Algebra Questions

1 a Question 1 7 NEXT BOOKMARK Keith received money from his family and friends for his birthday He decides to put the money in the bank Keith invests 3 050 at 13 7 interest compounded continuously Write an equation in y form to represent Keith s investment Use t for time 3 points 3 points x b If Keith s investment increases at the same interest rate each year how long will it take Keith s investment to double SHOW ALL WORK FOR HOW YOU SET UP THE PROBLEM AND USE LOGARITHMIC PROPERTIES TO ALGEBRAICALLY SOLVE THE PROBLEM

9 Determine whether the linear operator T R R defined by the equations is one to one if so find the standard matrix for the inverse operator and find T w w wz 10pts W x 2x Iz W 2x x 4x3 W3 7x 4x2 5x3

Let f x 6x 1 and g x Find f g x f g x fg x and 1 f g x 6x 1 Simplify your answer X f g x 6x 1 fg x 1 X Simplify your answer 6x 1 Simplify your answer x Simplify your answer 4 x Give the domain of each www

a fog x and its domain b gof x and its domain a fog x 5x 3 Simplify your answer The domain is 3 5 0 Type your answer in interval notation b gof x 5 x 3 Simplify your answer The domain is Type your answer in interval notation

6 The RED dotted graph represents the parent function of y Determine what transformations were made for the graph in BLUE 4 points DRAG DROP THE ANSWER Vertical compresion by 2 Vertical stretch by 2 Shifted 4 units left Shifted 4 units right Shifted 1 unit down Reflected over x axis Reflected over y axis Shifted 1 unit up Note Use CTRL D to drag the option via keyboard

Find the standard form of the equation of the hyperbola satisfying the given conditions x intercepts 24 foci at 26 0 and 26 0 The equation in standard form of the hyperbola is Simplify your answer Use integers or fractions for any numbers in the equation

Graph the hyperbola Give the domain range center vertices foci and equations of the asymptotes x y 225 64 1 x y Give the equations of the asymptotes for the hyperbola 225 15 OA y 8x 8 O B y 15X 225 O c y X 64 64 OD Y 225 x 1 has foci at 1 Choose the correct answer below 64 comma to separate answers as needed Type an ordered pair using intege

36 100 1 What are the foci of the ellipse 10 10 Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed What is the domain Type your answer in interval notation Round to the nearest integer as needed Use a comma to separate answers as needed What is the range porost integer as needed Use a comma to separate answers as needed

5 x 5 y 3 49 6 x 5 y 3 49 7 x 5 y 3 49 8 x 5 y 3 49 5 Drag each graph above to the correct exercise number below 6 7 ON 8 below 27 C G G

For the ellipse shown give the domain range center vertices and focl 16 9 1 Type your answer in interval notation Find the center Type an ordered pair Find the vertices Type an ordered pair Use a comma to separate answers as needed Find the foci CECH A

Question 1 13 Jse the dropdown menu to indicate the ustification of the previous step to the current step when solving the equation 3 5 2d z Statement 3 1 5 2d z 3 2 2d2 3 3 d 2 8 4 d 4 16 21 21 Justifi 1 Giv 12 3 4

Question 1 3 Which pair of functions are inverses of each other 9 2 2 5 f x 10x 10x 5 g x f x 7x 4 g x 3 5 0 0 0 2 f x x 9 g x x 5 3 4x 11 1 9 6 x 3 f x 6x 30 g x x 5

X 3 1 0 4 g x 5 1 1 9 h x x x 4 O 5 O 3 O 3 O 5

Use the selected values of a linear function g x in the table and the equation h x shown below to evaluate goh 3 X 3 1 0 4 g x 5 1 1 9 h x x 2 O 22 O 21 O 14 O 15

Question 1 2 Write an equation for the inverse of g x 3x 8 g x 8x O g x 8 00 O g 3 X 1 3 3 x 8 08 x O g 8 3

Question 1 4 Let f x x 4x 1 and g x 2x 3 Determine 2 f x g x 2x 6x 1 O 2x 2x 5 6x 2x 5 2x 3

Question 1 11 Evaluate 27 8 27 8 27 27 8 81 36 I 3 2

Question 1 16 Which of the following is equivalent to 2 6 2 6 5 2 6 2 6 5 2 6 2 O 2 6 2 6

9 3 27

Question 1 8 Multiply Express your solution with positive exponents 2a 566 7a b 146 a 14 ab 565 85 a ab

Question 1 10 3 Determine an equivalent form of 108a5 V 4a 4a 3 3a 4 1 6 36a 3a4a

Question 1 14 Simplify Assume that all variable exponents represent positive real numbers 2x 3 8x 2 27x 30 6x O 2x 6 3x 5 2x 6 3x 6x

Question 1 15 Determine an equivalent form by rationalizing the denominator 6 5 3 6 3 15 3 6 5 5 15 6 3 5 3 3 6 5

Simplify the expression O C 12 13 C 12 1 C6 3 15 13

1 B 9 Basics to Multiplying Rational Expressions Simplify each expression A 6b C 3 5 7b 8 9b 9b A 7 k 7 5 7k 5 k 6 C k 5 9 A 2v 56 81b 5 35v 45 A C v 3 4 n 3 49n 14 A 2 k 2 7k 5 2 k 8 k 2 B B b D 14v 18v n 1 6 n 2 B D 5 n 6 n 7 4 36 3a 7 21a 64a 35 3 a 1 k 1 4k k 7 k 8 21n 64n 20 9n 30n 5a a 6 a 10 6 v 2 v 9 100 9v B D 14a 10a 5a 45 B n 3 21n 8 9n D 2q 5 a 9 a 6 9a 2 4 6 2 6x A 9x 2x 4 5 r 6 r 2 10 6 8 10 A 6 3x 9 8 8 A C 0 A 10r r 2 r 6 r 5 7 x 4 5x 4 x 9 7n 6 18n 27n n 3 10n A B 7 D C n 9 n 2 10 30x90 6k k 3 9x 20 r 2 5 r 5 r 2 12k 60k 5k 22k 21 4 k 3 k 3 D B 1 10 r 9 D r 8 2n n 6 21n 18 B B D x 8 3x B D 10k 36k 70 4k 100 8 k 8 k 10 54k4 k 9 2 3n n 6 n 2 27n

OR Reduce the quadratic form 3x 2y 3z 2xy 2yz to normal Under form and discuss the nature of quadratic form

Receipt Chaos Name Sadaf Amici Use the percent proportion to fill in the missing parts of each receipt 1 Buffalo Wild Wings Receipt Medium wings 15 99 Sodas 3 21 Basket of Fries 3 99 TOTAL 2319 TIP 20 NEW TOTAL 23 19 123 19 2319 X 23 191 20 100 LO 23 19 Per

Graph the hyperbola Give the domain 64x 81y 5184 Graph the hyperbola Choose the correct graph below OA Q Q OD Give the domain for the hyperbola 64x 81y 5184 4 9 U 9 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed Give the range for the hyperbola 64x 81y 6 5184 Type your answer in interval notation Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed

2 0 5 Write a possible polynomial function for the graph given above 4

Graph the hyperbola x y 9 Give the domain range center vertices foci and equations of the asymptotes for the figure Type ordered pairs Use a comma to separate answers as needeu The foci are 3 2 0 3 2 0 Type ordered pairs Type an exact answer using radicals as needed Use a comma to separate answers as needed What are the equations of the asymptotes Choose the correct answer below OA y 3x B x y OC x 3y D y x Graph the hyperbola x y 9 The domain is 3 U 3 00 Type your answer in interval notation The range is tenual notation 4 Choose the correct graph below O A OB OD Q Q

Graph the hyperbola Give the domain range center vertices foci and equations of the asymptotes 25y 49x 1225 Simplify your answer Type an exact answer using radicals as needed Use a comma to separate answers as needed Type an ordered pair using integers or fractions 1225 Choose the correct answer below Give the equations of the asymptotes for the hyperbola 25y 49x 49 OA y 25x 5 B Y 7X 7 c y 5 25 OD Y 49x X rei of J www 4 word as needed Type an ordered pair using integers or fractions

ich of the polynomial functions in the list might have the given graph Circle all that apply a y x 1 x 2 b y x 1 x 2 c y x 1 1 4 2 d y x 1 x 2 e y x 2 x 1 2 x f y x 1 x 2 x 1 1 2

Sketch each of the following polynomial equations 3 f x x x 4 x 3 4 g x 3x 1 x 2

y x Graph the hyperbola 25 49 1 Give the domain range center vertices foci and equations of the asymptotes for the figure 7 B Y 5x 5 c y x y x 7 OD x 5Y Graph the hyperbola y x 25 49 1 The domain is 0 00 Type your answer in interval notation The range is rin interval notation Choose the correct graph below C 1 8 More B O D Q

Graph the hyperbola 25 49 equations of the asymptotes for the figure 5 OA X 7Y What are the equations of the asymptotes Choose the correct answer below 7 B y x 5 c y 7x 1 Give the domain range center vertices foci and 7 OD X 5Y Graph the hyperbola j x 25 49 1 CH The domain is Type your answer in interval notation Choose the correct graph below O C Q OB OD Q Q

Graph the hyperbola Give the domain range center vertices foci and equations of the asymptotes 64x 81y 5184 The hyperbola 64x 81y 5184 has its center at 0 0 Type an ordered pair The hyperbola 64x 81y 5184 has vertices at 9 0 9 0 Simplify your answer Type an exact answer using radicals as needed Use a comma to separate answers as needed Type an ordered pair using integers or fractions Give the equations of the asymptotes for the hyperbola 64x 81y 5184 Choose the correct answer below 64 A Y 81 8 OB y x 81 O c y 64x 9 8x OD y A

20x 560 7y Simplity your answer Type an ordered pair The vertices are 0 4 5 0 4 5 Simplify your answer Type an ordered pair Type exact answers for each coordinate using radicals as needed Use a comma to separate answers as needed The endpoints of the minor axis are 2 7 0 2 7 0 Simplify your answer Type an ordered pair Type exact answers for each coordinate using radicals as needed Use a comma to separate answers as needed The foci are 0 2 13 0 2 13 Simplify your answer Type an ordered pair Type exact answers for each coordinate using radicals as needed Use a comma to separate answers as needed Choose the correct graph of the ellipse below OA 90 OB D

y X Graph the hyperbola 25 49 equations of the asymptotes for the figure The vertices are 0 5 0 5 Type ordered pairs Use a comma to separate answers as needed The foci are 0 74 0 74 Type ordered pairs Type an exact answer using radicals as needed Use a comma to separate answers as needed What are the equations of the asymptotes Choose the correct answer below 5 x 7y O A X 7 OB Y 5x 1 Give the domain range center vertices foci and 5 O c y 7x y x O D X 5Y 4

Graph the hyperbola x y 9 Give the domain range center vertices foci and equations of the asymptotes for the figure The hyperbola has a center at 0 0 Type an ordered pair The vertices are 3 0 3 0 Type ordered pairs Use a comma to separate answers as needed The foci are 3 2 0 3 2 0 Type ordered pairs Type an exact answer using radicals as needed Use a comma to separate answers as needed What are the equations of the asymptotes Choose the correct answer below OA y 3x OB x y O C x 3y OD y x

Use rational exponents to simplify the radical Assume the expression is defined 3 9 The expression is equal to

Express 3 1 4 1 3 9 Simplify your answer Use integers or fractions for any numbers in the expression Use p 3 3 9 as a power of 3

Simplify the expression Assume all variables are positive X 13 1 5 X X

Use rational exponents to simplify each radical Assume all variables are positive x x

Simplify the expression Assume all variables are positive 2 3 y 7 7 5

9x 25y 225 The hyperbola 9x 25y 225 has its center at 0 0 Type an ordered pair The hyperbola 9x 25y 225 has vertices at 5 0 5 0 Simplify your answer Type an exact answer using radicals as needed Use a comma to separate answers as needed Type an ordered pair using integers or fraction Give the equations of the asymptotes for the hyperbola 9x 25y 225 Choose the correct answer below 5 A Y 3X 25 OB y gx X 3 O C y 5x 9 OD Y 25x 4

Use rational exponents to simplify the radical Assume the variable is positive

Simplify the expression Assume all variables are positive 4 7 x y N 1 3 4 64x y w 3

Simplify the expression 5 5 w c 9 3 3 10 3 10

X Graph the hyperbola 25 49 equations of the asymptotes for the figure The hyperbola has a center at Type an ordered pair 1 Give the domain range center vertices foci and

Graph the hyperbola Give the domain range center vertices foci and equations of the asymptotes 9x 25y 225 The hyperbola 9x 25y 225 has its center at 0 0 Type an ordered pair The hyperbola 9x 25y 225 has vertices at Simplify your answer Type an exact answer using radicals as needed Use a comma to separate answers as needed Type an ordered pair using integers