Algebra Questions

Solve the system State whether the system is inconsistent or has infinitely many solutions If the system has infinitely many solutions write the solution set with y arbitrary 5x 6y 1 10x 12y 2 Select the correct choice below and if necessary fill in the answer box to complete your choice OA There is one solution The solution set is Simplify your answer Type an ordered pair OB The system has infinitely many solutions The solution set is Simplify your answer Type an ordered pair Type an expression using y as the variable OC The solution is inconsistent

A nonlinear system is given along with the graphs of both equations in the system Verify that the points of intersection specified on the graph are solutions of the system by substituting directly into both equations Substitute the coordinates of the point 2 1 into the left side of the first equation x y 0 6 5 4 3 2 1 4 3 3 6 5 5 x y 5 116

Using the graph of f shown below find three intervals on which f is one to one making each interval as large as possible Ay 3 6 Q G The intervals on which f is one to one are 1 00 Simplify your answers 8 4 1 and

Sketch the graph of the inverse function 8 Ay 72225 Choose the correct graph below SOA OC A OB OD

Using the graph of f shown below find three intervals on which f is one to one making each interval as large as possible 6 Ay EXTE The intervals on which f is one to one are Simplify your answers and 1

Use analytical and or graphical methods to determine the largest possible sets of points on which the following function has an inverse 3 f x 2 2 List the intervals on which the function has an inverse Make each interval as large as possible Use a comma to separate answers as needed

16 Z 6 4 Z 5 2i I Find 2 22 in rectangular form I Find 2 22 in Polar form III Verify your answers from Part 1 Part I Tv Show 2 2 and 2 2 in an Argand Dia

Determine which graph is a function that is one to one on the interval co 1 but is not one to one on 00 00 Choose the correct graph below OA O C AY SEEEE OB OD Ay 2

K Wity that is not one to one on an interval I cannot have an inverse function on I Choose the correct answer below ACCE OA If a function is not one to one then at least one of the domain values of the function has more than one image OB If a function is not one to one then at least one of the range values of the function has more than one image OC The function can have an inverse as it is not one to one on the interval I

How to solve x from the following equation 5x4 2x 300 0

In how many different ways can a police department arrange a lineup if each lineup contains 10 people

Simplify Radicals Special Right Triangles 3 a 27m11n8 b 54a1261

Simplify 5 3 2 26a b c 3 8a bc

4 Find the exact value of the following logarithmic expression log 81 1081

15 2 17 15x 0 19 21 7n 21 126 14k 16 16 11 18 17x 204 12 20 m 13 22 143 11x 204 17

7 m 9 13 9 v 15 27 11 104 8 x b 18 13 6 8 p 6 5 10 n 16 9 12 14b 56 14 10m 40

19 21 7n 21 126 14k 20 m 4 13 22 143 11x

23 16 x 15 25 17 x 15 27 72 8 80 29 7 m 8 24 5 18 26 n 8 10 28 a 11 20 30 18 m 8

Solve each equation 1 26 8 v 3 15 b 23 5 m 4 12 7 m 9 13 2 3 p 8 p 5 4 15 n 9 6 x 7 13 x 20 8 p 6 5

Find the vertex of y x 6x 6 using the vertex formula Step 1 Find the x coordinate of the vertex For any parabola y Ax Bx C the x coordinate of the vertex will always be x ZA Using this formula what is the x coordinate of the vertex for the parabola y x 6x 6 x 3 Step 2 Find the y coordinate of the vertex Now that we know that the x coordinate of the vertex is x 3 we only need to find the y coordinate Fortunately we know that y x 6x 6 What is the y coordinate that corresponds to x 3 y 15 Give the vertex of the parabola y x 6x 6 as a point

Use the vectors in the figure at the right to graph the following vector 2v u 3w Select the figure with a vector that is equivalent to 2v u 3w O A B D

Find the area of the triangle ABC C 133 8 a 46 3 ft and b 36 4 ft Points 0 of 1 The area is square ft Simplify your answer Type an integer or decimal rounded to the nearest tenth as needed

Siven f x x 1 x 2 x 3 what are the zeros and end behavior of the function

Find the area of the triangle ABC a 10 2 m b 5 2m C 15 9 What is the area of the triangle 2 Points 0 of 1 m Simplify your answer Type an integer or decimal rounded to the nearest tenth as needed

Find the area of the triangle using the formula A bh 1 and verify that the formula A absin C gives the same result O Points 0 of 1 A 2 2 45 2 B 2 1 The area using bh is Simplify your answer Type an integer or a fraction Type an exact answer using radicals as needed Sav

Determine the remaining sides and angles of the triangle ABC A 26 36 B 26 48 c 10 68 m C

Determine the remaining sides and angles of the triangle ABC A 30 72 B 31 13 c 18 86 m C O P

Determine the remaining sides and angles of the triangle ABC c 9 mi B 35 51 C 30 69 Find the measure of angle A 0 A Type an integer or a decimal O Poi

Find the length of side a Do not use a calculator a O Points 0 of 1 A 60 2 2 75 ed B Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Determine the remaining sides and angles of the triangle ABC What is the measure of angle B 0 Simplify your answer Type an integer or a decimal B 62 6 ft 20 2 115 2 A

Select the correct choice that completes the sentence below For any triangle ABC its area can be found using the formula A 1 zab LE ab sin C ab sin B

Select the correct choices that complete the sentence below sin A sin B An alternative form of the law of sines is sin C

2 AC has length 2 find the length of AB and BC C A 45 X h 45 B

If BC has length 5 find the length of AC and AB AC AB y A C 30 X 5 60 B

Brian is 15 years old and Jeremy is 22 years old In how many years will Jeremy be 7 years older than three times Brian s age now

1 Do the following a Solve each equation for x Give ex log5 125 x log 4 1 log25 x

Determine the equation of the midline of the following graph 4 3 2 LO 5 4 3 2 1 1 2 4 5 y 2 3 5 4 5 6 7 8 X

h solving the triangle Enter your answer as a decimal value A ZA LB LC 19 38 b degrees a b C C 14

e A ZA LB LC 43 33 104 b degrees a 10 543 b C C 15 B

Finish solving the triangle Enter your answer as a decimal value You must be accurate to at least 3 decimal places ZA LB 20 b 31 31 degrees a b C 14

11 a 2 x 3y 9 a 1 x 6y 12 a K SS A 2 D 1 B 1 E 2 C 0

Find the explicit particular solution of the differential equation for the initial value provided dy x y 7x 0y y 1 10 10 dx The explicit particular solution of the differential equation is y

A ship is anchored off a long straight shoreline that runs north and south From two observation points 19 miles apart on shore the bearings of the ship are N 38 E and S 54 E What is the distance from the ship to each of the observation points Round your answers to one decimal place distance from northern point mi distance from southern point mi

3

9 Use the functions f x x 1 and g x 4x 4 tc answer the following m When f x 0 n When g x 0 p When f x g x

The temperature a of water in an ice cube tray is 75 F when it is placed in a freezer Its temperature n hours after being placed in the freezer is 20 less than 1 hour earlier a Find a formula for the nth term of the geometric sequence that gives the temperature of the water n hours after it is placed in the freezer an b Find the temperatures of the water 6 hours and 12 hours after it is placed in the freezer Round your answers to two decimal places a6 a12 F F c Use a graphing utility to graph the sequence to approximate the time required for the water to freeze Round your answer to one decimal place hr

If csc x 4 for 90 x 180 then sin 2 2 COS cos 2 2 tan 2

12 Given the function f x x2 1 where n is a Natural number using calculus methods determine the intervals of concavity Show all work for full marks

0 10 pts 399 Details Write an expression of the type A log x B or A log x B for the transformed logarithmic function shown below 5 4 3 2 1 6 5 4 3 2 1 1 2 3 A 5 6 1 2 3 4 5 6 f x Hint Use the vertical asymptote to find B To solve for A use a point on the graph and substitute the coordinates into y A log x B or y A log x B as appropriate

Oil leaked from a tank at a rate of r t liters per hour The rate decreased as time passed and values of the rate at two hour time intervals are shown in the table t h 0 2 4 6 8 10 r t L h 8 9 7 5 6 9 6 2 5 7 5 3 Find lower and upper estimates for the total amount of oil in liters that leaked from the tank over the interval 0 10 Use five equal subintervals lower estimate upper estimate