Algebra Questions

4 4i 3 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bi 2

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

Find the given power and write the answer in rectangular notation cos 90 isin 90 6 cos 90 isin 90 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bl

Raise the number to the given power and write the answer in rectangular form 2 cis 55 6 GCEE 2 cis 55 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bi

Find the power Write the answer in rectangular form 2 2 3 4 6 8 4 13 HW Score 0 0 of 9 poi O Points 0 of 1 2 2 3 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bi

The one to one function fis defined below f x 5x 10 Find f the inverse of f Then give the domain of fusing interval notation Domain of 8 6 0 0 0 0 QUO 0 0 0 0 8

Kyle works at a donut factory where a 10 oz cup of coffee costs 95 a 14 oz cup costs 1 15 and a 20 oz cup costs 1 50 During one busy period Kyle served 17 cups of coffee using 244 ounces of coffee while collecting a total of 20 10 How many cups of each size did Kyle fill Kyle filled 10 oz cup s 14 oz cup s and 20 oz cup s

Do 5 In the movie Diehard the prop gold bars are 10 0 inches by 2 50 inches by 1 50 inches one inch 2 54 cm exactly If these were a real gold bar what would their mass be the density of gold Au is 19 3 g cm 12k9

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

2x 20 3x 15 20 15 3x 2x 5ax x 5 2x 15 3x 20 5x 20 15 5 5 x 1 Equation Checklist Note You will not have all of these steps in every problem Distribute the outside factor to all terms within parentheses Check the left side of the equation combine like terms Cancel out the constant term Check the right side of the equation combine like terms If there are variable terms on both sides of the equation cancel out the one with the lower coefficient

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

2x 20 3x 15 2x 15 3x 20

5 If 3 2 r 10 2 r 10 19 what is 4r 6 Solve for s if 10 2 s 10 4 2s 5

Scaffolded Problems 1 Given the equation 3 4 2x 5x 27 what its the value of x Distribute Combine Like Terms Constant Term Coefficient 12 6x 5x 27 12 11x 27 12 39 divided 11 x 3 5 Check Did I solve for the unknown

Find w 12w 3w 4 77 4 Solve for t 6 21 3 2 12 t 16

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

5 If 6x 4 4 7 14 what is the value of x 3 6 What is the value of x 12 8x 24 12

3 What is the value of x 3 2x 7 3 4 Given 5 3x 5 4 4 find 3x 10

5 Given the equation 3 2 x 7 3 4 x find the value of 4x

Practice Calculator

Solve for x 2 x 5 4 6 Partner Practice 2 Solve for x 20 4 5 2n 8

4 x 1 3 2x 4 14 4x 4 6x 12 14 10x 16 14 X 2 16 16

Write the complex number 5 cos 358 isin 358 in the form a bi 5 cos 358 isin 358 Type your answer in the form a bi Round to the nearest tenth as needed

Learning Target I can solve equations that require distribution and combining like terms Example Problems

Write the complex number in rectangular form 20 cos 300 i sin 300 The complex number is Simplify your answer including any radicals Type your answer in the form a bi Use integers or fractions for any numbers LOVER

Write the complex number in trigonometric form r cos 0 i sin 0 with 0 in the interval 0 360 4 4i 0 4 4i 0 cos isin Type the value for r as an exact answer using radicals as needed Type the value for 0 as an integer or decimal rounded t

Write the following complex number in the form a bi 14 cos 0 i sin 0 14 cos 0 i sin 0 Type an exact answer

15 4 points For f x 2 3x and g x x 4 find and simplify the function fog x

n A 23 5 2422 Ke Safeware LLC 16 3x 6r n 3 5 B D 8 3r 3x 5yx 2 5x 8 1 8 A B C 7v 2v 4 3 x 2 3 v 2 10 8 3 x 2 8v 11

7 535 3T fic Sz 8 3 34 2 b 8 y

9 9 5n Sit 4 5 A B C D Sn 4 2n 3 10n 45m n 5 n 4 7n 2 n 1 2 1 5 2 2n 3 10 10 A B C 5 2x 2x x 3 D 10x 17 2x 2x x 3 7x 17 x 2x x 3 9 2x 4 x 4x 17 2x x 3

11 1 A B C 3 7r 3r 1 3 8r 3r 1 Sr 2 r 2 29r 12 7 2 5W 21 12 12 A 5 Sx 5x 2 x 6 17x 20 2x 3 x 5 35 7x 2x 3 x 5 x 6 25x 10x Hr 65x 2 B C 5x

11 5 points Use the graph of f x to sketch the graph of y f x 1 3 f x 31 4 1 1 0 F 2 1

2x 3y 323 3 A 2x x 2y 2yx B D A B C D x y 3xy x 2 2x x 2 3y 2y 3x 10x 3y y x 5y 154 6x 10x 15x 6y 10y 2x 3 2y 5 6 4

Software LLC 6 Sa 6 3b A B C D Sab 6a 4b b 3 5ba Sa 4b b 3 5ba 3a 5b b a 3b a 25a b 3a 12b 15b a Made with In fin ite Algebr

22 3 points The 1986 explosion at the Chernobyl nuclear power plant in the former Soviet Union sent about 1000 kilograms of radioactive cesium 137 into the atmosphere The function f x 1000 0 5 30 describes the amount f x in kilograms of cesium 137 remaining in Chernobyl x years after 1986 If even 100 kilograms of cesium 137 remain in Chernobyl s atmosphere the area is considered unsafe for human habitation Find f 80 for the function f x 1000 0 5 30 in order to determine if Chernobyl will be safe for human habitation by 2066 Round your answer to the nearest whole number

1 3 Adding Rational Expressions Simplify each expression 1 9x A B C D 3 2x 5y 9x 3x 5y 9x 2x 8xy 6y 81x x 5xy 6y 81x 21 A B O 9x 2x x 2y 210 Dy x 1 3xy x 2 2x 2 3y 2 4 2 4 6b 3b A A O 26 3 6b3b 28 4 6b3b 2 2x 6 x 9 x 2x x 3 2 2x 3 6b 3b B D B D 26 3 b 26 3 26 2 b 2b 3 6 x 2x x 3 3x 9x 2 2 x 3

23 5 points Using the compound interest formula A P 1 2 fit A P n find accumulated value of an investment of 5000 for 10 years at an interest rate is 5 1 compounded quarterly Round your answer to the nearest cent

20 3 points Condense the logarithm expression as much as possible Be sure the final answer has coefficient of 1 log 17 log x 6log 2

13 5 points Find an equation for the line perpendicular to the line 2x 3y 6 having a y intercept of 4

25 4 points Melissa s dinner serves desserts One serving of ice cream and 2 servings of apple pie provides 800 calories 3 servings of ice cream and 2 servings of apple pie provides 1280 calories Set up a system of equations define your two variables and use either method you choose to determine how many calories are in one serving of ice cream

For problem 14 An arrow is fired into the air the height in feet of the arrow 1 seconds after it was shot into the air is given by the function h t 161 641 5 14 4 points Find the maximum height of the arrow

21 5 points Solve for x log x log x 4 log 12