Answer:
The roots are;
x = (2 + i)/5 or (2-i)/5
where the term i is the complex number representing the square root of -1
Step-by-step explanation:
Here, we want to use the completing the square method to solve the quadratic equation;
f(x) = -5x^2 + 4x -1
Set the function to zero
0 = -5x^2 + 4x - 1
So;
-5x^2 + 4x = 1
divide through by the coefficient of x which is -5
x^2 - 4/5x = -1/5
We now take half of the coefficient of x and square it
= -2/5^2 = 4/25
add it to both sides
x^2 - 4x/5 + 4/25= -1/5 + 4/25
(x- 2/5)^2 = -1/5 + 4/25
(x - 2/5)^2 = -1/25
Take the square root of both sides
x - 2/5 = √( -1/25
x - 2/5 = +i/5 or -i/5
x = 2/5 + i/5 or 2/5 - i/5
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $7,000
Interest rate (i)= 2.5%
<u>To calculate the future value after x years, we need to use the following formula:</u>
FV= PV*(1 + i)^x
<u>Now, for 9 years:</u>
x= 9
FV= 7,000*(1.025^9)
FV=$8,742.04
Answer:
y = (1/3)x - 4
Step-by-step explanation:
Any line perpendicular to the given equation y = -3x + 4 will have a slope which is the negative reciprocal of -3; that is, +1/3.
Start with the general slope-intercept form y = mx + b.
Insert the coordinates 6 and -2 into y = mx + b: -2 = (1/3)(6) + b, or
-2 = 2 + b. Thus, b = -4, and the desired equation is
y = (1/3)x - 4
You could buy 6 keychains spending 4 dollars each. 6 * 4 = $24.
