Quadratic equations Questions and Answers

Listen Determine the area of the given polygon 2 ft 38 ft 42 ft 23 ft 14 ft 5 ft 2 ft

Determine two different Hamilton paths in the following graph A B E CD F G J KL Select all that apply H A A E I J F B C D H G K L B B F E I J K L H G B D A C E F G H L K J I E A B C D J K L H D C G F B A E I

Kristin has to pick up her children who all attend different schools She is at home H and needs to go to Children First Preschool C Braden River Elementary School B and Stephens Middle School S Kristin estimates the distance among these locations as follows H to C is 10 miles H to B is 6 miles H to S is 11 miles C to B is 9 miles C to S is 21 miles and B to S is 12 miles Answer parts a through c below H 6 B 10 11 C H S B 6 9 10 12 11 C H 21 6 S B 10 OA H C B S H or H S B C H or H C S B H or H B S C H OB H B C S H or H S C B H OC H C S B H or H B S C H or H B C S H or H S C B H O D H C B S H or H S B C H OE H C S B H or H B S C H OF H C B S H or H S B C H or H B C S H or H S C B H G All of the routes are of equal distance 12 C 21 b Use the brute force method to determine the shortest route for Kristin to start from home pick her children up and return home Choose the correct answer below S

Listen A manufacturer of tablets has total revenue given by the function R x 70x and has total cost given by C x 12 500 20x where x is the number of laptops produced and sold How many laptops must be produced and sold to break even 1 250 2 139 3 179 4 89

13 Find 2u 3v u 4i v 5j O 4i 5j O 8i 15j 8i 15j O 15i 8j O 8i 15j

7 If u 3i 6j and v 6i 5j find w 3u 5v w 39i 45j w 39i 43j w 33i 43j w 16i 12j w 27i 55j

A ball is launched straight up in the air from a height of 5 feet Its velocity feet second 1 seconds after launch is given by f t 321 288 Find t average velocity between 26 seconds and 5 5 seconds feet second The average velocity is Round answer to nearest tenth

8 Sketch the quadratic y x 1 x 7 Clearly label 3 key points and show your work

3 5 6 4a 10a A B C 4 D A 3 2a 21 5a 2a 2a 5 21 6a 2a 2a 5 21 15a 4a 2a 2a 5 21 10a 2a2 2a 2a 5 5 6 6 7 8 6 5n n 2 n 6 20n 5n n 6 n 2 11 6n 3n A B C D K 4n 8n 24 n 6 n 2 14n 24 5n n 6 n 2 9

2 x 4 3 x 1 11 x 4 x 1

5 A B 4a 10a C 77 9 D A B 4n n 2 C D A 6 B C D 21 5a 2a 2a 5 21 6a 2a 2a 5 21 15a 4a 3 2a 2a 2a 5 21 10a 2a 2a 2a 5 2n 3n 6 5 5n 6 21n 27n 10 5n 6 n 2 7 2n 3 21n 22n 16 5n 6 n 2 20n 29n 10 5n 6 n 2 2 4n 20n 1 3 n 2 n 5 2n 2 17n 6 4n 4n 20n 3n 6 6n n 2 n 5 1 4 n 5 6 8 10 A 4 n 2 B C D 8 A 2 r 2 B D 10 A B C 5n n 6 20n 5n n 6 n 2 11 6n D 3n 4n 8n 24 n 6 n 2 14n 24 5n n 6 n 2 4 3r 3 12 8r 3 r 2 r 1 2 2r 2r 5 5r 14 3 3 r 2 r 1 2r 14 3 r 2 r 1 6 2x 2x 18x 12x 48x 6 18x 12x 49x 2x 7 18x 12x 49x 2 x 9x 6x 24x 3 X 27x 17x 72 3x 3x 4 x 2

3 Subtrating Rational Expressions Simplify each expression 1 A 6n C A 4x 2 B n 5 C D 18n 5 2 6n 18n n 1 6n 18n n 8 3n 9n 6 4x 6x 3x 12x 6x 4 3 2x 1 37 x x 1 x 5 x 37 x 1 x 5 36 x 1 x 5 B D 2 3n 9n n 5 6n 18n 4 2 2 4 b 5 6b 186 A B C D A B 66 4k 3 23 1 3b 9b 3b 1 b C D 0 186 1 6b 18b b 3 6b 186 k 6 6k 15 3k 7 6 3 k 30 k 4k 3 k 6 8k 21k 6 3 2k 5

A population characteristic is normally distributed Approximately what percentage of the population lies within two standard deviations of the mean A 48 B C 68 95

Maggle claims that the function g x Which statement provides a correct analysis of Maggie s claim A B C D 4 is the inverse of the function of f x 3x 4 Maggie s claim is correct because if you add 4 to g x and then multiply it by 3 you get x Maggle s claim is correct because when g x is substituted into every occurrence of x in f x f g x x and when f x is substituted into every occurrence of x in g x Maggie s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x 8 therefore g x is not the inverse of f x Maggie s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x therefore g x is not the inverse of f x

12 Write the slope of the line that passes through the given points 12 through 4 2 and 5 4 Write the point slope form of the equation of the line that passes through the given points 13 13 through 3 2 and 0 3 x 3 A y 2 5 B y 2 x 3 C y 3 x 2 D y 3 x 2 Solve each system by elimination 414 9x 6y 18 21 9x 7y Divide 5 15 a 8a 9a 6 a 2 A a 6a 2 B a 6a 3 C a 8a 3 D a 8a 2 2 a 2 4 a 2 Find each product 16 16 2x 8x 8 2x 3x 2 A 4x4 24x 16 B 4x4 22x 36x 8x 16

3 cos x 0 351 0 x

2 4 2 sin x 3 sin x 1 0

A paper manufacturing company converts wood pulp to writing paper The profit per unit of writing paper is modeled by p x 2x 15x 105 Evaluate the profit for converting 5 units of writing paper 1 170 2 230 3 130 4 118

D Determine drug dosage by patient s weight For each kilograms of a person s weight 15 milligrams of a drug is to be given What dosage should be given to a person who weighs 240 pounds Use 1 pound 0 45 kg Multiply by 10 for each step to the right x 10 km hm dam m dm cm mm Divide by 10 for each step to the left 1 1 620 mg 2 8 000 mg 3 26 67 mg 4 3 600 mg 10

3 3 31 244 3 y 3x 3 Oy 3x 3 Oy 3x 1 Oy x 3

Evaluate the function at the given value of the variable f x 2x 4x 2 f 3 4 28 14 46 None of these

Use the chart to convert 5 621 cm to m kilo 56 21 m 5 621 m 56 210 m 562 100 m hecto deka base meter liter gram decl centi

A flagpole casts a shadow of 25 ft Nearby a 7 ft tree casts a shadow of 5 ft What the height of the flag pole 35 ft 1 4 ft 875 ft 17 9 ft

Find the standard form of each quadratic 11 y x 2 4 13 y x 3 6 12 y 2 x 7 4 14 x x 2 4

11 8x 10X 3 0 13 4x 12x 9 0 Method Method 12 2x 14x 36 14 3 1200 0 Method

3 x 3x 4 Method 10 3x 11x 4

3 D 3 v 6X5v 6 4 24 84 10 13 4k A 2 k 5 B r 6 5v 6 C D 3k 13 A 2 k 5 34 124 15k 2 R 1 5 6k 24 29k 4 2 k 1Xk 5 4 D 4 5m 1 30m 60m 30m A B 9 21m 1 5 3 2m 10 D 45 3m 16m m 20m 3m 4 25m 1 20 40mm 30mm 1 12m 4m 5 5 3m 1 44 3m 16m m 20m 3X 4

7 x 5 5x x 4 x 2 A B C D 5x 17x 6 x 4 x 2 6x 2 x 2 6x 21x 6 x 4 x 2 6x 23x 10 x 4 x 2 8 8 5p A B C D P 4 18p 114p 120p 5p 3 4p 90p 570p 600p p 4 6p p 5 3p 4 2 4p 2p 5 10p p 3 p 2

Simplify each expression 3v S 6v S 36v 36 6 1 A B C D Su 36v 39v 4 v 6 5v 6 S 36v 40v 3 v 6 5v 6 S 36v 39v 5 v 6 5v 6 4p 4v v 6 5v 6 12 2 2 5 m 5 A B C 5 2m 2 25 2m 8m 5 m 5 D 12m 12 5 m 5 15m 15 2 m 1 m 5 3 2m m 10

270 4 a Fill in the table with the exact values and their approximations where necessary 4 44 T 5 K 44 42 2 und S A TE 2n 7n 4 4 51 4 3 n 4 X IT 2 sin x CSC X sinx b Sketch y csc x for 2 Pi x 2 I 4 0 10 0 und 5 0 wam 4 AT 4 21 I 4 2 3 4 K it 0 5 4 3 2 T 7x 4 42 1 2 2 T 7 2 4 und

a Fill in the table with the exact values and their approximations where necessary X 0 5 COS X 0 b Sketch y cos x for 0 x 2 0 5 LA 3r jer T 3 r 5 m 4 4 7x 5R 2 T 3R 7r 2f

2 7T 14 5 2 A a Fill in the table with the exact values and their approximations where necessary T 7 T 4 57 5 T TC 4 b Sketch y sec x for 27 x 2 3 4 X COS X sec x 1 COSX TU 2 10 JU 4 0 1 0 I 4 0 TL 2 4 T 3 R 4 TO 34 5 m 4 44 3 r 2 2 7 J 20

9 2 1 0 1 Graph y 2sin x 4 2 3 t 3 T ST 3x 2 21 9 f 5 n 2 11 n

6 a Fill in the table with the exact values and their approximations where necessary 27 44 2n 7n 4 ST TO C HT SR n 3 n 4 4 X J 2 sinx COSX tan x b Sketch y cot x for 27 x 2 T B sin COS X Ita 4 10 0 0 0 1 0 4 42 42 I wer 4 4 2 1 lo 0 und 7 2 34 22 SHE 3 r 4 TC I 0 ol 42 S 3 4 2 und 4 42 1 7 2 4 27 0

triangle VX W 3 V Write your answers as integers or as decimals rounded to the nearest tenth

Try It Again Problem If y 3 4x 6 3z what is the value of x if y 30 and z 4

3 Graph 2 y x 2on the coordinate system What will happen when we change the to

1 Determine the surface area of his food container radius 20 cm height 25 cm Show your work here SA 2 TT r 2 rh SA 2x 3 14 2x 3 14x20x

1 point The domain of the function g x log x 64 is and 1 o

Find an equation of the circle whose diameter has endpoints 3 4 and 3 4 8 0 0

Find the following power Write the answer in rectangular form 7 cos 30 i sin 30 1 CO 7 cos 30 i sin 30 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bi

Given that z 2 cos 60 i sin 60 then the following is true z cos isin 00 0 i or simply 11 Questic

Practice No Calculator 3 y 42 12 2 Solve for a 10 9 3a 2 36

1 point Determine the speed s t of a particle with a given trajectory at a time to in units of meters and seconds c t ln t 1 t to 3

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 O P RA sin 2nft P RA cos 2nft OP RA sin 2ruft P RA RA cos 2 ft P RA sin 2 ft P 1 RA cos 2nft OP RA sin 2ruft P RA RA cos 2nft

Find the solution of the logarithmic equation logo x 20 log 15

5 2 x 1 3 x 2 6 x 3x 8

Extended Practice Variables on both sides Solve for the unknown in the equations shown below 1 5x 10 6x 12 2 12x 2 10x 8

5 2x 4 4x 10 6 4 2x 4x 10

1 2x 4 10 Guided Examples 2 3x 4 11