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# Solving for r Using Complex Numbers

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Part 1

1. Solve for r
r^2+3r=5
The solution are r =
(use a commas to seperate answers type n. if there is no solution.

2. Sove for x

1+8/x +52/x^2 =0

The solution are____
Express cmplex numbers in the trms of i use a comma to seperate answers as needed

3. The width of a rectangle is 14ft less than the lenth. The are is 10ft^2. Find the lenth and the width.
(round to the nearest hundreth)

4. find and label the vetex and the line of symmetry. graph the function f(x) =-3(x+2)^2
the vertex is _______
(type an ordered pair)

5. graph the function, label vertex, and draw the axis semmetry.

f(x) =-1/3 (x-4)^2
the vertex is ____
(type an ordered pair)

6. find the vertex, the line of symmetry the maximum or minimum value of the quadratic function, and graph function
f(x)=-x^2+10x+6
the vertex is _________
(type an ordered pair)

7. find the x- intercepts and y intercepts for f(x)
f(x)=x^2 -5x+4

the x intercepts(s) is (are)__________
the y intercept(s) is (are)__________
(Type an odred pair, type an itneger or a decimal. round to the narest tenth. use commas to seperate answers as neede. type N is no intercept.

8. x^2+40<14x
The solution set is {x| }
Use at least on inequality

10. solve.

the hypotenuse of a right triangle is 24 ft. long. the lenght of one lig is 14ft more then the other. Find the lenghts of the legs.

the length of the shorter leg is approximately ____ft.(round t the nearest. hundreth)
__________________________________________________________________________ Part 2

2. x^2-9/9x+63*x+7/x-3
simplify your answer. use integers or fractions for any numbers in the expression.

3. x^2-49/x^2-12x+36(divided)x+7x-49/x^2-3x-18
the simplified quotient is _____
type your answr in a factored form.

4. add simplify by removing a factor of 1 when possible

c^2/c-a+a^2/a-c

the sum is _____

5. z-6/5z+45(subtraction)z+5/7z+63
the difference is ____________

6. simplify.

16a^2-b^2/ab/4a-b/b

7. solve.

30/7-30/y-6 +3/y
the solution is y=____

type an integer or a fraction. type n is thee is no solution.

8. Sue, an experienced shipping clerk, can fill a certain ordr in 5 hours. Billa new cler, need 6 hours to do the same job. Working together, how will will it take them to fill the order?

9. Cambridge Slim ate 49 sausages in the first 25 min of high stakes eating contest. Assuming that he continued at the same pace, how many sausges would he have eaten by the end of the 30 minutes contest.
Cambridge Slim would have eaten ____sausage during the contest.
(round to the nearest whole number)

10. A steam boat travels 12kh/h faster then a freighter. The steam boat travels 92 km in the same time the freighter travels 44 km. Find the speed of each boat.

The speed of the freighter is ____km/h
__________________________________________________________________________Part 3

1. simplify by factoring.

radical sign. the 28 is in the inside.

2. multiply

radical sign ^3 on the outside 7 in the inside multiplied by ^3 on the outside of the radical and 49 in the inside.

3. subtract. simplify by collecting like radical terms if possible
radical sign 2 on the outside 18 in the inside (multiplied) another radical sign 2 on the outside and 2 in the inside .

radical sign 4 on the outside 8 in the inside (add) radical sign 7 on the outside 72 in the inside.

7. parathesis 4+radical sign 2 on the inside of the radical close parethesis. ^2

10. (9-i)+(-2+3i)

https://brainmass.com/math/basic-algebra/solving-r-complex-numbers-184825

#### Solution Summary

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## Math questions ... (Please see attachment for 33 problems)

1.Factor the trinomial

Type N if the trinomial is not factorable

2.Multiply

3.If a pro basketball player has a vertical leap of about 20 inches, what is his hang time? Use the hang-time function V=
The hang time is ----seconds (Simplify your answer. Type an integer or a decimal. Round to nearest tenth)

4.If the sides of a square are lengthened by 7cm, the area becomes . Find the length of a side of the original square. The length of the original square is ...cm

5.Simplify by removing factor of 1.

6.Factor completely

Type N if the expression is not factorable

7.Solve

Use a comma to separate answers. Type N if the solution is not a real number

8.Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function

(a)The vertex is (type an ordered pair
(b) The line of symmetry is
(c) What is the maximum/minimum value of f(x)
(d) Is the value, f (-8) =1 a minimum or maximum

10.Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers.

11.Convert to decimal notation

12.Jack usually mows is laws in 3 hours. Marilyn can mow the same yard in 5 hours. How much time would it take for them to mow the lawn together?

13.Express using a positive exponent.

16.Solve

Simplify your answer. Type an exact answer, using radicals as needed. Rationalize all denominators. Use a comma to separate answers as needed. Type N if there is no solution

17.Factor.

Type N if the trinomial is not factorable.

18.Factor Completely

Type N if the binomial is not factorable

19. Solve

Use at least one equality or compound inequality to express your answer. For answers with more than one equality, separate the inequalities by a comma or word. Type R if the answer is all real numbers. Type N if there is no solution.

20.Solve.

21.Find the following

Simplify your answer. Type N if the root is not a real number.

22.

23.Find the following. Assume that variables can represent any real number.

24.Perform the indicated operations and simplify.

25.Divide and simplify

Type exponential notation using positive exponents

26.Use the quadratic formula to solve the equation

Simplify your answer. Type an exact answer, using radicals as needed. Express complex numbers in terms of . Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.

27.Subtract. Simplify, if possible.

28.Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function

(a)The x-coordinate of the vertex is (type a simplified fraction)
(b) The y-coordinate of the vertex is (type a simplified fraction)
(c) The equation of the line of symmetry is
(d) The maximum/minimum of f(x) is..(type a simplified fraction)

29.Find the greatest common factor for the group of terms.

30.Find the x-intercepts for the graph of the equation

The x-intercepts are
(Type an ordered pair. Use a comma to separate answers

31.Multiply

32.Find a polynomial for the perimeter and for the area
Z+9

Z