4. If the determinant delta of a quadratic equation is positive, the equation has two real roots. If the determinant is negative, it has two imaginary roots. In this case, delta=b^2-4ac=(-1)^2-4*1*4=-15. Therefore, this equation has two imaginary roots.
The solution to system is x = 0 and y = -1
<em><u>Solution:</u></em>
<em><u>Given system of equations are:</u></em>
-8x + 2y = -2 ----------- eqn 1
4x + 4y = -4 ---------- eqn 2
We have to solve the system of equations
We can solve the equations by elimination method
<em><u>Multiply eqn 2 by 2</u></em>
8x + 8y = -8 ------ eqn 3
<em><u>Add eqn 1 and eqn 3</u></em>
-8x + 2y = -2
8x + 8y = -8
( + ) ---------------
0x + 2y + 8y = -2 - 8
10y = -10
Divide both sides by 10
y = -1
<em><u>Substitute y = -1 in eqn 1</u></em>
-8x + 2(-1) = -2
-8x - 2 = -2
-8x = -2 + 2
x = 0
Thus the solution to system is x = 0 and y = -1
Answer:
First, converting R percent to r a decimal
- r = R/100 = 2.7%/100 = 0.027 per year.
Solving our equation:
- P = 6774.5 / ( 1 + (0.027 × 22)) = 4250
- P = $4,250.00
- The principal investment required to get a total amount, principal plus interest, of $6,774.50 from simple interest at a rate of 2.7% per year for 22 years is $4,250.00
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16m^4 - n^4
= (4m^2 + n^2)(4m^2 - n^2)
= (4m^2 + n^2) (2m + n)(2m - n)
