Answer:
x = - 1, x = - 11
Step-by-step explanation:
Given
2| x + 6 | - 4 = 6 ( add 4 to both sides )
2|x + 6 | = 10 ( divide both sides by 2 )
| x + 6 | = 5
The absolute value function always gives a positive result, but the expression inside can be positive or negative, that is
x + 6 = 5 or - (x + 6) = 5
solve both
x + 6 = 5 ( subtract 6 from both sides )
x = - 1
or
- (x + 6) = 5 , that is
- x - 6 = 5 ( add 6 to both sides )
- x = 11 ( multiply both sides by - 1 )
x = - 11
Greater because the product of the fraction is greater than 1
20 = 40e^-0.1446t
e^-0.1446t = 0.5
t = ln 0.5 / -0.1446
t = 4.8 days
Answer:
y = (x-3)^2 - 17
Step-by-step explanation:
To complete the square, take the middle term bx and divide it in two. Then take the square.
x^2 - 6x - 8 has bx = -6x. Take -6/2 = -3. Square -3^2 = 9.
Now to finish completing the square add 9 and subtract 9 from one side.
y = x^2 - 6x - 8
y = (x^2 - 6x +9) -9 - 8
y = (x-3)^2 - 17
Answer:
a) 46.98%
b) increasing rate of change
Step-by-step explanation:
In year 1987, investment worth $29800
In year 1997, investment worth $43800
Rate of change = 1997investment - 1987investment / 1987investment × 100
Rate of change = 43800 - 29800/29800 × 100
= 14000/29800 × 100
= 0.46979 × 100
= 46.98%
Therefore, the rate of change of the investment during the time period is 46.98%.
b) The rate of change of the investment is increasing. This is as a result of the following reasons. First, the value of rate of change is positive. Second, there is no value for rate of change for period before the time period so we cannot compare rate of change.
