Answer:
31/4 cups of flour have left.
Step-by-step explanation:
3 1/2=7/2
4 3/4=19/4
--------------
16-7/2-19/4
64/4-14/4-19/4
31/4
The area of the room is 147.5 square feet so Michelle's reasoning was incorrect.
Step-by-step explanation:
Step 1:
To calculate the area of the given room, we divide the unknown shape into known shapes.
The room's shape is made of 2 rectangles.
The area of a rectangle is the product of its length and its width.
One rectangle has a length of 10 feet and a width of 12 1/2 feet.
The other rectangle has a length of 15 - 10 = 5 feet and a width of 4 1/2 feet.
Step 2:
The area of the first rectangle = (10)(12 1/2) = (10)(12.5) = 125 square feet.
The area of the second rectangle (10)(4 1/2) = (5)(4.5) = 22.5 square feet.
The total area of the room = 125 + 22.5 = 147.5 square feet.
Answer:
32x² + 36x + 9
Explanation:
To answer the question, we will simply multiply each term from the first bracket by each term from the second bracket and then combine like terms to get the final expression.
This can be done as follows:
(8x + 3)(4x + 3)
8x(4x) + 8x(3) + 3(4x) + 3(3)
32x² + 24x + 12x + 9
32x² + 36x + 9
Hope this helps :)
Answer:
404.990 in^2
Step-by-step explanation:
I think, I cant be 100% sure but I'm pretty sure that's the answer, sorry if I'm wrong
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!