Answer:
7 coats (cups) of paint
Step-by-step explanation:
The dimensions of the room are;
The length of the room, l = 4 m
The width of the room, w = 3 m
The height of the room h = 2.5 m
The area one coat (taking the coat to mean cup) of paint can paint, A/c = 5 m²/cup
The total surface area of the room wall, A = 2 × l × h + 2 × w × h
∴ A = 2 × 4 m × 2.5 m + 2 × 3 m × 2.5 m = 35 m²
The amount of paint to be used, c = A/(A/c)
∴ c = 35 m²/(5 m²/cup) = 7 cups
The amount of paint to be used, c = 7 cups
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
Given:
The equation is,
Explanation:
Simplify the equation by using logarthimic property.
Simplify further.
Solve the quadratic equation for x.
From the above equation (x - 6) = 0 or (x - 3) = 0.
For (x - 6) = 0,
For (x - 3) = 0,
The values of x from solving the equations are x = 3 and x = 6.
Substitute the values of x in the equation to check answers are valid or not.
For x = 3,
Equation satisfy for x = 3. So x = 3 is valid value of x.
For x = 6,
Equation satifies for x = 6.
Thus values of x for equation are x = 3 and x = 6.
Alright, so the answer for:
3) is 3v + 4
