High School Algebra Questions

4 The graph f x x has a vertical compression of by a factor of is shifted up 6 and right 5 What is the quation of the function after the transformation

A party favor bag must have a volume of 140 cubic inches and the dimensions that are shown below The equation x3 6x 27x 140 can be used to find x Length xin Height x 9 in Width x 3 in What are the dimensions of the party favor bag Use a graphing calculator and a system of equations to find the answer The length is 4 inches the width is 1 inch and the height is 13 inches The length is 7 inches the width is 4 inches and the height is 16 inches The length is 3 inches the width is O inches and the height is 12 inches The length is 5 inches the width is 2 inches and the height is 14 inches

What are the roots of the polynomial equation x 5x 5 2x 5 Use a graphing calculator and a system of equations Round noninteger roots to the nearest hundredth 2 24 2 2 24 2 24 2 2 24 0000 3 5 3 5

J x sin 2 Use the sine tool to graph the function The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point Move 6 28 Sine 3 14 5 4 3 2 0 1 2 3 Ay Undo 3 14 Redo x Reset 6 28

The table of values shows the height of a car of a Ferris wheel as it travels in a circular motion Which statements are true Select each correct answer The radius of the Ferris wheel is 30 ft O The maximum height of the Ferris wheel is 64 ft The car makes a complete revolution in 5 s If the car is loaded at 0 s then people are loaded at the lowest point of the Ferris wheel Time seconds 0 2 5 5 7 5 10 12 5 15 17 5 20 Height feet 34 64 34 4 34 64 34 4 34

Over a 24 hour period the temperature in a town can be modeled by one period of a sinusoidal function The temperature measures 70 F in the morning rises to a high of 80 F falls to a low of 60 F and then rises to 70 F by the next morning What is the equation for the sine function f x where x represents time in hours since the beginning of the 24 hour period that models the situation Enter your answer in the box f x

In the function f x x is replaced with 2x and 1 is added to the function f x 3 sinx What effect does this have on the graph of the function O The graph is vertically stretched by a factor of and shifts down 1 unit O The graph is horizontally compressed by a factor of and shifts down 1 unit O The graph is vertically stretched by a factor of and shifts up 1 unit O The graph is horizontally compressed by a factor of and shifts up 1 unit

What is the equation of the midline for the function f x f x cos x 5 Enter your answer in the box

What is the minimum value for the function shown in the graph Enter your answer in the box 3 2x K 0 5 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 5 5 6 6 5 T 55 2 3n

6n 3n 8n 6 3n 7n 5n 3n

by Long Division 10 5p 40p 120p 41 5p 10

3n 3n 2n 8n 7n 5n 2 6n 3n 8n 6 3n 7n 5n 3n

Divide You pick which method 12 v 16v 8 v 4

4 4 9 x 18 2x 5 10 4 x 3 Xx 8 16x Determine which expressions if any are 6x 2 x

Below is the graph of y Transform it to make the graph of y 8 1 SCH 1 X 2 3 V X

Graph all vertical and horizontal asymptotes of the rational function 6x 13 f x 2x 7 X

Write each expression with a single rational exponent Show each step of your process Which expressions are equivalent Justify your reasoning A 4x B C 10 5 D

Identify the vertex of each 7 y 2x 12x 28 A 3 10 C 7 1 B 1 7 D 1 7 9 y x2 10x 25 A 5 0 C 0 5 B 5 0 D 0 5 10 8 8 y x 6x 15 A 3 6 C 3 6 10 y 2x 24x A 3 6 C 7 2 B 3 6 D 3 6 75 B 6 3 D 6 3

A roller coaster s height is given by the equation h 046t2 5t 75 where t represents the time in seconds How long will it take riders to pass over the hill and reach ground level Hint Seth 0 122 05 seconds 75 00 seconds 54 35 seconds

Rewrite in simplest rational exponent form xx Show each step of your process

Rewrite in simplest radical form 516 1 X6 Show each step of your process

Rewrite in simplest radical form 1 3 Show each step of your process X 6

Is the expression x3 x3 x3 equivalent to x3 3 3 Why or why not Explain your reasoning

Writing an Equation From a Graph 1 3 20 11 y 00 2 dy do 4 3 0 1 2 3 1 O X P 2 4 19 4 2 O 2 4x 4 2 4 2 y 10 4 2 2 4 X

12 1 point Solve each equation Round to the nearest ten thousandth 8 4 38 1 7493 No Solution 2 2507 0 7493

10 1 point Solve the equation Round to four decimal places e 8 0 3010 0 6931 6 2389 2 0794

4 3 2 1 Y 3 24 T 2 3 1 2 3 What is the slope of the line I

Veterinarians use different medications to treat fleas in dogs Once administered the medication typically decays exponentially One treatment decays by half each week A dog receives 4 mL of medication and the function f gives the number of mL of medicine left after w weeks 1 Find the amount of medication in the dog s bloodstream 1 week 2 weeks and 3 weeks after it is administered 2 Write an expression to represent the amount of medication in its bloodstream 1 day after it is administered 3 Explain what f means in this context

0 y 36 y 8y 12 y 2x 35 y 9y 14

x 1 x 5 x 3 x 6x 5

9 11a 24 6a 18 3a 15 a 6a 1

x 3 x 2 6x 7 x 2 x 1

8 6 x 3 4x 11 x 9

4x x 2 x 3 x 2

x 1 x 1 2 x x

4 2 x 3 5x 7 x 3

3 7x 8 2 x 5 3x 2 2 x 5

1 a 9 4a 3 6a 4a 3

6 Sy 2y 1 y 3 2 1

y 2 y 2 3 y 2

4 d 3 2d 1 4 1 20 1

3 1 1 2 12 20 2x 2x

a 11 3a 5 a 21 3a 5

Which polynomial function has a leading coefficient of 3 and roots 4 i and 2 all with multiplicity 1 f x x 3 x 4 x i x 2 2 f x x 3 x 4 x 1 x 1 x 2 f x 3 x 4 x 1 x 2 Of x 3 x 4 x 1 x i x

iya aced in the last activity that between the 2 triangles you only need to know 4 angles to show that they are similar She wondered which fourth angle would work to prove that triangle RST is similar to triangle EFG In triangle RST Angle R is 90 Angle S is 25 Angle T is z In triangle EFG Angle E is 90 Angle F is y Angle G is z Draw a sketch of the triangles Then pick one angle measurement that would prove the triangles are similar Explain to Priya why knowing that angle would be enough

Solve using the quadratic formula 7d 2d 8 0 Write your answers as integers proper or improper fractions in simplest form or decim rounded to the nearest hundredth d or d

20 1 point For a period of time an island s population grows exponentially If the continuous growth rate is 2 per year and the current population is 1613 what will the population years from now 1730 1068 2824 1855

17 1 point Mark is investing 47 000 in an account paying 5 26 interest compounded continuously What will Mark s account balance be in 17 years 114 925 39 114 925 46 114 921 47 114 932 80

3 1 point Condense the following Logarithmic expression In 6 6 ln z In y In O In 6 0 6 2 5 y In 6 v 2 In

18 1 point Jeremy is investing 47 000 in an account paying 9 26 interest compounded continuously What will Jeremy s account balance be in 42 years 2 295 840 63 2 197 362 46 2 289 042 36 2 296 973 35