Algebra Questions

Section 5 1 3 8 6 C C Obc 3 C 10 O 4r 1

6 From a point 125 m from the foot of a building the angles of elev the building s flagpole are 40 and 38 respectively 380 409 125 m Calculate a the height of the building the Height of the building is 236 66m Tall Pe 125 38 125 x x 138 125 125 7 125 78m T H 164 88 125 78 b the length of the flagpole 230 66 104 88 O X x Tanus Tan 88 125 78 x 104 88m 125 Tan 38 buo a Tan38 125 78 Tan 40 X Tan Uc

7 From the top of a cliff 108 m high the angles of depression of two small boats on the water are 90 and 15 20 Boat A 9 15 2 Boat B Calculate the distance a from the foot of the cliff to the closer boat 108m b between the boats if they are sighted in the same direction

From the top of a fire tower the angle of depression of a cabin is observed to be 210 Find the distance from the cabin to the foot of the tower if the tower is 212 m tall

7 Find an angle that has the same cos ratio as 497

6 Find the exact value of tan e when sec calculator 227 e is in Q4 Do not use

express the function of the following function in canonical form according to the number of literals requested 1 X X XYZ X Y to three literals 2 X Y Z X Z to two literals 3 W X Z X Z X W W YZ to one literal 4 AB A B C D CD AC to four literals

A group of data items and their mean are given Find a the deviation from the mean for each of the data items and b the sum of the deviations in part a 140 147 149 154 155 Mean Oa 9 2 0 5 6 b 0 Oa 9 2 0 5 6 b 22 149 Oa 9 2 0 5 6 b 0 a 9 2 0 5 6 1122

Solve Ix 3x 2 2

Listen A tree casts a shadow 14 feet long At the same time a person who is 6 feet tall casts a shadow that is 4 feet long How tall is the tree 21 feet 12 feet 25 feet 19 feet Page

A garden is in the shape of a rectangle 56 feet long and 32 feet wide If fencing 5 25 a foot what will it cost to place fencing around the garden 924 00 181 25 462 00 9 408 00

Listen Determine the area of the given polygon 2 ft 38 ft 42 ft 23 ft 14 ft 5 ft 2 ft

Write a formula for the general term the nth term of the arithmetic sequence Then use the formula for a to find a20 the 20th term of the sequence an an 1 4 a 12 O A an 12n 8 a20 232 O B a 4n 8 a20 88 OC an 8n 4 a20 164 O D a 4n 16 a20 96

Write a formula for the general term the nth term of the arithmetic sequence Then use the formula for an to find a20 the 20th term of the sequence 10 6 2 2 O A an 14 4n a20 66 OB an 4n 10 a20 70 OC an 4n 14 a20 66 O D an 10 4n a20 70

an 6am 1 a 3 OA 18 108 648 3 888 23 328 OB 3 3 9 15 21 OC 3 18 108 648 3 888 OD 6 18 108 648 3 888 m www

Determine two different Hamilton paths in the following graph A B E CD F G J KL Select all that apply H A A E I J F B C D H G K L B B F E I J K L H G B D A C E F G H L K J I E A B C D J K L H D C G F B A E I

Kristin has to pick up her children who all attend different schools She is at home H and needs to go to Children First Preschool C Braden River Elementary School B and Stephens Middle School S Kristin estimates the distance among these locations as follows H to C is 10 miles H to B is 6 miles H to S is 11 miles C to B is 9 miles C to S is 21 miles and B to S is 12 miles Answer parts a through c below H 6 B 10 11 C H S B 6 9 10 12 11 C H 21 6 S B 10 OA H C B S H or H S B C H or H C S B H or H B S C H OB H B C S H or H S C B H OC H C S B H or H B S C H or H B C S H or H S C B H O D H C B S H or H S B C H OE H C S B H or H B S C H OF H C B S H or H S B C H or H B C S H or H S C B H G All of the routes are of equal distance 12 C 21 b Use the brute force method to determine the shortest route for Kristin to start from home pick her children up and return home Choose the correct answer below S

Determine two different Hamilton circuits in the following graph Select all that apply A A B C F I H G D A B G E D A B C F I H G C A B C F I H E G D A D G E H I F C B A D G De H

Determine two different Hamilton paths in the following graph Select all that apply A A D F G E C B B A D F G E D B C A F G E C B D A D A D B C E G F G B E C

Kristin Wilson lives in Florence South Carolina and wishes to visit relatives in the following South Carolina cities Columbia Greenville and Charleston In how many ways can she vis each of these cities and return to her home in Florence There are different ways that Kristin can visit each city and return home

9 In the expansion of 4x 1 the coefficient of the term in x is 1248 Find the value of n

Listen A manufacturer of tablets has total revenue given by the function R x 70x and has total cost given by C x 12 500 20x where x is the number of laptops produced and sold How many laptops must be produced and sold to break even 1 250 2 139 3 179 4 89

Listen Based on the scatter plot choose the best estimate of the correlation coefficient 0 0 5 00 5 00 9 0 0 9

23 Find the component form of v if v 8 and the angle it makes with the x axis is O 8 3 8 O 4 4 3 O 8 8 3 O 4 2 4 2

Use the accompanying sinking fund formula to determine the payment needed to reach the accumulated amount Semiannual payments with 6 interest are compounded semiannually for 5 years to accumulate 40 000 The semiannual invested payment is Do not round until the final answer Then round up to the nearest cent p H 7 nt

8 Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector Initial Point 0 8 Terminal Point 9 12

15 Find values for b such that the triangle has no solutions 1 51 a 10

13 Find 2u 3v u 4i v 5j O 4i 5j O 8i 15j 8i 15j O 15i 8j O 8i 15j

10 Find values for b such that the triangle has no solutions A 24 a 13

9 Find the component form of v if v 8 and the angle it makes with the x axis is 30 O 8 3 8 O 4 4 3 O 4 3 4 O 4 2 4 2

7 If u 3i 6j and v 6i 5j find w 3u 5v w 39i 45j w 39i 43j w 33i 43j w 16i 12j w 27i 55j

If a is an integer greater than 1 what is the possible value of R Indicate all such values A 0 37 B 0 45 C 0 73 D 0 98 E 1 06 To lim G 9 a a atl 1

A ball is launched straight up in the air from a height of 5 feet Its velocity feet second 1 seconds after launch is given by f t 321 288 Find t average velocity between 26 seconds and 5 5 seconds feet second The average velocity is Round answer to nearest tenth

6 Estimate the value of 1 2n 1 when x 0 5 Your estimate should be accurate x2n 1 n 0 to within 5 decimal places

Does M8 n 1 1 1 2n 4 converge absolutely converge conditionally or diverge

7 10 Represent f x 12x as a power series What is its radius of convergence

10 Represent f x 12 as a power series What is its radius of convergence

Does 3 converge absolutely converge converge absolutely n5 AFT converge conditionally or diverge n 1 0 1 505 22

Four thousand bass were stocked in a certain lake with no bass population If the population of bass is expected to grow at a rate of 22 per year how long will it take the population to double Step 1 The time in years required for a population to double is given by t Step 2 Substitute r t In 2 t Evaluate rounding to the nearest tenth yr into the formula In 2 where r is the annual growth rate r annual growth rate

Find the interval of convergence of the power series n 1 x 5 n 5 n

10 Represent f x 2x as a power series What is its radius of convergence 1 2x

Write an equation for the line graphed below 7 6 5 4 3 2 1 7 6 5 4 3 2 1 1 2 3 4 5 6 7 1 2 3 4 5 6 7 q

8 Sketch the quadratic y x 1 x 7 Clearly label 3 key points and show your work

9 7 7 9 A B 4n 2 C D A B C 2n 3n 6 21n 27n 10 5n 16 n 2 7 2n 3 5 5n 6 21n 22n 16 5n 6 n 2 20n 29n 10 5n 6 n 2 2 4n 20n 3 n 2 n 5 2n 2 17n 6 4n 4n 20n 3n 6 10 8 8 10 2 r 2 A B C D A B 4 3r 3 12 8r 3 2 1 2x 2 2r 2r 5 5r 14 3 3 r 2 r 1 2r 14 3 2 r 1 2x 18x 12x 48x 6 18x 12x 49x 2x 7 18x 12x 49x 9x 2x 6x 24r 3

3 5 6 4a 10a A B C 4 D A 3 2a 21 5a 2a 2a 5 21 6a 2a 2a 5 21 15a 4a 2a 2a 5 21 10a 2a2 2a 2a 5 5 6 6 7 8 6 5n n 2 n 6 20n 5n n 6 n 2 11 6n 3n A B C D K 4n 8n 24 n 6 n 2 14n 24 5n n 6 n 2 9

1 Subtrating Rational Expressions Simplifych expression 1 n 5 6n 18n A C 5 6n 18n n 1 6n 18n n 8 3n 9n 6 B D 2 3n 9n n 5 6n 18n 2 2 b 5 6b 186 A B C 1 3b 96 6b 18b 1 6b 18b 3b 1 b b 3 6b 186 2

7 4n n 2 A B D 5n 6 21n 27n 10 5n 6 n 2 2n 3 21n 22n 16 5n 6 n 2 20n 29n 10 5n 6 n 2 00 8 B 2 2 12 8r A 3 2 1 D 3r 3 2 2r 2r 5 5r 14 3r 3 2 1 2r 14 3 r 2 r 1

1 24 23 229 4 x 3

2 x 4 3 x 1 11 x 4 x 1

7 Graph the system of inequalities on the set of axes below y 3x 3 x 5 2y 4 X tom of inequalities Explain your answer