Answer:
(2x – 7) × (2x + 7)
Step-by-step explanation:
From the question given above, the following data were obtained:
Area (A) = (4x² – 49) m²
Dimension =?
The picture in the question above has a rectangular shape. Thus, the area is given by:
Area (A) = Length (L) × Width (W)
A = L × W
The dimension of the shape will be:
L × W
Now, we shall determine the dimension (L × W) as follow:
Area (A) = (4x² – 49) m²
Dimension (L × W) =?
A = L × W
L × W = 4x² – 49
Recall:
4 = 2²
49 = 7²
Thus,
L × W = 2²x² – 7²
L × W = (2x)² – 7²
Different of two squares
L × W = (2x – 7)(2x + 7)
L × W = (2x – 7) × (2x + 7)
Dimension = (2x – 7) × (2x + 7)
Therefore, the possible dimension (L × W) of the shape is (2x – 7) × (2x + 7)
Answer:
4 √6
Step-by-step explanation:
We have a few right triangles. We know that a²+b²=c², with c being the side opposite the right angle. Representing the side without a value as z, we have:
m²+z² = (8+4)² = 12²
4²+n²=z²
8²+n²=m²
We have 3 equations with 3 unknown variables, so this should be solvable. One way to find a solution is to put everything in terms of m and go from there. First, we can take n out of the equations entirely, removing one variable. We can do this by solving for it in terms of z and plugging that into the third equation, removing a variable as well as an equation.
4²+n²=z²
subtract 4²=16 from both sides
z²-16 = n²
plug that into the third equation
64 + z² - 16 = m²
48 + z² = m²
subtract 48 from both sides to solve for z²
z² = m² - 48
plug that into the first equation
m² + m² - 48 = 144
2m² - 48 = 144
add 48 to both sides to isolate the m² and its coefficient
192 = 2m²
divide both sides by 2 to isolate the m²
96 = m²
square root both sides to solve for m
√96 = m
we know that 96 = 16 * 6, and 16 = 4², so
m = √96 = √(4²*6) = 4 √6
Answer:
√97
Step-by-step explanation:
12 feet below would be -12. from -12 to 0 would be 12 feet.
from 0 to 32 above would be 32 feet.
Total distance = 12 + 32 = 44 feet.
Answer:
r
=
1
Step-by-step explanation:
