High School Algebra Questions

Match each trigonometric ratio with its reciprocal ratio tan sin Cos POSSIBLE POINTS

Look at the graph 101 50 10 5 0 5 10 5 10 What is the equation of the horizontal asymptote

Look at the graph 10 5 10 0 5 5 10 x 10 10 What is the equation of the vertical asymptote

at graph 10 5 X 10 5 0 5 10 5 10 What is the equation of the horizontal asymptote

A pack of 36 black sharp tip markers costs 34 49 What is the price of one marke 0 96 0 90

Use the formula A Pe to solve 11 IF 5000 is invested in a savings account that pays 7 85 interest compounded continuously how much money wil be in the account after 12 years

4 2 4x 62 5 12e3x 2 8 6 log3 x 1 4

12 If 10 000 is invested in a savings account that pays 8 65 interest compounded continuously in how many years will the balance be 250 000 Round to the nearest tenth

3 Which of the ordered pairs below is a solution to the system of equations a 10 0 b 0 8 c 12 2 d 2 12 x y 10 2y x 16

HW 2 12 Given the system of equations below would it be better to solve by elimination or substitution explaining why Then solve listing your answer as an ordered pair 2x y 12 2x 4y 30

2 Which of the following is a solution to the system of equations shown below A 2 2 B 15 5 C 5 0 D 3 1 2x 4y 10 y 8 3x

Simplify the rational expression 52 10 2 4 3x 6 x2 4x 4 A 15 x 2 B 5 x 2 3 x 2 C 15 x 2 x 2 D 5 x 2 3 x 2

Solve 64 16

Solve 63 6 x

Solve 625 1252m 2 514 m

Solve the equation 4 4 1 n

FLUENCY 1 The point 2 7 is a solution to the system of equations given below a Show that this point is a solution 3x 2y 20 3c2 207 20 6 1920 2 7 5 x y 5 b Add the two equations together and show that 2 7 is a solution to the result

Consider the system of equation x 4y 13 3x 2y 19 a Multiply both sides of the second equation by 2 What equation results b Add the equation from a to the first equation What happens What can you now solve for c Now that you know the value of x how can you find the value of y Find it d What could you have multiplied both sides of the first equation by to eliminate the x instead of the y

A triangle has sides with lengths 5 12 and 13 a Verify this is a Pythagorean triple show work or clearly explain b Approximate the acute angles in this triangle Round angles to the nearest tenth smallest angle

Select all true equations cos 37 sin 53 tan 37 tan 53 sin 37 cos 53 sin 37 sin 53 cos 0 sin 90 0

Kiran is flying a kite He gets tired so he stakes the kite into the ground The kite is on a string that is 12 feet long and makes a 45 degree angle with the ground How high is the kite 45 12 ft 8 49 ft 16 97 ft 7 ft 12

What value of 0 makes this equation true sin 30 cos 0 30 60 90 180

The Americans with Disabilities Act states that ramps must have an angle less than or equal to 4 8 degrees Remember a 4 8 degree angle in a right triangle has a 1 12 ratio for the legs Select all ramps that meet the Americans with Disabilities Act requirements 30 30 15 40 40 120 10 12 2 1

Technology required Mai is visiting Paris to see the Eiffel Tower She is 80 feet away when she spots it To see the top she has to look up at an angle of 85 7 degrees How tall is the Eiffel Tower round to two decimal places Height feet

What is the length of side AB Round your answer to two decimal places B AB 6 30 C

Find the least common multiple for the following expressions x and x 3 x 3 x x 3 Or 3 3x

Simplify x 7x 30 823 6422 3 8 08 2 3 4 x 8 2 3 4 x 8 0 2 3 O 4 x 8 8x2 4x 40

Simplify x x 20 2 3x 15 8x 16 4 x 4 3 8 x 4 3 3 x 4 8 8 x 2

Which expression is equivalent to the complex fraction 2 7 2 1 2 2 3 0 7 2x 1 7 3 2 3 2x 1 2 2 7 3 2x 1 2 7 2 2z 3

3 A riverboat travels at an average of 14 km per hour in still water The riverboat travels 110 km east up the Ohio River and 110 km west down the same river in a total of 17 5 hours To the nearest tenth of a kilometer per hour what was the speed of the current of the river

2 Water flowing through both a small pipe and a large pipe can fill a water tank in 9 hours Water flowing through the large pipe alone can fill the tank in 17 hours Write an equation that can be used to find the amount of time t in hours it would take to fill the tank using only the small pipe

8 x 3 3x 17

Given the equation f x 4 2 2 answer the following A Growth or Decay B h C k D Horizontal Asymptote E Find f 1 Write as a coordinate pair

hich graph represents f x 3 4 2

A parabola has the equation f x x 3 2 4 Complete The first one is done for you 1 What is the horizontal translation 2 What is the vertical translation 3 What is the vertex 3 to the right The following graphs are translations of y x2 Use them for 4 9 The first one is done for you 0 4 What is the horizontal translation 8 0 7 What is the horizontal translation 5 What is the vertical translation 8 What is the vertical translation 6 What is the quadratic equation 9 What is the quadratic equation Graph the following equations for parabolas 10 y x 1 2 2 11 y x 3 2 4 2

A parabola has the equation f x 2 x 3 2 4 Complete 1 The vertex is 3 The function has a minimum value of 2 The graph opens The following graph is a translation of y x Use it for 4 7 4 What is the horizontal translation 5 What is the vertical translation 6 What is the sign of a 7 What is the quadratic equation for the graph Graph the following parabolas 8 y 2 x 2 5 12 9 y x 3 2 A ball follows a parabolic path represented by f x 2 x 4 8 Use this equation for 10 12 10 What is the vertex 11 Graph the parabola 12 Why does the graph stop at x 2 and x 6 12

Name m the x y axis y tan L ymptotes y 4csc 2 T symptotes angat

7 Let f x 2tan x 3 and let g x 7 tan x 2 3 What are all values of x in the xy plane 0 x 27 for which f x g x For work shown either sketch a graph or use a unit circle to identify the intervals for the solutions Finally put your answer in interval notation

Two trains left the station traveling in opposite directions The distance Train A traveled is modeled by the function d t 81t where c represents distance in miles and t represents time in hours Train B traveled a total of 324 miles in 4 hours How does the distance Train A traveled in 1 hour compare to the distance Train B traveled in 1 hour O The distance Train A traveled in 1 h is equal to the distance Train B traveled in 1 h O The distance Train A traveled in 1 h is greater than the distance Train B traveled in 1 h O The distance Train A traveled in 1 h is less than the distance Train B traveled in 1 h

Which description is correct for the x intercept s of Function A and Function B Function A 3 O 2 1 X Function B f x x 2 Function A has two x intercepts Function B has one x intercept O Both functions have the same number of x intercepts Function B has two x intercepts Function A has one x intercept Both functions have the same x intercept s g x 3 0 2 1 0

Which comparison is correct for the values of f a and g x when x 1 Function A f x x 1 Function B X 3 1 0 2 o f 1 g 1 Of 1 g 1 9 x 7 4 1 2

Subtract the rational expressions by typing your response in the box provide x 1 x 7 82 6 x 7

Add the rational expression by dragging the integers to their corresponding box to complete the statement POSSIBLE POINTS x 1 x2 3x 4 x 7 x2 3x 4 FILJ 2 x 2 x x x x x

2 Determine the number of solutions of the equation in the complex number system 8x3 9x 10 0 8x 9x 10 0 has degree 9 so there are three solutions in the complex number system 8x3 9x 10 0 has degree 8 so there are no solutions in the complex number system 8x3 9x 10 0 has degree 8 so there are three solutions in the complex number system 8x3 9x 10 0 has degree 9 so there are no solutions in the complex number system 8x 9x 10 0 has degree 3 so there are three solutions in the complex number system 3 Solve the equation Write complex solutions in standard form x 3 0

You have placed some money into an account and it is modeled by this equation Based on the information in this equations how often was it compounded monthly daily semiannually none of these choices quarterly annually continuously

At 100 1 12 You have placed some money into an account and it is modeled by this equation Based on the information in this equations how much money was you initial deposit 100 120 346 78 12 125 1250 10 1200

1 Determine the number of solutions of the equation in the complex number system 52 2x 0 52 2x 0 has degree 4 so there are four solutions in the complex number system 52 2x 0 has degree 2 so there are two solutions in the complex number system 52 2x 0 has degree 0 so there are no solutions in the complex number system 52 2x 0 has degree 4 so there are no solutions in the complex number system 52 2x 0 has degree 1 so there are four solutions in the complex number system

2 Solve the equation Write complex solutions in standard form 13x 1 0 13 x 13 x 13 x 13 13 x 13 x 1

3 Solve the equation Write complex solutions in standard form 16 x 1 0 x 5 5 x 5 3 x 5 3 x 5 3 x 5 3

No calculator Which of the ordered pairs below represents a solution to the system of equations shown elow 1 6 2 8 3 10 4 12 y 2x 4 3x 2y 22 3x 2 2x 4 22 3x 4x 8 22 7x 8 22 7x 14