Chapter Chapter Opener Try It Yourself (p. ). + ( ) 7.. + 8. ( ) +. 7. ( 7) + 7 7. 8 () 0 + 8. 7. ( 7) 8 0.. 8. Section.. Activity (pp. ). Triangle Angle A (degrees) Angle B (degrees). a. The sum of the angle measures of a triangle is 80. b. Answer should include, but is not limited to: The sum of the angle measures of each triangle should be 80. Some might be a little off due to rounding.. a. x + 7 + 8 80 x + 0 80 0 0 x 7 So, x 7. b. x + + 80 x + 80 x 8 So, x 8. c. x +. + 77 80 x +. 80.. x 0. So, x 0.. Angle C (degrees) A + B + C a. 0 0 0 80 b. 0 80 c. 0 0 0 80 d. 0 0 0 80 d. x +. +. 80 x + 8.7 80 8.7 8.7 x. So, x... Sample answer: If you notice a pattern, you can use inductive reasoning to write a rule. Then you can test your rule using several examples. You can use the rule to write an equation that can be used to solve a problem.. On Your Own (pp. ). b + b + 7 + b 7 The solution is b 7.. g.7 0. +.7 +.7 g 0.8 The solution is g 0.8.. k + k. The solution is k. r π π + π + π r π The solution is r π. g.7 0. 0.8.7 0. 0. 0. k + + π π π π π r π π. t t + + t, or The solution is t... + z 8.. z. The solution is z... + z 8. +. 8 8 8 Copyright Big Ideas Learning, LLC Big Ideas Math Algebra
Chapter y 7. 7 y ( 7) y 8 The solution is y 8. y 7 8 7 7 7 8. π π x π π x π π x π π( ) π π π π x The solution is x.. 0.0w.8 0.0w.8 0.0w.8 0.0( 0).8 0.0 0.0.8.8 w 0 The solution is w 0. 0. p 8. q + 0 q + 0 p + + 0 0 p q 8 The solution is p. The solution is q 8.. Words: The melting point of mercury k ( ) k k The melting point of krypton is C.. Exercises (pp. 7 ) is of the melting point of krypton. Variable: Let k be the melting point of krypton. Equation: Vocabulary and Concept Check. Addition and subtraction are inverses of each other. Multiplication and division are inverses of each other.. x x x x x x yes; The equations are equivalent because they have the same solution. k. x x + + + + x x x x 0 + + + + x x The equation x does not belong because its solution is x, whereas the other three equations all have the solution x. Practice and Problem Solving. x + 8 + 0 80 x + 8 80 x So, x.. x + 7 + 80 x + 80 x 7 So, x 7.. x + 7 + 80 x + 80 x So, x. 7. x + 7 x The solution is x. 8. g 8 + + g The solution is g.. + p + + p The solution is p. 0. 0.7 + y. 0.7 0.7 y.0 The solution is y.0. x + 7 + 7 7 7 g 8 8 8 8 + p + 0.7 + y. 0.7 +.0... Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter. x 8π π + 8 π + 8π x π x 8π π π 8π π π π. n.. +. +. n. n....... The solution is x π. The solution is n... π w π.. + π + π 0 π w The solution is w 0 π. + d d, or d The solution is d + d + +. π π r + 8 8 7 r The solution is r 7. r + 8 7 + 8 7 + 8 8 8 8 π 0π π π π. Let p be the original price. p.0 +.0 +.0 7.0 p The original price is $7.0. 7. a. Let y be your final score. 0 y + y Your final score is. b. Let x be your score from the 0th frame. 8 + x 8 8 x no; Your total score from the 0th frame is, which is what is already shown on the score card. So, you did not make a spare. 8. 7x 7x 7 7 x The solution is x. 7x 7. 0.8n 0.8n 0.8n 0.8 0.8 0.8 n The solution is n. w w 0. 8 8 w ( 8) 8 8 8 8 8 w The solution is w 8. m m. 7. 7. π π m 7.π π π 7. 7. π π m 7.π 7. 7. The solution is m 7. π. Copyright Big Ideas Learning, LLC Big Ideas Math Algebra
Chapter..g.8.g.8.. g The solution is g..g.8..8.8.8. Let a be the amount earned per hour..a..a... a.0 You earn $.0 per hour.. k 0 0 0 k 0 k The solution is k.. 7.8x. 7.8x. 7.8 7.8 x 0. The solution is x 0... p 7 7 7 ( ) p 7 7 p The solution is p 7. k 0 0 7.8x. 7.8 0.... p 7 7 7 0. Let x be the current time. Rewrite the launch time as a mixed number. 0 hours 0 minutes + hours hours 0 x +.7.7.7.7 x 7 7 x 7 7 7 hours 7 + hours 7 + hours 0 7 hours minutes So, it is 7: A.M. now.. π d π π d π π π d The solution is d. π d π π π π π 7. The number. should have been added to each side.. + k 8. +. +. k.7 8. The solution is k.7. Words: The number of packages The equation x packages. times the number of balls per package is the total number of balls ordered. Variable: Let x be the number of packages. Equation: x represents the number x of. Let x be the original balance. 7 0 x 7 0 x 7 7 0 x The original balance is $0. So, the interest earned was $0 $0 $0.. Let h be the height of the Mantis. h + 0 h The Mantis is feet tall.. h + 8 h + 7 h The solution is h 7. h + 8 7 + 8 7 + Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter. w 7 w 7 + 7 + 7 w The solution is w.. q +.. q +.... q. The solution is q.. w 7. d.8 0. d + + d 0 The solution is d 0. d.8 0. 7. x + 0.8 0. 0 8 7 8 7 x + 7 7 8 7 8 x The solution is x. 8 7 8 7 + + 8 8 x + 8 7 7 q +... +... +.... 8. p p 0 + + + + p The solution is p. p 0. To solve x, divide each side by. Because a negative number divided by a negative number is positive, x must be positive. So, x is greater than. 0. Sample answer: x 8 + + x x x x. Let a be each ant s weight. 800 0a 0 0a 0 0a 0 0 a Each ant weighs about milligrams. Copyright Big Ideas Learning, LLC Big Ideas Math Algebra
Chapter. Let g be the total number of girls and b be the total number of boys.. Girls: g g g Boys: 7 b 8 8 7 8 b 8 b There are girls and boys in the eighth grade. So, there are + 0 students in the eighth grade. V Bh 7π π h 7π π h π π 8 h The height of the cylinder is 8 inches.. a. Let x, y, and z be the amounts (in dollars) of each share. Because the money is divided in the ratio : :, you can write the following equations: x y 0 0 0 0 x y 0 0 0 0 0 0 0 0 x 8 y 7 z 0 0 z 0 0 0 0 z So, the amounts of each share are $8, $7, and $. b. Sample answer: The money may not be divided evenly because each individual may have spent different amounts of time helping paint the garage. Fair Game Review. ( x ) + x x + x x + x x + x 7x. 0.b. +.b 0.b +.b..b. 7. g + g g + g g 8. A; Words: Temperature dropped. Expression: The temperature at P.M. was C. Section.. Activity (pp. 0 ). a. n + n + 80 n + 80 n 8 n 8 n So, n and the angle measures of the triangle are,, and. b. x + ( x + 0) + ( x + ) 80 x + x + x + 0 + 80 x + 0 + 80 x + 80 x x x So, x and the angle measures of the triangle are, 0, + 0. ( + ) and c. q + q + q 80 q 80 q 80 q So, q and the angle measures of the triangle are,, and 08. + + + 0 80 m + 0 80 0 0 m 70 m 70 m. So, m. and the angle measures of the triangle are.,. 8, and d. m m ( m ) (. + 0).. Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter e. y ( y ) + 0 + 0 80 y + y + 0 0 80 y + 0 0 80 y + 0 80 0 0 y 0 y 0 y 0 So, y 0 and the angle measures of the triangle are 0, 0, 0 0 0. and f. ( t + ) + + t 0. 0 80 t + t + 0. + 0 80 t + 0. + 0 80 t + 00. 80 00. 00. t 7. t 7. t. So, t. and the angle measures of the triangle are (. + 0.) 7, 0, and... Indigo triangle: t + x + x 80 0 + x + x 80 0 + x 80 0 0 x 0 x 0 x The angle measures of the indigo triangle are 0,, and. Violet triangle: n + n + n 80 n 80 n 80 n 0 The angle measures of the violet triangle are 0, 0, and 0. The angles of the indigo triangle, violet triangle, and blue triangle form a straight angle, which measures 80. Use this fact to solve for p. x + n + p 80 + 0 + p 80 0 + p 80 0 0 p 7 Blue triangle: p + p + m 80 7 + 7 + m 80 0 + m 80 0 0 m 0 The angle measures of the blue triangle are 7, 7, and 0. Yellow triangle: w + ( t + ) + n 80 w + ( 0 + ) + 0 80 w + + 0 80 w + 80 w The angle measures of the yellow triangle are, 0, and. The orange triangle and the yellow triangle form a corner of the rectangle. So, that angle measures 0. Use this fact to solve for f. f + w 0 f + 0 f Orange triangle: p + f + y 80 7 + + y 80 0 + y 80 0 0 y 0 The angle measures of the orange triangle are, 7, and 0. The blue triangle and the green triangle form a corner of the rectangle. So, that angle measures 0. Use this fact to solve for s. s + p 0 s + 7 0 7 7 s Copyright Big Ideas Learning, LLC Big Ideas Math Algebra 7
Chapter Green triangle: s + k + m 80 + k + 0 80 k + 80 k The angle measures of the green triangle are, 0, and.. a. The sum of the degrees of the parts of the circle graph is 0. x + x + 0 + x + x 0 x + 0 0 0 0 x 70 x 70 x Monday: x Tuesday: x ( ) Wednesday: 0 x 08 Thursday: Friday: x ( ) 7 b. Monday: 0., or 0% 0 Tuesday: 0., or % 0 0 Wednesday: 0., or % 0 Thursday: 08 0., or 0% 0 7 Friday: 0., or 0% 0 c. Monday: 0% of 00 0. 00 0 people Tuesday: % of 00 0. 00 0 people Wednesday: % of 00 0. 00 0 people Thursday: 0% or 00 0. 00 0 people Friday: 0% of 00 0. 00 0 people d.. Sample answer: To solve a multi-step equation, use inverse operations. To check the reasonableness of a solution, make sure the solution makes sense and substitute the solution back into the equation.. On Your Own (pp. ). z + 7 z + 7 ( ) + 7 z z + 7 z 7 7 z. The solution is z. x + + x x x The solution is x. Monday Tuesday Wednesday Degrees 0 Percent 0% % % People 0 0 0 Thursday Friday Degrees 08 7 Percent 0% 0% People 0 0 x 8 Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter. n 8n + 7 n + 7 The solution is. ( x ) ( x) 7 7 n n n n. n 8n + 7 8 + 7 + + x + x x + x x + + x x x The solution is x + + 7. ( x ) + + x + + + 8 +. 0.. ( d ) ( d) +.. 0. + d. 0. d +. 0... d d d The solution is d. ( d ) ( ) +. 0. +. 0. +. 0. +. 0.. 0. 0. 0.. Let x be your score on the fourth test. 88 + + 87 + x 0 7 + x 0 7 + x 0 7 + x 0 7 7 x You need a score of on the fourth test.. Exercises (pp. ) Vocabulary and Concept Check. Let n be the number. + n 7 n n n The solution is n.. Sample answer: First use the Distributive Property to eliminate the parentheses. Then combine like terms. Undo the subtraction to isolate x. Finally, undo the multiplication to solve for x. Copyright Big Ideas Learning, LLC Big Ideas Math Algebra
Chapter Practice and Problem Solving. + k + k 80 + k 80 k k k The angle measures of the triangle are,, and ( ) 0.. a + a + a + a 0 a 0 a 0 a 0 The angle measures of the parallelogram are 0, 0 0, 0, and 0. b + b + + 0 + b 0 + b 0 b + b + b + b + + 0 0 0 b + 0 b b b 0 The angle measures of the pentagon are 0, ( 0 + ), 0, ( 0 0) 0, and ( )... 0x + 0x 0 0x 0 0 0 x The solution is x. 0x + () 0 + 0 + 7. c 7 c c c The solution is c. 8..x +.x. 0.x. 0 +. +..x..x... x The solution is x..x +.x. 0.. +.. 0 h h + 8 h + 8 h h h The solution is h.... 0 c 7 7 0 0 h h + 8 ( ) ( ) + 8 + + 8 8 8 7 7 7 0 Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter 8 + 0. ( v) ( v) 8 + 0 8v + 8v 8v 8v 8 8 v The solution is v. ( v). ( x) ( x) 8 + 8 + + + + + x + x x + x x The solution is x x x x. ( x) + x + 0 8 0 8. The negative sign was not distributed correctly to each term inside the parentheses. 7 ( y) + 7 ( y) + + y + 0 + y + 0 + 0 y y y The solution is y.. C n + 8 8 n + 8 8 8 00 n 00 n 0 n When the cost is $8, 0 watches are made.. x + x + x + x 0 x 0 x 0 The height of each story is 0 feet.. A w ( b + ) b( ) + ( ) b + b b b The width of the message is inches. Copyright Big Ideas Learning, LLC Big Ideas Math Algebra
Chapter. Let p be the cost per serving of pancakes..0 0.( p +.0) + p +.0.0 0.( p) + 0.(.0) + p +.0.0 0.p + 0. + p +.0.0.p +.7.7.7.77.p.77.p... p One serving of pancakes costs $.. 7. 80 + 0 + x 000 00 + x 000 00 + x 000 00 + x 000 00 00 x 00 8. The attendance must be 00. x + a a a x a. bx 7 bx 7 b b 7 x b 0. bx bx 8 bx 8 bx 8 b b 8 x b. cx b b + b + b cx b cx b c c x b c. ax b. + b + b ax. + b ax. + b a a. + b x a. ax + b c b b ax c b ax c b a a x c b a. a. The highest and lowest scores are 8. and.. So, you do not need to consider these scores. Final score 0.( degree of difficulty) ( sum of remaining scores) Let d be the degree of difficulty. 77.7 0.( d)( 7. + 8.0 + 7.0 + 7. + 7.0 ) 77.7 0.( d)( 7 ) 77.7. d 77.7.d... d The degree of difficulty is.. b. Sample answer: Let s be the sum of the scores after the highest and lowest scores are dropped. 7. 0.(.0) s 7..s 7..s.. 0. s So, the sum of the scores after the highest and lowest scores are dropped is 0.. Find five scores that add up to 0.. One possibility is 8.0, 7.,.0, 7., and 8.. The highest score must be greater than or equal to.0 and the lowest score must be less than or equal to 7.. So, one possibility of the highest and lowest scores is. and 7.0. The judges could have given the diver the scores 8.0, 7.,.0, 7., 8.,., and 7.0. Fair Game Review. a Because <, a <.. b + 7 + 7 Because, b + 7. Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter 7. a 0b + 8 0 + 8 0 + 8 Because >, a > 0b + 8. 8. D; x + x + 0 0 Study Help (p. ) Available at BigIdeasMath.com. Quiz.. (p. 7). y + + y The solution is y. π + w π + π + π w π. The solution is w π...m 0..m 0... m 0. The solution is m 0... q +.7 0. q +.7 0..7.7 q. The solution is q... k + 7 7 7 k k k The solution is k. y π + w π π + π π π π.m 0.. 0. 0. 0. 0. q +.7 0.. +.7 0. 0. 0. k + 7 + 7 + 7. z + 8 8 8 z z z The solution is z. 7. ( n ) + + 7 n + 7 n + n n n n The solution is n. ( n ) 8. ( t ) + + 7 + + 7..t + + 7.t + 7 + +. t 0.t 0.. t 8 The solution is t 8. + 7 z + 8 + 8 + 8. t. 8. Copyright Big Ideas Learning, LLC Big Ideas Math Algebra
Chapter + + 80. x ( x ) x + 0 80 0 0 x 0 x 0 x 0 So, x 0. The angle measures of the triangle are 0,, 0. and + + + 0 7 x 8 0 + 8 + 8 7 x 7 x 7 7 x So, x. The angle measures of the quadrilateral are, ( ), ( ), 0. x ( x ) x ( x ) and ( ) 80.. P.m +.m + 80. m 80.m.. m The cost of the materials is $.. x + x +.x + 80.x + 80 80 80.x 7.x 7.. x 0 The length of each side is 0 feet, ( 0) 0 feet,.( 0) 7 feet, and 80 feet.. Let h be the number of hours. 0h 0h 0 0 h. It takes the machine. hours to print posters.. + + 8 + p 0 8 + p 0 8 + p 0 8 + p 80 8 8 p You need to score points in the fourth game. Section.. Activity (pp. 8 ). a. Perimeter Area x + x x + x x x x Perimeter: x + ( ) + + 8 ft Area: x ( ) 8 ft b. Perimeter Area + x x 8 + x x x x 8 x 8 x x 8 + x 8 + 8 + 8 ft Perimeter: Area: x ( ) ft Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter c. Perimeter Area 8 + x 8 x + x 8x x x x x. x + x +. +. 0. ft Perimeter: Area: 8x 8(.) 0. ft d. Perimeter Area x + x x + x x x x x 0 x Perimeter: x + 0 + 0 + ft Area: x 0 ft e. Perimeter Area + + x + + x + + + x x + 8 + x x x 8 + x x Perimeter: x + 8 ( ) + 8 + 8 0 ft Area: + x + ( ) + 8 0 ft f. Perimeter Area + + ( x + ) + x + + + + + x + x + x + ( x) + x + x + x + x + x + x x x + x x x ( x ) Perimeter: x + + + ft Area: x + + 8 + ft g. Perimeter Area x + + + x + + x x + x + x + + x + + x + 0 x + x + x x + 0 x x x 0 x 0 x x Perimeter: x + 0 + 0 + 0 ft Area: x ft. a. Surface area Volume x + x + x x + x + 7 x x + 7 x x x 7 x 7 x x Surface area: x + 7 + 7 + 7 in. x in. Volume: Copyright Big Ideas Learning, LLC Big Ideas Math Algebra
Chapter b. Surface area Volume x + x 8 + 8 x 8 8x + x + x x + x x x 8x 8x 8 8 8 x Surface area: x + () 8 + + in. x 8 in. Volume: Perimeter of 0% of perimeter. larger triangle of smaller triangle x + +.( 8 + x + 0) x +.() 8 +.() x +.( 0) x + +.x + x + 7 +.x. x.x 0.x + 7 0.x 0.x 0. 0. x The dimensions of the smaller triangle are 8,, and 0. The dimensions of the larger triangle are,, and.. To solve an equation with variables on both sides, collect the variable terms on one side of the equation and the constant terms on the other side. Sample answer: x + x + x x x + x. On Your Own (pp. 0 ). x x + x x + x x + x x 7 8 + 7 7 x The solution is x.. ( p) () ( p) p + p + p p + + p + p The equation has infinitely many solutions. m ( m) ( 0) m m m m 0 The equation 0 is never true. So, the equation has no solution.. m m ( m 0 ). 0k + 7 0k + 0 k + 0k 0k + 7 7 7 0k 0 0k 0 0 0 k The solution is k. 0k + 7 0 k 0 + 7 0 + 7 + Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter x x. x + ( x). x + x x x x So, r x + +. The area of each circle is πr π π. Distance from first Distance from second island to second island island to first island.x ( x + ).x ( x) + ( ).x x + 0 x x 0.x 0 0.x 0 0. 0. x 0 The boat travels 0 miles per hour for. hours on the initial trip. So, the distance between the islands is. 0 0 miles.. Exercises (pp. ) Vocabulary and Concept Check. x x () () no; Because substituting for x in the equation results in a false statement, x is not a solution of the equation.. Sample answer: x + x + x x x + x Practice and Problem Solving. Surface area Volume + x + x x + x + x x + 8x x 8 x 8 x x x. x So, x. inches.. Surface area Volume π(.) + π(.) x π(.) x.π + πx. πx πx πx.π. πx.π.πx.π.π 0 x So, x 0 centimeters.. Surface area Volume x + x + x x + 0x + 0 0 x x + 0 0 x x x 0 8 x 0 8x 8 8 7. x So, x 7. inches.. m m m m m The solution is m. m m 8 8 Copyright Big Ideas Learning, LLC Big Ideas Math Algebra 7
Chapter 7. k 7k + k k k + k k k The solution is k. k 7k + 7 + + 8. x + 0 ( x + ) x + 0 ( x) x + 0 x 0 + x + x 0 0 The equation 0 0 is never true. So, the equation has no solution.. p p 8 8 + p + p 8 8 p ( ) p 8 p The solution is p 8. p p 8 8 8 8 8 8 + 8 8 8 0. ( w 0) ( w ) ( w) 0 ( w) 0w 00 0w 00 0 w 0 w 00 00 The equation 00 00 is always true. So, the equation has infinitely many solutions. + n ( n) + () n n + n n n. ( n ) 0 The equation 0 is never true. So, the equation has no solution. 7 + z. ( z ) ( z) 7 + z z + z z z The equation is always true. So, the equation has infinitely many solutions.. 0.x 0.( x + ) 0.x 0.( x) + 0. 0.x 0.x + 0. 0. x 0. x 0.x 0. 0.x 0. 0. 0. x The solution is x. 0.x 0.( x + ) ( ) ( + ) 0. 0. 0. 0. 0. 0. 8 Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter d + ( d) d + d d d. d + ( d ) d + + + + 7 d 7 d d The solution is d. d + ( d ) ( ) + ( ) + 7. In the fourth step, should be added to each side, not added to one side and subtracted from the other. x x + x x x + + x..0 p +.0.0( p + ).0 p +.0.0( p) +.0( ).0 p +.0.0 p +.0.0 p.0 p.0 0. p +.0.0.0 0.0 0. p 0.0 0.p 0. 0. p You need pounds of peanuts. 7. Let m be the number of miles. Cost to rent green car Cost to rent blue car + 0.0m + 0.m 0. m 0.m + 0.m 0.m 0 0.m 0 0. 0. m 0 You must drive 0 miles to have the same cost for each of the car rentals. 8. x x + + x + x + x x x x x Side length Perimeter The perimeter is units.. ( x ) ( x) x x x x x x x + + x x. x x Perimeter (.) 7. Side length. 7.. The perimeter is 7. units. Copyright Big Ideas Learning, LLC Big Ideas Math Algebra
Chapter 0. x x + 7 x x x 7 + + x x x Side length x + 7 + 7 Perimeter 8 The perimeter is units.. Sample answer: a. 8 ( x + ) ( x ) 8 ( x) + 8 ( x) x + 8 x 8 x x 8 8 The equation 8 8 is never true. So, the equation has no solution. b. 7 ( x + 7) x + 7 ( x) + 77 x + x + x + x x The equation is always true. So, the equation has infinitely many solutions.. Let w be the weight of the DVD with packing material. Cost of mailing Cost of mailing envelope ( express) box ( priority ) 8.0w +.0.0w +..0 w.0 w w +.0..0.0 w. w. w 0. The weight of the DVD with its packing material is about 0. pound.. Sample answer: Use fractions to solve 0.x + 7 x 8 because written as a decimal is repeating.. 0.x x. 0.x. 0.x. 0. 0. x 0 The total amount of blood drawn is 0 millimeters.. Let x be the total number of grams of fiber you need daily. x + 0.x 0. x 0.x 0.8x 0.8x 0.8 0.8 x You should consume grams of fiber daily.. Perimeter of square Perimeter of triangle x + ( x + ) + x 7x + 7x + ( x + ) + + x + x x x x x x ( x ) The side lengths of the square are units. The side lengths of the triangle are 7 units, units, and + 0units. Fair Game Review 7. V Bh (. )( )(. ).7 The volume is.7 cubic centimeters. 8 The volume is cubic inches. 8. V Bh. V π r h (. )( 7 ) ( ) (. )( )( ).8 The volume is about.8 cubic feet. 0 Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter 0. C; Let x be the number of miles per gallon. 80 x 80 x x The car travels miles per gallon. Extension. Practice (pp. ). x 0 or x 0 The solutions are 0 and 0. 0 0 0 0. x or x + + + + x or x The solutions are and. 0. The absolute value of an expression must be greater than or equal to zero. The expression + x cannot equal. So, the equation has no solution.. x 8 or x 8 + + + + x x x x x or x The solutions are and. 0. x + 7 x + 7 x + 7 x + 7 or x + 7 7 7 7 7 x x x x x or x The solutions are and. x + 7 + 7 + 7 x + 7 + 7 + 7 0. x + x x or x + + + + x or x The solutions are and. x + + + + x + + + + Copyright Big Ideas Learning, LLC Big Ideas Math Algebra
Chapter 7. x + + x 8 x 8 x x or x + + + + x x x x x or x The solutions are and. x () + + 8 8 x 8 + + 8 8. Sample answer: x 0 x 0 or x 0 + 0 + 0 + 0 + 0 x or x. Sample answer: x 8 x 8 or x 8 + + + + x or x Section.. Activity (pp. 7). a. P + w P + w P w P w P w w P (.) 8 The width of the rectangle is inches. b. A bh A bh A bh A bh b b A b h h A 0 0 0 8 b The height of the triangle is 8 inches. c. C π r C π r π π C r π r C 8π π π The radius of the circle is centimeters. d. A ( B + b) h A ( B + b) h A ( B + b) h A ( B + b) h B + b B + b A B + b h h A 0 B + b + 0 The height of the trapezoid is inches. Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter e. A bh A bh b b A h b A h 7 b 8 The height of the parallelogram is 7 meters.. a. V Bh V Bh B B V B h h V 0 B The height of the prism is inches. b. V Bh V Bh V Bh v Bh h h v h B B V 8 h The area of the base of the pyramid is square feet. c. V Bh V Bh h h V h B B V 8π h π The area of the base of the cylinder is π square centimeters. d. V Bh V Bh V Bh V Bh B B V B h h V 8 ( π ) π B π π The height of the cone is meters.. Sample answer: You can solve a given formula for a different variable to form a new formula that can be used to solve for the variable. For instance, suppose a rectangle has a length of inches and an area of 0 square inches. You can solve the formula for the area of a rectangle for w, and use the new formula to find the width. A w A w A w A 0 w The width of the rectangle is inches.. On Your Own (pp. 8 ). y x 0 y x + x 0 + x y 0 + x y 0 + x y 0 + x y + x. x y x x y x y x y x y x y + x. x + y x x x + y x y x y x y x y Copyright Big Ideas Learning, LLC Big Ideas Math Algebra
Chapter. A bh A bh h h A b h. S πr + πrh. I Prt I Prt rt rt I P rt S π r πr πr + πrh S πr πrh S πr πrh πr πr S π r π r h + +. + 7. 7. F C Because 7. F is greater than 70 F, C is greater than room temperature.. Exercises (pp. 0 ) Vocabulary and Concept Check. The equation x is not a literal equation because it 8 has only one variable.. The fourth question is different because it asks to solve for x, whereas the other three questions ask to solve for y. x y x x y x y x y x y x y + x x y x y + y + y x + y x + y x + y x + y Practice and Problem Solving. a. A bh b. A bh A bh A bh A bh h h A b h 7 c. A b h The base of the triangle is millimeters.. a. V Bh b. V Bh V Bh h h V h B c. B V h The area of the base of the prism is square inches... x + y x x + y x y x x + y 7 x x + y 7 x y 7 x y 7 y x ( x) Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter 7. x + y x x x + y x y x y x y x y 8. π 7x y π 7x 7x 7x y π 7x y π 7x y π 7 + x y..x.y..x.x.y..x.y..x.y..x.. y..x. y. + x 0. y.x 8 y.x +.x 8 +.x y 8 +.x y 8 +.x y 8 +.x y + x. After x was subtracted from each side, each side should have been divided by. So, the equation is y x.. a. K C + 7. K 7. C + 7. 7. K 7. C b. C K 7. 00 7..8 00 Kelvin is.8 C.. a. I Prt I Prt Pr Pr I t Pr I 7 7 b. t Pr ( 00)( 0.0) So, t years.. d rt d rt r r d t r. R C P R R C P R C P R C P R C P + R. e mc e mc c c e m c 7. A π w + w A πw πw πw + w A π w w A π w w w w A π w w V 8. B h V B h h h Bh V Bh V Bh V g + 0 g w + 0 g 0 w + 0 0 g 0 w. g ( w + 0) ( w ) 0. It is useful to rewrite a formula in terms of another variable because the rewritten formula is a general solution that can be reused. Copyright Big Ideas Learning, LLC Big Ideas Math Algebra
Chapter + 7. K 7. ( F ) + 7. 7. K 7. ( F ) ( K 7.) ( F ) ( K 7.) F ( K 7.) + F + ( K 7.) + F F K 7. + ( 7. 7. ) + ( 0 ) + 0 +. a. K ( F ) b. The freezing point of water is F. C F. So, the formula for K becomes K C + 7.. K C + 7. 78. + 7.. Because 77.K is less than.k, liquid nitrogen is colder. c. Note that. a. C π r C π r π π C r π C.. r 70 π (.).8 The radius of the Navy Pier Ferris Wheel is about 70 feet. b. Let f be the first Ferris wheel s circumference.. 0. f. 0. f 0. 0. 78 f The circumference of the first Ferris wheel is 78 feet. C 78 78 r π (.).8 The radius of the first Ferris wheel is feet. c. Speed Distance Time 78 87. The Ferris wheel was moving at a rate of about 87. feet per minute.. V πr V πr V πr V πr π π V r π V 8.. r. π.. Use guess, check, and revise to find r. You know and. So, r is between and. Guess.8. r.8 0.. Too high, so revise. Guess.. r. 8.8. Too low, so revise. Guess.. r.. So, the radius of the sphere is. inches. Fair Game Review.., or 8. 8.... 8 8 7 7 7., or 0 8. D; written as a decimal is 0.7, written as a ratio is :, and written as a percent is 7%. Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter Quiz.. (p. ). ( x ) ( x). + x + + x + x + 8 x + + x + x 7x + 8 8 8 7x 7 7x 7 7 7 x The solution is x. ( x + ) x + () + + + s s s s 7 s 7 s 7 7 s The solution is s. s s. 8.z.z + 0.. z. z.z 0..z 0... z. The solution is z.. 8.z.z + 0. 8.... + 0. 0.7 0. + 0. 0.7 0.7. ( b + ) ( b ) ( b) + ( b) b + 8b 0 b b b 0 + 0 + 0 b b 7 b The solution is b 7. ( b + ) ( b ) 7 ( + ) 7 ( ) ( ) ( ). d + 0 d + 0 or d + 0 0 0 0 0 d or d The solutions are and. 8 0 8. w 8 w 8 w w or w + + + + w or w The solutions are and. 0 7. x y x x y x y x y x y + x Copyright Big Ideas Learning, LLC Big Ideas Math Algebra 7
Chapter 8. 8 y 0x 8 + 0x y 0x + 0x 8 + 0x y 8 + 0x y + x y. V πr h V πr V πr r h π πr h A hb+ B A h b + B 0. A h( b + B) ( + B) A hb h h A b + B h A B b + B B h A B b h 8. C ( F ) Because C is greater than C, the water temperature in Portland is higher.. I Prt I Pt I Pt Prt Pt r I 0 0 r 0.0, or % Pt 00 000 The interest rate is %. x + + x + x + x x + x x x x + + x x x Route that passes beach: x + + x + + + 8. () The length of the route that passes the beach is 8 + miles. Route that passes park: x x () The length of the route that passes the park is + miles.. a. P a + b + c b. P a + b + c a c a c P a c b c. b 0 7 b feet Chapter Review (pp. ). y + 8 y + 8 8 8 + 8 y The solution is y... 0. n. 0.n 0. 0. 8 n. The solution is n 8. t π t t π ( π ) The solution is t π.. 0. n. 0. 8.. t π ( π ) π π π 8 Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter. 7y + 7. 7y 7y 7 7 y The solution is y. 8 b 8 8 b b b () The solution is b. + 0. ( z ) + 0 + 0 ( z ) ( z ) + + z + 7 z 8 z 8 8 z 8 The solution is z. ( z ) + 0 8 + 0 8 + 0 7y + 7 7 + 7 + 7 7 7 8 b 8 ( ) 7 0 0 8 + 7. n n + n + n 0 n 0 n The solution is n. 8. ( x ) ( x) n n + + + 8 +. 0.. 0 0x 0 0x 0 0 + 0 + 0 0x 0 0x 0 0 0 x The solution is x. ( () ). x 0. 0. 0. 0 0 0 0 Copyright Big Ideas Learning, LLC Big Ideas Math Algebra
Chapter. w + w w + + w w w w w The solution is w. w + w + 0 + 0. 0 + x + x 80 0 + x 80 0 0 x 0 x 0 x So, x. The angle measures of the triangle are 0, ( ) 0, and.. x + x + x + x 0 x 0 x 0 x 0 So, x 0. The angle measures of the trapezoid are 0, 0, ( 0 ) 0, and 0. + + + + 0 x + x + x + x + x 0 x 0 + + x 7 x 7 x. x ( x ) x ( x ) ( x ) So, x. The angle measures of the pentagon are,, 0 0,, and 0.. m m + m m + m m + m + + 0 + m The solution is m.. ( p ) ( p ) ( p) ( p) p p p p 0 p + + 0 p 0 p 0 0 p The solution is p. ( p ) ( p ) ( ) ( ) 0 Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter 0 n + + 0 n + n + 0 n n n + 0 0. n + ( n + ) ( n) n 0 0 0 0 n 0 0 n The solution is n. 0 n + ( n + ). x + 7 ( ) + ( + ) 0 8 + 0 x + 7 or x + 7 x or x The solutions are and. 7. w x + 7 + 7 7 7 7 7 x + 7 + 7 7 7 7 7 w w or + + + + w 0 w 8 w 0 w 8 w or w The solutions are and. w w 8 () 0 8. y 7 + 0 8 0 0 y 7 8 y 7 8 y 7 y 7 or y 7 + 7 + 7 + 7 + 7 y y y y y or y The solutions are and. y 7 + 0 8 7 + 0 8 7 + 0 8 + 0 8 Copyright Big Ideas Learning, LLC Big Ideas Math Algebra + 0 8 8 + 0 8 8 8 y 7 + 0 8 7 + 0 8 7 + 0 8 + 0 8. x y 0 x x y 0 x y 0 x 0 x y y + x + 0 8 8 + 0 8 8 8
Chapter 0. 8x + y 8 x 8 x 8x y 8x y 8x y 7 x y. y x y x y x y x y x + x +. a. F ( K ) ( F ) ( F ) 7. + F F ( K 7.) + ( K 7.) ( F ) ( K 7.) ( F ) K 7. + 7. K 7. + 7. + 7. K A hb+ B. a. A hb ( + B ) b. A h( b + B) ( + B) A h b + B A hb b + B b + B A h b + B A 7 c. h b + B 8 + The height of the trapezoid is centimeters. Chapter Test (p. ). + y. y. The solution is y.. + y. +.... x x. 8 8 x 7 8 8 x 7 8 8 x 7 x 7 The solution is x 7. + 7. ( 0 ) + 7. ( 08 ) + 7. 00 + 7. 88.7 b. K ( F ) So, 0 F is about 88.7 Kelvin. Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter. z 8 + + z z + 8 8 + 8 8 z + z The solution is z. z 8 8 8 8 8. r + + r + r + r The solution is r...8n.n +. n. n.n + +.n 8.n 8.. n 7. The solution is n 7...8n.n +.8 7.. 7. + 8. 0. +.. r. ( d ) ( d) 8 + d 8 + + d 7d + d 7d d d d 0d + + 0d 0 0d 0 0 0 d The solution is d. ( d ) 8 + d 8 + 7. x x ( x ) + + + + 8 80 x + 8 80 + + 8 8 x 7 x 7 x So, x. The angle measures of the triangle are, 8, + 8. ( ) and x + x + + x + x 0 x 0 x 0 x 0 So, x 0. The angle measures of the quadrilateral are 0, 0 87, 0 + 8 8, 8. ( ) and ( 0 ) 8. Copyright Big Ideas Learning, LLC Big Ideas Math Algebra
Chapter. p 7 p 7 or p 7 + + + + p 0 p p 0 p p or p The solutions are and. 0 0. v 8 0 v 8 0 v 8 The absolute value of a quantity cannot be a negative number, so this problem has no solution...x y 8.x.x y 8.x y 8.x y 8.x y 7 + 0.x. 0. 0.y 0.x 0. + 0.x 0.y 0.x + 0.x 0. + 0.x 0.y 0. + 0.x 0.y 0. 0.. + 0.x y. P + w P + w P w P w P w. d rt d rt t t d r t. Let s be your team s score. s 7 + + s 8 Your team s score is 8.. Let x be the number of hours of biking. x 8x x x 0 x + + x x x It takes you C ( 7 ) C ( ) C 0. 7. C ( F ) hour to catch up to your friend. So, 7 F 0. C. The temperature of 0 C is greater than 7 F. 8. Let h be the number of hours worked. 8h 0 + 0 + 0 8 h 8h 8 8 8 h You worked 8 hours. Chapter Standardized Test Practice (pp. 7 ). A; The value x 8 makes the equation true because 8.. I; m + m m m 8 Your taxi ride was 8 miles long. Big Ideas Math Algebra Copyright Big Ideas Learning, LLC
Chapter. B; t t + + t + t. x + ( x + ) x + ( x) + ( ) x + x + 0 x x x + 0 x 8 x + ( 8) + + The length of one side of the square is units. P + w P + P + P 0 The perimeter of the square is 0 units.. G; d rt d rt r r d t r. B; x + ( x + 7) x + x + 7 Using the Distributive Property to multiply x by and 7 by is a correct first step to solve the equation. 7. Part A: 00 + 0.0( 000) 00 + 0 0 You earned $0 last week. Part B: Earnings for week 00 + 0.0 total sales for week 0 00 + 0.0s Part C: 0 00 + 0.0s 0 00 00 + 0.0s 00 0 0.0s 0 0.0s 0.0 0.0,000 s Your total sales that week were $,000. 8. H; Maria's age today + 0 m + 0 An equation that can be used to find m is m + 0.. B; y + 8 7y + y y 8 y + y y y The solution is y, or 0.7. 0. I; F C + F C ( F ) C ( F ) C. ; Let x be the number of additional weeks needed to save enough money for the cell phone. 7 + 0x 7 + 0x 0 0x 0 0x 0 0 x You need to save money for more weeks.. C; 8x x + x + x x + x + + x + x The equation is always true. So, the equation has infinitely many solutions. Copyright Big Ideas Learning, LLC Big Ideas Math Algebra
Chapter. F; x + x + x + x + or x + x x x x x or x The solutions are and. x x 7 ( x) x 7 x 8 x 7 x x x 8 7 + 8 + 8 x x. The solution is x... D;. F; Let m be the weight of a mug and t be the weight of a trophy. m + t t m + t t t t m t m t m t A mug weighs one-third as much as a trophy. Big Ideas Math Algebra Copyright Big Ideas Learning, LLC