, y = (x - h) + k you can see the sign change.
Now we can simplify of course and get the final equation: y = x + 5 or in function form f(x) = x + 5
Answer:
y = 3.2
Step-by-step explanation:
Simplifying
5y + -6 = 10
Reorder the terms:
-6 + 5y = 10
Solving
-6 + 5y = 10
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '6' to each side of the equation.
-6 + 6 + 5y = 10 + 6
Combine like terms: -6 + 6 = 0
0 + 5y = 10 + 6
5y = 10 + 6
Combine like terms: 10 + 6 = 16
5y = 16
Divide each side by '5'.
y = 3.2
Simplifying
y = 3.2
Answer:
0.13 ft/min
Step-by-step explanation:
We are given that
We have to find the increasing rate of change of height of pile when the pile is 12 ft high.
Let d be the diameter of pile
Height of pile=h
d=h
Radius of pile,r=
Volume of pile=
h=12 ft
Substitute the values
We know 1 meter = 3.28084 feet
So 1 square meter = 3.28084 × 3.28084 square feet.
Now to convert from square feet to square meters, we need to divide by 3.28084 × 3.28084.
The area given in the news paper advertisement is 1330 square feet.
So to convert to square meters we divide by 3.28084 × 3.28084
We get
1330 square feet = 
Hence 1330 square feet of area is equal to 123.56 square meters.
Answer:
Boundedness requires that there is only a bounded number of different kinds of parts
Step-by-step explanation:
