# Solving for r Using Complex Numbers

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

(type an integer or a fraction. Simplify your answer)

__________________________________________________________________________Part 3

1. simplify by factoring.

radical sign. the 28 is in the inside.

(type an exact answer, using radicals as needed)

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 .

(simplify your anser. type an exact answer, using radicals as needed)

4. add. simplify by collection like radicals term if possible

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

(simplify your anser. type an exact answer using, radicals as neeed.)

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

simplify your answer. type an exact answer using radicals as needed.

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

the answer is _____

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#### Solution Summary

Neat solutions to all the problems is provide. All answers are highlighted. Graphs are drawn appropriately.