We do completing the square as follows:
1. Put all terms with variable on one side and the constants on the other side.
<span>5x^2 - 3x = 25
2. Factor out the coefficient of the x^2 term.
</span>5(x^2 - 3x/5) = 25
3. Inside the parentheses, we add a number that would complete the square and also add this to the other side of the equation. In this case we add 9/100 and on the other side we add 9/20.
5(x^2 - 3x/5 + 9/100) = 25 + 9/20
4. We simplify as follows:
5(x^2 - 3x/5 + 9/100) = 25 + 9/20
5(x - 3/10)^2 = 509/20
(x - 3/10)^2 = 509/100
x1 = √(509) /100 + 3/10
x2 = -√(509) /100 + 3/10
Assuming that this is a compounding interest rate, we use the future value formula which is expressed as: F = P ( 1 + i )^n where F is the future value, P is the present value, i is the interest rate and n is the compounding periods. We do as follows:
F = P ( 1 + i )^n
8000 = 4000 ( 1 + 0.0553)^n
n = 12.88 yrs or about 13 years
Therefore, option D is the answer.
Answer:
No.
Pytagorean theorem only applies for right triangle, which is basically a triangle with a 90° angle
=> Just from the image alone, we can see that technically all three angles of that triangle is larger or smaller than 90°, so it is impossible to find the missing side by using Pytagorean theorem.
Answer:
b=4
Step-by-step explanation:
A = 1/2 b*h
24 = 1/2 b* (3b)
combine like terms
24 = 1/2 *3 * b^2
24 = 3/2 b^2
multiply by 2/3 on each side
24 * 2/3 = 2/3 * 3/2 * b^2
16 = b^2
take the square root of each side
±sqrt(16) = sqrt(b)
±4 =b
but since b is a length it can only be positive
4 =b