Answer: The side lengths of mirror and painting are 7 ft and 9 ft respectively.
Step-by-step explanation: Given that a square mirror has sides measuring 2 ft less than the sides of a square painting and the difference between their areas is 32 ft.
We are to find the lengths of the sides of the mirror and the painting.
Let x ft represents the length of the side of mirror. Then, the side length of square painting is (x+2) ft.
According to the given information, we have

Therefore, the side length of mirror is 7 ft and the side length of painting is (7+2) = 9 ft.
Thus, the side lengths of mirror and painting are 7 ft and 9 ft respectively.
Answer:
The gradient of the straight line that passes through (2, 6) and (6, 12) is
.
Step-by-step explanation:
Mathematically speaking, lines are represented by following first-order polynomials of the form:
(1)
Where:
- Independent variable.
- Dependent variable.
- Slope.
- Intercept.
The gradient of the function is represented by the first derivative of the function:

Then, we conclude that the gradient of the staight line is the slope. According to Euclidean Geometry, a line can be form after knowing the locations of two distinct points on plane. By definition of secant line, we calculate the slope:
(2)
Where:
,
- Coordinates of point A.
,
- Coordinates of point B.
If we know that
and
, then the gradient of the straight line is:



The gradient of the straight line that passes through (2, 6) and (6, 12) is
.
1/4 = x/360
4×9 = 36 so 4 × 90 = 360
also multiply the numerator by 90 and you get
1/4 × 90/90 = 90/360
Answer:
10,692
Step-by-step explanation:
GCF stands for Greatest Common Factor.
The way to find it is easy once you have the prime decomposition.
Search for common factors in the decomposition and take the least power, then multiply them all.
So, in our case, as the numbers are already broken down into prime factors
, we have

Answer:
68% of the sample can be expected to fall between 28 and 32 cm
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 30
Standard deviation = 2
What proportion of the sample can be expected to fall between 28 and 32 cm
28 = 30-2
28 is one standard deviation below the mean
32 = 30 + 2
32 is one standard deviation above the mean
By the Empirical Rule, 68% of the sample can be expected to fall between 28 and 32 cm