9-7. a: Solutions vary. Possible solution shown at right. b: Answers vary. Assuming there are no hidden cubes, V = 11 units 3.

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1 Lesson a: Solutions vary. Possible solution shown at right. b: Answers vary. Assuming there are no hidden cubes, V = 11 units a: 4 5 b: 196:1 c: 9: Since the perimeter is 100, each side is 10. The central angle is = 6. The right triangle has acute angles 18 and 7. Area = units (6 9π ).86 units a: (4, ) b: ( 6, 4) c: ( 1, 1) 9-1. a: An area model is not possible because there are more than two events. A tree diagram follows part (b). b: From the following tree diagram, P(long pants) = = 1, or, # successes 6 long pants total # possible = 1 students = 1. clothing shoes gender long pants male 0 shorts dress or skirt long pants female shorts dress or skirt 9-1. A c: Using M or F for gender, and L, S, or D for clothing, and T or O for shoes, the union is {MLT, MLO, MST, FLT, FLO, FST, and FDS}. The intersection is {MLT, FLT} Selected Answers 1

2 Lesson a: square mm b: 400% is 4 times as large. Therefore, its area increases by a factor of 4 ; ,778.6 square mm a: See solutions at right. b: 4 units 9-. a: 151 b: Yes; a regular 6-gon has interior angles of 170. c: = 4860 F R T 9-. a: x + 4x + 7x 6 + x +1 + x +10 = 540, x = 1 b: 4x x = 180, x = or 7.9% decrease 9-5. a: units b: ( 1, 6), (x, y) (x, y) c: (8, 5) d: (, ) cm 9-7. D Lesson square units; As a midsegment, DE must be half the length of BC. If the ratio of lengths is 0.5, then the ratio of areas is 0.5 = Base Area = 509. cm ; Height = 5 cm; SA = cm 9-5. Yes, by AAS By the Addition Rule, 0.07 = P(long and lost), resulting in a probability of % that the food took too long and the rider got lost a: 6 or 6 b: No solution because absolute value cannot be negative. c: x = or π (6) (14.5) = 5π in. ; 5π in. 1 1 gallon 1 in. 7.1 gal Selected Answers

3 Lesson If she needs the balloon to double in width, then the volume will increase by a factor of 8. That means the balloon requires 4 breaths to blow it up. Since she has already used breaths, she needs 1 more to fill the balloon a: SA = 180π in. ; V = 4π in. b: 4π 7 = 7,48.65 in Circumference of each circle = 10π; total distance = 0π 6.8 feet a: x 10. b: No solution because the hypotenuse must be the longest side of a right triangle. c: The length of the base of the composite triangle must be 6. The smaller triangle has a base length ; x a: See diagram at right. b: V = 16 cubic units; SA = 5 square units The line should be solid, and the shading should be to the right of the line See the area model below. A tree diagram would have worked as well = % red oak white oak maple 9-5. D granite tile F R T 9 Selected Answers

4 Lesson b: c: 4 and 96; ratio = 4; It is the square of the linear scale factor. d: 6 and 48; ratio = 8 =. It is the cube of the linear scale factor a: Height of the tank = in., so V = = inches b: c: 5 fish 0.06 fish in 5 fish in 1 inch 1 foot 1in or about 0.06 fish per cubic inch. 1 inch 1 foot 1 inch fish 1 foot 1ft a: False (isosceles trapezoid) b: True c: True d: False (parallelogram) (1x + 7) = 0x 4, so x = a: x = b: x = 5, 1 c: x = d: x =, a: 0.85 b: f (t) = 7000(0.85) t c: $11, a: It is possible D b: Not possible. Same-side interior angles should add up to 180 c: Not possible. One pair of alternate interior angles are equal, but the is not for the same pair of lines cut by a transversal; or, the vertical angles are not equal. Selected Answers 4

5 Lesson a: A rhombus b: They are perpendicular and intersect each at their midpoints. Or, the diagonals bisect the angles of the quadrilateral. c: 55.4 units d: 55.4 units a: See diagram at right. b: 000 ft c: 4.8 ft d: 0. butterflies per cubic foot because 65butterflies 000ft x 5 = x + 9 ; x = a: Not congruent since side ratio 1 b: ΔABC ΔDBC (HL ) c: ΔABC ΔMLK (SSS ) 9-7. y = 6x 9-7. See the answers in the Checkpoint Materials section B 0.1 butterflies ft. 15' 0' 10' Selected Answers 5

6 Lesson b: It got longer. c: Although the change is minute, the line segment got a bit longer. d: It is possible, although not using Karen s incremental strategy. One way: Construct a hypotenuse for a right isosceles triangle with leg lengths 1 cm Possible response: Construct a circle of any radius. Then choose a point on the circle and mark off two radius lengths in each direction along the circle circumference. Connect the original point to each of the two points Area of whole circle = 16π m ; Area for dog to roam = (16π ) = π.51 m 9-8. Height = 9 m, so A = π ft (0+14)(9 ) = m (7 ) Equilateral triangle: 60 sides = 10 ; regular heptagon: , so the measure of the interior angle of a regular heptagon has greater measure See graph at right. x-intercept: (4, 0), y-intercept: (0, 6) C y x Selected Answers 6

7 Lesson a: See diagram below right. b: 4 cubic units c: The volume of the new solid must be 1 8 reduced volume must be cubic units. the original, so the mat plan 9-9. ΔABC ΔEDF (given), so B D ( s parts ), so DG BG (if base angles of a triangle are congruent, then the two sides opposite those angles are also congruent) and ΔDBG is isosceles (definition of an isosceles triangle) a: 74. m b: 6. meters c: 6 goats 74. m goats 0.1, or approximately 1 10 m goat per square meter Using equations: n + q = 14 and 0.05n + 0.5q =.90, so n = and q = a: It has 8 sides. b: ft DA CB and m DAB m CBA (given), AB BA (reflexive property), so DAB CBA (SAS ). Then C D ( s parts ) f (x) = 7.68(.5) x B Selected Answers 7

8 Lesson a: 14π 4.98 cm b: BA 19. ft, so V (19.)(7) 15. ft She should construct an arc centered at P with radius k so that it intersects n and m each once (call these intersections R and S). She should then construct two more circles with radius k, centered at R and S. The fourth vertex lies where these two circles intersect = 180,000 y square miles a: See graph at right. b: f (x) = 10(.) x x c: y = 4, 000(0.75) 5, 9967 d: 60 = 5(b) 10, b = 1.09, 9% increase a: b: C Selected Answers 8