Algebra Questions

37 Construction The roof of a house is to extend up 13 5 feet above the ceiling which is 36 feet across If the edge of the roof is to extend 2 feet beyond the side of the house and 1 5 feet below the ceiling find the length of one side of the roof

Three different rays share endpoint A as shown in the figure A a How many different angles are formed by the three rays 3 b Describe the types of angles that are formed by the three rays There are two acute angles and one right angle There are two obtuse angles and one right angle There is one obtuse angle and one acute angle There is one acute angle and one right angle There are two acute angles and two right angles c Describe a special relationship between two of the angles ute and obtuseX angles are complementary angles

Mic 1 Aare pa 2 HAHT 1 P m p ne 8600 325 576 x 42 165 220 480 2 P n e p 5 4a a 6 3 3 11 12 7 8 a 6 6 7 4 2 3 9m 7m m 8 m 16m 64 49 a 27 4 Y 9m 65 8m 64 m 64 5 x 7x 4 0 x m 8 16 2 x 3 12 x x 3 x 3 x 9x 3 x a 3 1 7 15 2 a 27a a 27a 40 a 2 2 a 3a 9 16 a 8 x x 1 x x 1 6 1 4 a

b Yes the polygon is regular It is both equilateral and equiangular No the polygon is not regular It is equilateral but it is not equiangular No the polygon is not regular It is equiangular but it is not equilateral No the polygon is not regular It is neither equilateral nor equiangular c 7 m 7m 8 m 8 m 94 7m 94 7 m Yes the polygon is regular It is both equilateral and equiangular No the polygon is not regular It is equilateral but it is not equiangular No the polygon is not regular It is equiangular but it is not equilateral No the polygon is not regular It is neither equilateral nor equiangular x X not equiangular war it is both equilateral and equiangular

The interior reflex angles of the polygon below are congruent The interior acute angles are also congruent The measure of each interior reflex angle is 252 Find the measure of each interior acute angle 126 Need Help DETAILS Read It Watch It onds to a reflex angle that has a measure between 180 and Je LARMPMT1 10 3 005 MY NOTES ASK YOUR TEACHER

d No the polygon is not regular It is equiangular but it is not equilateral No the polygon is not regular It is neither equilateral nor equiangular 94 94 Yes the polygon is regular It is both equilateral and equiangular No the polygon is not regular It is equilateral but it is not equiangular No the polygon is not regular It is equiangular but it is not equilateral O No the polygon is not regular It is neither equilateral nor equiangular X

b isosceles trapezoid kite 3 parallelogram rectangle rhombus right trapezoid square X

59 a Find y if the radius of the circle is 100 feet and 0 30 b Use the information from Part a to find x

Find the remaining sides of a 30 60 90 triangle if 39 The shortest side is 1 41 The longest side is 8 40 The shortest side is 3 42 The longest side is 5

Find the remaining sides of a 45 45 90 triangle if 49 The shorter sides are each 1 50 The shorter sido

b Regular octagon XC

a Consider the following 48 Find the value of x in the triangle X 66 acute Classify the triangle in as many ways as possible Select all that apply equiangular equilateral isosceles obtuse to right scalene to b Consider the following

Consider the lantern shown below a Which semiregular polyhedron does the lantern resemble small rhombicosidodecahedron snub dodecahedron truncated icosahedron icosidodecahedron O truncated dodecahedron b The lantern has 90 edges and 60 vertices How many faces does the lantern have

Consider the following 1 2 rectangle square 3 Classify the numbered quadrilaterals in the woodwork as specifically as possible quadrilateral 1 right trapezoid quadrilateral 2 quadrilateral 3 many rhombuses that are not squares do you see

e whether the figure is a triangle D This is a triangle This is not a triangle in your reasoning State whether the figure is a triangle This is a triangle This is not a triangle explain your reasoning c State whether the figure is a triangle This is a triangle This is not a triangle reasoning

a Consider the following Classify the polyhedron made by the net as regular or semiregular Oregular Osemiregular Name the polyhedron Ododecahedron truncated dodecahedron O octahedron truncated octahedron Otetrahedron truncated tetrahedron

b 36

b Obtuse Select all that apply A c Right Select all that apply B B A 73 B

79

Use the revenue and cost graphs on the right to find the approximate profit from manufacturing 24 000 cell phones What is the approximate profit from manufacturing 24 000 phones Dollars in millions 5 4 3 2 1 0 8 Revenue 16 Cast 24 32 40 48 o Q G

21 It takes the earth 24 hours to make one complete revolution on its axis Through how many degrees does the earth turn in 12 hours

The graph on the right gives the annual per person retail availability of beef chicken and pork in pounds from 2007 to 2012 What is the approximate annual per person retail availability of beef chicken and pork in 2012 The annual per person availability of beef in 2012 is approximately 62 pounds The annual per person availability of chicken in 2012 is approximately pounds G Pounds 70 65 60 55 50 45 beef porke 40 35 2007 2008 2009 2010 2011 2012 Year

Problems 15 and 16 refer to Figure 18 A D FIGURE 18 15 Find AB if BC 4 BD 5 and AD 2 16 Find BD if BC 5 AB 13 and AD 2 17 What acute positive angle does the line y B C x make with the positive x axis

Simplify the expression Write the answer using only positive exponents 68 6 9 6 10 68 6 9 10 6 Type exponential notation with positive exponents

Tell whether each figure is convex or concave a b c convex O concave d convex concave convex O concave convex O concave

K Write the rational expression in lowest terms Z 5z 6 z z 6 z 5z 6 z z 6 2 Simplify your answer

9x 27 6x 18 expres 9x 27 6x 18 Type an integer or a fraction

plify the given rational expression Assume that the denominator in each case is nonzera 4214 54t 1 A 214 QUE OROor Use positive exponents only

Ifferent rays share endpoint A as shown in the figure A a How many different angles are formed by the three rays b Describe the types of angles that are formed by the three rays There are two acute angles and one right angle There are two obtuse angles and one right angle O There is one obtuse angle and one acute angle There is one acute angle and one right angle There are two acute angles and two right angles c Describe a special relationship between two of the angles The Select angles Select ales

Find the missing number of vertices faces or edges for each polyhedron a Hexagonal pyramid 6 lateral faces 7 vertices b Octagonal prism 8 lateral faces c Polyhedron edges vertices 24 edges faces 20 vertices 30 edges

Help c Regular nohagon 9 gon Read It

b Regular octagon O

4 4 Ip H y f x X

6 A football team consists of 23 players three goalkeepers eight defenders seven midfielders and five forwards How many different match lineups are possible if we assume that a lineup must consist of exactly 11 players and include exactly one goalkeeper four or five defenders at least three midfielders and at least one forward

5 How many five card subsets of the set of 52 cards of the usual deck con taining four akes four kings four queens etc contain simultaneously a least two aces at least one king and at least one queen

4 In how many ways can the elements of an eight element set be divided into four pairs there can be different answers depending on when we treat two ways of dividing as different please formulate clearly your assumptions and calculate accordingly

c Right Select all that apply C B O B

Find and sketch an angle that is complementary to the angle O 90 b Consider the following 45 145 O 45 135

3 Let X be the set of all ten letter words that can be obtained by permuting the letters of the word COLLATERAL How many elements does X contain ii How many elements of X begin and end with L iii How many elements of X contain three neighbouring letters L iv How many elements of X contain at least two neighbouring letters L v How many elements of X contain no neighbouring vowel letters letters A E O

MY NOTES Find the value of x for each polygon X ASK YOUR TEACHER b 120 124 to 158 to 120 128 111 1219 PRACTICE A

1 Let X be the set of all five digit numbers that can be obtained by permu ting the digits of the number 12558 i How many elements does X contain ii How many even numbers are there in X iii How many odd numbers are there in X

4 1 Points DETAILS Sketch an isosceles triangle Need Help Read It Submit Answer LARMPMT1 10 1 021 MY NOTES ASK YOUR TEACHER

2 y f x D

Exercises 111 114 Critical Thinking The graph of a function f is shown Complete each of the following Use interval notation when appropriate a Give the zeros of f b Give any x and y intercepts on the graph of f c Identify where f is negative or positive d Identify where f is increasing or decreasing e Is the average rate of change of f from x 4 tox 4 positive negative or zero 4 4 y f x

2 FAKT RYEL VE B LME LEM 13 a b ve c do al say lard r 6 b a oldu una g re c nin alabilece i ka farkl de vard r A 5 B 6 C 7 D 8 E 9

Suppose that M is an m x m matrix with entries M20 such that 1 M 1 for each of the olumns j 1 m Show that 1 is an igenvalue of Mk for any k EN

3 In how many ways can we put 20 identical silver coins into five coloured boxes so that at most 3 coins go into the blue box at least 4 into red and at most 5 into green The remaining boxes are yellow and black and may contain any number of coins Every box except the red one may also remain empty

SAMPLE RIAL PROBLEMS 1 Let X be the set of all different eight letter words that can be obtained by permuting the letters of the word DEBUNKED How many elements does X contain In how many of them there are neighbouring identical letters In how many elements of X there are no neighbouring vowels terminology E U are vowel letters while B D K N are consonant letters

2 Assume that a basketball line up must consist of 5 players 2 guards 1 center and 2 forwards A coach has in total 12 players in the team there are 5 guards 2 centers 4 forwards and additionally Peter Williams who can play as center or forward How many 5 player subsets of this 12 element set are acceptable line ups In how many of them does Peter Williams appear

1 Let X be the set of all different eight letter words that can be obtained by permuting the letters of the word DEBUNKED How many elements does X contain In how many of them there are neighbouring identical letters In how many elements of X there are no neighbouring vowels terminology E U are vowel letters while B D K N are consonant letters 2 Assume that a basketball line up must consist of 5 players 2 guards 1 center and 2 forwards A coach has in total 12 players in the team there are 5 guards 2 centers 4 forwards and additionally Peter Williams who can play as center or forward How many 5 player subsets of this 12 element set are acceptable line ups In how many of them does Peter Williams appear 3 In how many ways can we put 20 identical silver coins into five coloured boxes so that at most 3 coins go into the blue box at least 4 into red and at most 5 into green The remaining boxes are yellow and black and may contain any number of coins Every box except the red one may also remain empty 4 How many solutions of the equation a b c d 80 in integers greater than 0 satisfy simultaneously all the following conditions a 30 10 c 40 and a b c d are all even REMARK If your answer is eg 3 56 you don t have to compute the numerical answer 546875 Just write 3 56 as the final answer