Answer:
(x - 5)² = 41
Step-by-step explanation:
* Lets revise the completing square form
- the form x² ± bx + c is a completing square if it can be put in the form
(x ± h)² , where b = 2h and c = h²
# The completing square is x² ± bx + c = (x ± h)²
# Remember c must be positive because it is = h²
* Lets use this form to solve the problem
∵ x² - 10x = 16
- Lets equate 2h by -10
∵ 2h = -10 ⇒ divide both sides by 2
∴ h = -5
∴ h² = (-5)² = 25
∵ c = h²
∴ c = 25
- The completing square is x² - 10x + 25
∵ The equation is x² - 10x = 16
- We will add 25 and subtract 25 to the equation to make the
completing square without change the terms of the equation
∴ x² - 10x + 25 - 25 = 16
∴ (x² - 10x + 25) - 25 = 16 ⇒ add 25 to both sides
∴ (x² - 10x + 25) = 41
* Use the rule of the completing square above
- Let (x² - 10x + 25) = (x - 5)²
∴ (x - 5)² = 41
Answer:
-25/3
Step-by-step explanation:
Answer:
11/100
here's your solution
Step-by-step explanation:
=> percent means divided by 100
=>. so. 11% =. 11/100
=>. 11/100
hope it helps
Answer:
Step-by-step explanation:
surface area of cuboid=2(l*b+b*h+h*l)
=2(15*15+15*7+7*15)
=2(225+105+105)
=2*435
=870
Answer:
Mean = 528 ppm
Standard deviation = 90.8 ppm
Step-by-step explanation:
Assuming a basis of 100 trees
6 trees with 350 ppm (minimal growth)
10 trees with 450 ppm (slow growth)
47 trees with 550 ppm (moderate growth)
37 trees with 650 ppm (rapid growth)
Mean = xbar = Σx/N
x = each variable
xbar = mean
N = number of variables = 100
Σx = sum of all variables = sum of all the ppm = (6×350) + (10×450) + (47×550) + (37×550) = 52800
xbar = 52800/100 = 528 ppm
Standard deviation = σ = √[Σ(x - xbar)²/N]
x = each variable
xbar = mean = 528
N = number of variables = 12
Σ(x - xbar)² = [6(350 - 528)²] + [10(450 - 528)²] + [47(550 - 528)²] + [37(650 - 528)²] = 824400
σ = √[Σ(x - xbar)²/N] = √(824400/100) = 90.8 ppm
