Answer:
Step-by-step explanation:
Givens
Area = L * w
w = x
l = x + 4
Area = 32
Solution
32 = x(x + 4)
32 = x^2 + 4x
x^2 + 4x - 32
(x + 8)(x - 4)
Only x - 4 is going to make any sense
x - 4 = 0
x = 4
The width is 4
The length is 4 + 4 = 8
4*8 = 32 which is the area.
We have a sample of 28 data points. The sample mean is 30.0 and the sample standard deviation is 2.40. The confidence level required is 98%. Then, we calculate α by:
The confidence interval for the population mean, given the sample mean μ and the sample standard deviation σ, can be calculated as:
Where n is the sample size, and Z is the z-score for 1 - α/2. Using the known values:
Where (from tables):
Finally, the interval at 98% confidence level is:
Answer:
x = 6 , 5. For these values of x they are equal.
Step-by-step explanation:
2x² - x + 55 =(x +5)²
2x² - x + 55 = x² + 2*x*5 + 5²
2x² - x + 55 = x² + 10x + 25
2x² - x + 55 - x² - 10x - 25 = 0
2x² - x² - x - 10x + 55 - 25 = 0
x² - 11x + 30 = 0
x² -6x - 5x + 30 = 0
x(x - 6) - 5(x - 6) = 0
(x - 6)(x - 5) = 0
x - 6 = 0 ; x - 5 = 0
x = 6 ; x = 5