27 college algebra homework

1 . ) Solve the following equation by factoring.
9×2+4=12x
 
2.) Solve the following equation by the square root method.
(x9)2=36
 
 
3.)  Solve the following equation by completing the square.
x2+2x=35
 
 
4.) Use the quadratic formula to find the real solutions, if any, of the equation.
x26x1=0
 
 
5) Find the real solutions, if any, using the quadratic formula.
5y2y+8=0
 
 
6)  Find the real solutions, if any, of the following equation. Use the quadratic formula.
4xx1+2x=5
 
 
7) Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution, without solving the equation.
x25x+9=0
 
 
8)  Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution, without solving the equation.
4x219x+25=0
 
 
9)  Find the real solutions, if any, of the quadratic equation.
7+44z=35z2
 
 
10 )  Find the real solutions, if any, of the following equation. Use any method. Verify your solution using a graphing utility.
7(x4)+5=0
 
 
 
11 )  Find the real solutions, if any, for the following equation. Use any method.
x2+x=7
 
 
List all elements of the set
85, 8, 5, 2.51, 4.73773777…, 02, , 204, 58, 9
that are also elements of the set of rational numbers.
Select all the rational numbers from the given list.
2.51
02
5
4.73773777…
85
9
58
204
8
 
 
12.  State whether the following statement is true or false.
Rational numbers and irrational numbers are in the set of real numbers.
 
 
13..  Fill in the blanks.
In the complex number
5+2i,  the number 5 is called the ________ part, the number 2 is called the__________ part, and the number i  is called the_______ .
 
 
14. Fill in the blank.
The equation x2=4  has the solution set ______ .
 
 
 
 
15. State whether the following statement is true or false.
The conjugate of 2+5i  is 25i.
 
 
16.  State whether the following statement is true or false.
All real numbers are complex numbers.
 
 
 
17. State whether the following statement is true or false.
If 23i is a solution of a quadratic equation with real coefficients, then 2 + 3i
is also a solution.
 
 
18. Write the expression in the standard form a + bi.
(43i) (7+i)
 
 
19. Write the expression in the standard form a + bi.
6I / 6+ I
 
 
20. Write the expression in the standard form, SIMPLIFY YOUR ANSWER
A + bi.
 
 
21.  Write the expression in the standard form a+b i. i43
 
22. Write the expression in the standard form a +b i. (8+i)3
 
23).  Solve the equation in the complex number system. x2+81=0
 
24).  Solve the equation in the complex number system. x4+17×2+16=0
 
25).  Without solving, determine the character of the solutions of the quadratic equation in the complex number system. 3x29x+1=0
 
26).  Write the following expression in the standard form a+b i. zz,  where z=74i
 
27). The impedance Z, in ohms, of a circuit element is defined as the ratio of the phasor voltage V, in volts, across the element to the phasor current I, in amperes, through the elements. That is, Z=V / I. If the voltage across a circuit element is 18+16i volts and the current through the element is 42i amperes, determine the impedance.
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