Algebra Summer Math HW check

Transcription

1 Lesson Practice 1 a) Integers, rational numbers, real numbers b) Rational numbers, real numbers c) Irrational numbers, real numbers Whole numbers; Sample: There can be d) no people or any number of people. Irrational numbers; Sample: Area is equal to pi times the radius squared, so e) the answer will be irrational. Rational numbers; Sample: The value of the coins will have tenths and f) hundredths. C D = {20}; C ᴜ D {4, 5, 8, 10, 12, 15, g) 16, 20} C D = { } or Ø; C ᴜ D {6, 7, 12, 14, 18, h) 21, 24, 28} 2) or 1 4) 6) 8) Sample: 10) 12) 720% 14) Whole numbers 16) B ( ) False; Sample: A right angle and an obtuse angle have a sum of more than 18) 180 True; Sample: by definition, an acute 20) triangle has only acute angles. 22) Rational numbers 24) Yes, the ones digit is even. a) 18 square feet b) rational numbers, integers, whole 26) numbers, and natural numbers 28) Yes 30) Rational numbers Lesson Practice 2 a) 65, 12; q, r, s, x b) 4, 71; g, h, y, z c) 17, d, e, f; 17 d), u, v; e) -3, s, t; -3 f) a, b, c; 1 g) 8v, 17yz, h), 18s, 47jkl i) 3 j) 6.5, 3.25, 0.75 k) h, b 2) 14 4) 30 6) 8) Coefficients: 2, 7; variables: x, y, w False; Sample: Zero is a whole number, but it is 10) not a natural number False; Sample: By definition, the sets of rational and irrational numbers do not have any 12) members in common. 14) Whole numbers, integers, and rational numbers 16) 17 18) straight 20) 0.3% 22) Natural numbers Constants: 2 and π, variables r and v; 24) coefficient: 2π 26) Student B; Student A listed two terms. 28) C (trapezoid) 30) Whole numbers

2 Lesson Practice 3 a) 1296 b) 1.96 c) d) 1,000,000 e) f) g) 2) ) ½ 8) Coefficients: 23, ; variables: t, w False; Sample: Fractions are real numbers, 10) but they are not integers. True; Sample: By definition, the set of irrational numbers is a subset of the set of 12) real numbers. 14) 16) {, -3, -2, -1, 0, 1, 2, 3, }; temperature Student B; Sample: Student A multiplied 18) the exponents instead of adding them. 20) Yes; The number is divisible by 2 and 3. 22) B ( ) a) ) b) dollars; $1,000,000,000 A (a triangle with angle measures of 45, 26) 45, and 90 ) 28) ½ a) 2 terms 30) b) l and w Lesson Practice 4 a) b) c) d) e) π 2) (add inside parentheses) (multiply) 12 (subtract) (simplify exponents) 72 3 (multiply and divide) 69 (subtract) (simplify exponents) (multiply) (add and subtract) 2 (divide) 6) ) 10) L = {-15, -8, 0, 1, 3, 6, 7,12} 12) Irrational and real numbers 14) 55.6% B (a triangle with angle measures of 16) 40, 120, and 20 True; A square has 4 right angles and its opposite sides are parallel and 18) congruent. Student B; Sample: Student A has an extra factor 3, which results in a 20) product of 324. a) n, x, y 22) b), 3xy, 19 24) B ($23.25) a) 12 $ $ $0.25 = $1.80 b) 10 $ $ $0.25 = $ ) c) Ashley 28) Volume of cube = 30) $43.61

3 Lesson Practice 5 a) 3.4 b) c) 8 d) -23 e) f) - g) true h) true i) 22 F 2) 1 6) ) ) L = {-12, -8, -4, 0, 4, 8, 12} Student B; Sample: The 12) irrational. 14) 3 feet, 1.25 yards, 1 yards 16) -11 = 11 18) $1.30 True; The opposite sides of rectangles 20) are congruent and parallel. 22) 26 F 24) D (all of these) 26) $500 + (-$34.65) = $ ) points 30) 16 F is Lesson Practice 6 a) 36 b) -23 c) d) - False; Sample: Counterexample: 5 12 = e) -7 f) true g) -24,000 feet 2) 18 6) ) ) 3 7 No; The sum of the digits is ) 6 =13 which is not divisible by 3. 14) 1 ; feet 16) D (5.8) 18) B ( ) 20) ) -$65.49 No; Sample: After the rainfall, the lake level is at -2 feet, which is more 24) 26) 28) than 2 feet below normal. Student A; Sample: Student B added 11 floors instead of subtracting. a) 16, -4, 21 b) 4 c) 16c 4d efg; Subtracting a number is the same as adding its inverse. 30) 1195 ft

4 Lesson Practice 7 a) 18 b) 10 c) 77 d) 4( ) 6 + (simplify in the parentheses) 4(9) 6 + (simplify exponents) (multiply and divide) 18 (add) e) Sample: Begin inside the parentheses. Square the height. Next, divide the weight by the new denominator. f) Then multiply the quotient by ) 47 4) 11 6) 1.4 8) ) Integers 12) Yes; the number formed by the last 14) three digits is divisible by 8. 16) ; ) 20) 22) Sample: Perimeter = (2 40) + (2π 15) = 127.1feet a) 6 = 864 b) (2 ) + 4( ) = 944 c) ; Box A 24) units 26) -4 planes 28) 5 (-2) = 7 feet 30) 120 Lesson Practice 8 a) 184,800 feet per hour b) c) Yes; Sample: 46,300 = 46.3 d) $ ) 1 4) 1 6) ) 10) 63 12) No; The ones digit is not a 0 or a 5. 14) 1.75 km per minute 16) 42 Student A; Sample: Student B incorrectly wrote the unit ratio, multiplying by 10 to cancel the units 18) instead of dividing by 10 a) km/hr 20) b) mph 22) grams per cubic inch Student A; Sample: Student B needed to simplify inside the parentheses 24) first. 26) Profit of 5.5 million Student A; Sample: Student B 28) incorrectly used b as and c as 30) a) 64 sq. in. b) 100 sq. in. c) 36 sq. in. d) 44 sq. in.

5 Lesson Practice 9 a) 62 b) -10 c) d) F 2) 20 4) 1 6) 5.8 8) ) 12 12) ) 16) C (42) a) 80 ft/sec 18) b) 48 ft/sec Student B; Sample: Student A made an error in evaluating the negative 20) number raised to a power. 22) total blocks 24) ; ) ) 1 30) 525 words Lesson Practice 10 a) b) 7.39 c) -1,,, 0.85 d) e) seconds 2) 7 6) 2 8) ) ) Acute 14) 41.8 km 16) A (-2.9) 18) hour or 55 minutes 20) a) Sample: 1000b b) 400 feet 22) Student B; Sample: Student A only multiplied by the unit ratio once instead of twice. 24) a) π( b) [ π( ] = ) $ ) -4.4 points 30) 68 feet 6 inches

6 Investigation 1 1) certain 2) Impossible 3) As likely as not 4) unlikely 5) Students work will vary 6) Students work will vary 7).320 a) 3.2% b) 96 pistons 8) c) $26,640 9) Students work will vary 10) Students work will vary Investigation Practice a) As likely as not b) Likely c) Unlikely d) Likely e), 36%,, 24%,, 40% C; Sample: The letter C has the greatest f) probability of occurring. g).360 h) Students work will vary