Quadratic equations Questions and Answers

Solve the triangle if possible A 97 a 16 3 in b 18 7 in GEREN If possible identify the equation below that uses the law of sines to find angle B Select the correct choice below fill in the answer boxes to complete your choice Type integers or decimals A There is a solution to the triangle and angle B can be found using the equation lo 16 3 sin B B There is a solution to the triangle and angle B can be found using the equation OC There is a solution to the triangle and angle B can be found using the equation OD There is a solution to the triangle and angle B can be found using the equation E Angle B cannot be found since there are no possible solutions for this triangle sin sin 265 69 sin 16 3 10 265 69 sin sin B sin B sin B

You generally don t need a personal identification number PIN to access your bank account using the ATM O False True

2 1 Rewrite 53 without using exponents 2 3 5 2 Solve 5 x 13 4 53 V5 x 13 4 13 4 10 70 7 IDK 3 Solve x 7 3 0 16 3 x 7 3 0 8 91 4 51 1 H4 4 Let p 3 91 and q 4 5i Write each expression in the form a bi b p q a p q 3 91 4 51 MO 7 4 H c p q 91 4 57 E 12 451 J

4 Let p 7 31 and q 2 9i Write each expression in the form a bi a p q b p q

3 Solve Show work a x 1 3 h

5 Explain why 3x 2 4 1 has no real solution

Given f x 2x 3 g x 5x 1 find gof x Select one O a 50x 20x 5 O b 10x 8 O c 10x 14 O d 10x 4

Find the f x 5x 3 difference quotient Select one O a 5h O b not possible O c 5 O d 5x 3 f x h f x h

Solve for m t 3m 3w Select one O a t W O b 3t 3w O c t 9w O d t 3w 3

Find the equation for a circle whose endpoints are 5 2 and 4 1 Write the equation in standard form Select one O a O b O c O d x 2 12 R v 12 2 x x 12 2 v 1 22 10 x I 2 12 2 2 2 1 X 1 2 12 0 92 100 221 2 1 2 2 10 10

Write the interval notation for x 1 6 x 6 Select one O a 6 U 6 O b 6 U 6 O c 6 6 O d 6 6

If f x 2x x find f 4 f 9

The terminal arm of an angle in standard position passes through each of the following points Find the radian value of the angle in the interval 0 2pi to the nearest hundredth a 7 8 b 6 1 c 4 2

f Csc 4 T 3

D 6 cos2x 5 cos x 6 2 sin x 3 cos x 3

B 150 a 10 b 3

42 y s X

6 Kristin spent 131 on shirts Fancy shirts cost 28 and plain shirts cost 15 If she bought a total of 7 then how many of each kind did she buy

x r coso 2 A y r sino A Prove That J J 1 Jocobian

a What factors limit the rate of photosynthesis Why Blair down the rate of a

Factor each completely 11 3m 21m 4m 28 13 18x 6x 3x 1 15 28k 20k 7k 5 17 12x 28x 9x 21 19 9n 15n 24n 40 12 18m 15m 6n 5 14 40m 56m 35m 49 16 8k k 48k 6 18 14x 6x 35x 15 20 8m m 56m 7

Factor each completely 1 15a 24a 10a 16 3 14n 6n 7n 3 5 7v 49v 8v 56 7 7a 9a 2 2 18m 3m 30m 5 4 12x 2x 6x l 6 21x 49x 12x 28 8 2x 7x 15

3 70m 7m 28m 63m 7m 10m 1m 4M 9 5 7x 70x 63x 35 Factor each completely ult 7 b 5b 24 b 3 6 8 9 a 14a 48 48 Xa 6 20 ultiply 11 6k 54k 120 6CK 4k 20 ks k4 4 30x 5x 15x 20 6 96 276 3b 3 8 x 6x 27 10 2 48 12 2a 18a 28

Factor each completely 21 2x 17x 9 23 5x 4x 12 25 36 206 12 27 86 14b 3 29 4x 41x 10 22 5x 16x 12 24 2x x 15 26 3k 19k 14 28 6x x 2 30 4n n 3

Factor each completely 1 5x 17x 6 3 3k k 2 5 7m 9m 2 7 6n 5n 4 2 2n 3n 2 4 2r r 36 6 5r 21r 20 8 6a 1la 30

9p 20p 4

4k 23k 6

Solve each system by the method of your choice 4 x 2y 4 5x 3y 15 5 4x 7y 17 x 2y 7 6 5x 3y 31 7x 2y 0 7 8x 5y 29 5x y 19

Solve each system of equations by the method of your choice 4 x 4y 9 3x 2y 13 6 y x 6 2x 3y 18 5 4x 3y 19 3x 2y 27 7 2x 3y 11 3x 7y 8

O Solve by graphing 2x 3y 6 y 2r 2 12 Solve by substitution 2a 5b 19 7a b 17 3 Solve by elimination 3x 4y 1 5x 3y 13

Without solving determine the number of solutions for each system 3 10 y x 2 4 3x 4y 11 12 6x 4y 14 0 21 11 2x 5y 17 2y 5x 9

13 The school band held a barbecue to raise funds for a trip The band sold hot dogs for 2 and burgers for 3 Total sales were 437 and 173 items were sold How many of each item were sold

1 Solve by graphing n y x 3 x y 7 2 Solve by substitution y 5 3x 2x 3y 7 3 Solve by elimination 3x 5y 24 3x 2y 11

rite a possible formula for the polynomial assuming that what you see from the graph includes all of the roots Assume that the leading coefficient is either 1 or 10 5 y 10 10 10 X

25 Find values for b such that the triangle has two solutions A 66 a 307 6 307 6 b O 307 6 b 307 6 b O 307 6 6 307 6 b 307 6 sin 66 307 6 sin 66 307 6 sin 66 307 6 sin 66 307 6 sin 66

28 Determine the exact value of the cotangent of the quadrant angle undefined 0 1 3 2 3

22 A Global Positioning System satellite orbits a 12 900 miles above Earth s surface see figure Find the angle of depression from the satellite to the horizon Assume the radi Earth is 4000 miles Round your answer to two decimal places 80 31 O 79 31 77 31 78 31 76 31 4000 mi Not drawn to scale a mi Angle of depression GPS satellite

27 Find the reference angle 0 5 7 O 0 2 5 7 O 0 5 7 O 0 5 7 2 O 0 5 7 O 0 2 5 7

O O O O 23 Find the point x y on the unit circle that corresponds to the real number t t t t t t 25 3 25 3 corresponds to the point 25 25 1 3 25 3 O 25 t 3 corresponds to the point corresponds to the point corresponds to the point corresponds to the point 1 1 12 5 1 3 1 1 3 2

20 The angle of elevation of the sun is 33 Find the length 1 of a shadow cast by a tree that is 35 feet tall Round your answer to two decimal places O 1 39 82 feet O 1 53 90 feet O 1 41 73 feet O 1 53 30 feet 1 64 26 feet

O 9 Find if possible the complement of the following angle I 5 Complement Complement Complement 5 3 TT 3 3 TT Complement 10

11 Find the exact value of the given expression 2 5T 3 sin O 3 1 2 2 O 3 1 2 2 O 3 1 2 2 O 3 1 2 2

12 2 Determine the quadrant in which an angle 0 lies if 11 1st quadrant O 4th quadrant 2nd quadrant 3rd quadrant

10 Consider the function given by y x 5cosx Use a graphing utility to select the graph of the function

5 Write the given expression as the cosine of an angle cos 60 cos 25 sin 60 sin 25 O cos 60 O cos 35 cos 85 cos 25 cos 50

The power dissipated in an electric circuit is given by the expression P RI2 where R is the resistance of the circuit and I is the current through the circuit For a sinusoidal alternating current the current might be represented by the relation I A sin 27ft where A is the amplitude f is the frequency and t is time Write an expression for P involving the sine function and use a fundamental identity to write P in terms of the cosine function OPRA sin 2 ft P RA RA cos 2 ft OP RA sin 2 ft P RA cos 2 ft OPRA sin 2 ft P RA cos 2nft P RA sin 2 ft P RA RA cos 2uft

T X 14 Find the reference angle and sketch and in standard position 0 155

X 15 The point 8 15 is on the terminal side of an angle in standard position Determine the exact value of cot 0 17 15 O cot e cot 8 cot 0 cot 8 cot 8 15 17 15 17 15 8 15

X 17 Select the graph of the function below Include two full per TCX

X 20 Evaluate the following expression x n where n is a whole number 5 sec x 5 5 sec x 5 cot x O 5 cot x 5 tan x 5 tan x