Proof for the equations are given below.
Step-by-step explanation:
- Step 1: The diagram is made up of 1 square and 4 rectangles, and the whole figure is a square. So the area of the larger square (figure) must be equal to the sum of the areas of the 4 rectangles and 1 square. Find the area of the figure or the larger square.
Area of a square = (side length)²
Here, the length of the side of the larger square = a + b
⇒ Area of the square = (a + b)²
- Step 2: Find the sum of the areas of the 1 square and 4 rectangles.
Here, the side of the square = a - b
⇒ Area of the square (in the center) = (a - b)²
Area of a rectangle = length × width
Here, length = a and width = b
⇒ Area of the 4 rectangles = 4 × a × b = 4ab
∴ Sum of the areas = (a - b)² + 4ab
Now, both these areas are the same.
⇒ (a - b)² + 4ab = (a + b)²
- Step 3: Expand the above equation.
Left Hand Side = (a - b)² + 4ab = a² - 2ab + b² + 4ab = a² + 2ab + b²
= (a + b)²
= Right Hand Side of the equation
2x + x = 15
I'm not sure if that's what your asking but that's the equation used to find x.
76% would be your test score
Answer:
Step-by-step explanation:
x > -2
x < -2
Answer: 0.3413
Step-by-step explanation:
Given: an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard deviation is 2 pounds.
Let 
.
Let x be the random variable that denotes the amount of newspaper for garbage generated by each household each month.
If the data conforms to a normal distribution and a household is selected at random, the probability of its generating between 28 and 30 pounds per month is about
Hence, the required probability is 0.3413.
