Grade 9 Answers

Grade Nine Answers

1)
ANSWER:
x - Distance of Uphill Y - Distance of Downhill Z - Distance Level Ground Total walking time=6=(x/2+y/6+z/3)+(x/6+y/2+z/3)(This is used for her walking back --- uphill turns to down hill and downhill turns to uphill) 6(x/2+y/6+z/3+y/2+x/6+z/3)=36 36=4(x+y+z) ===> x+y+z=36/4=9 ====> She walks 18km in total.

2)
ANSWER:
Area of half Circle

Area of radius 2-> A=Pi*r² Pi/2 = Pi/2 =Pi (1)² =Pi Area of little circle. A=Pi² =Pi(.5)² =Pi(.23) =Pi/4 Pi/4 * 1/2 = Pi/8 Pi/2 - Pi/8 = area of one 4Pi/8 - Pi/8 = 3Pi/8 3Pi/8 * 2 = 6Pi/8 = 3Pi/4 m²

3)
ANSWER:
Area of large circle A=Pi*r² =Pi(1.5)² =2.25Pi 2.25Pi - area shaded = 2.25Pi - .75(Pi)m² = 3Pi/2m²

4)
ANSWER:
Volume of the water = Volume of 1/2 of tank = 1/2 100cm * 40cm * 60cm = 120,000 1/2 (120,000) = 60,000 60,000 = 100 cm * 60 cm * d 10 cm = d

5)
ANSWER:
->250m ahead Let x = time for Alex to finish Let t = time for Fred to finish Alex Fred Thomas --------------------------------------------------- dist at x 1000m 800m 600m Speed 1000m/x 800m/x 600m/x Find the time it will take Fred to finish 200m/speed(Fred)=t 200m / 800m / x 200 * x / 800 = t x/4 = t How far can Thomas go in that time(Fred was 200 ahead and will go antoher 200) t*speed(Thomas) 600m/x * x/4 = 150m in that time 400 - 150 = 250m Thomas has 200m left to go.

6)
ANSWER:
Angle F = 105 degrees

7)
ANSWER:
14 1+1, 1+2, 1+3, 1+5 1+7, 1+9, 2+3, 2+5, 2+7, 2+9, 3+9, 5+9, 7+9, 9+9.

8)
Answer:

4² + 3² = c² 16 + 9 = c² 25 = c² c = 5

(2 * 4) + (2 * 3) + (4 * 5) = 34

9)
ANSWER: Let the number of girls or boys = x 2(x-8) = x 2x - 16 = x x=16 There are 2x students in the class, therefore there are 32 students.

10)
ANSWER:
Let x = the mark on the eighth exam. 56% = .56 (.56 * 7 + x)/8 = .60 3.92 + x = .60 * 8 3.92 + x = 4.80 x = 4.80-3.92 x = .88 = 88%

11)
ANSWER:
Area of circle = (Pi)r² = (Pi)4cm² = 4Picm² 15 + 15 + 4Pi cm,sup>2 = 42.6 cm

12)
ANSWER:
If 4 or fewer are quarters and the rest dimes and nickels, it wouldn't bring the total to $1.45 with the 4 dimes or nickels.
5 are quarters -> $1.25 Other 3 dimes or nickels make up 20 cents. PROBABILITIES: Losing a quarter = 5/8 chances Losing a dime = 1/8 Losing a nickel = 2/8 = 1/4 Greatest probability -> quarter <- Answer

13)
ANSWER:
t Joe Nick Tom 4 16 16 16 3 8 8 32 2 4 28 16 1 26 14 8 Joe - 26 Nick - 14 Tom - 8 Peanuts

14)
ANSWER:
6 students
REASON: If exactly 5 A's were given in the class, then the students who scored these A's saw their own grade. If six A's had been given then each of the A students could have seen the other 5 A's in the class. 6 is the minimum.

15)
ANSWER:
X = # OF 30 cent candy = # of 35 cent candy .30 x + .35 x = 22.75 x = 35 candies total # of candies = 2x = 70

16)
ANSWER:
27 + 27 + 6 + 6 = 66

17)
ANSWER:
s - Students d - Dollars each contributes d/s 15 don't contribute d/s = 15d/s to be split among s-15 students (15d/s)/(s - 15) = 15d/s * 1/s-15 15d/(s² - 15s) each student must contirbute this amount extra

18)
ANSWER:
Can't be in row b or d Not divisible by 4 -> therefore not in c 2 + 8x = 1002 6 + 8x = 1002 8x = 1000 x = 124.5 <- not a whole # x = 125 Therefore 1002 lies in a.

19)
ANSWER:
A = 4 - The last student. 2A4 A + 1 + 2 = B 5 A + 3 3 A = 1 or A = 4 +329 A + 3 = B ----------- A is not equal to 2, ----- 3 5, 3, 6 or 7 5B3

20)
ANSWER:
X² = (1)² + (1)² X = 2^1/2 2^1/2/2 = BD (2^1/2/2)² + (BD),sup>2 = 1m² (BD)² = 1 - 1/5 (BD) = (1/2)^1/2 m = .707m

21)
ANSWER:
a = 1/2bh b = 8 - 1 = 7 a = 1/2(47) h = 5 - 1 = 4 = 1/2(28) a = 14 Units²

22)
ANSWER:
Bob's speed (100km/h)*(1h/3600sec)*(1000m/km) = 27.7778m/sec In 10s Bob travels 10s*27.7778m/sec=277.778m Therefore Melissa must have travelled 277.778 m + 100m = 377.778m Melissa's speed is 377.778m/10s=37.7778m/s (37.7778m/s)*(1km/1000m)*(3600s/1h)=136.00km/h Melissa got a very big speeding ticket.

23)
ANSWER:
-> 1.906 units² 1/4 of circle r = 2 A = (Pi*r²)(1/6) 1/6*Pi*2² 1/3 Pi Area of triangle = 1/2 bh = 1/2 * 2 * 2 = 2 2 - 1/3 Pi = one part of shaded area = .953 * 2 <- two equal parts = 1.906 units²

24)
ANSWER:
(x + 5 + 9 + 12) /4 = 9 (x + 26) /4 = 9 x + 26 = 36 x = 10

25)
ANSWER:
3x + 7 = 7x + 15 -4x = 8 x = -2 (-2)² + k = 7 (-2) + 15 4 + k = -14 + 15 k = 1 - 4 k = -3

26)
Answer:
42 -> use trial and error 42 = 24/3 + 34

27)
Answer:
2200km/27km = 27 * 24 = 648km for 24 gallons stop 1 after 648 km stop 2 after 1296 km stop 3 after 1944 km 3( 4 tanks of gas becasue he starts full) stops to complete his trip?

28)
Answer:
Even, less than 100, four factors Reverse the digits -> prime number 74 = 11 47 -> prime factors = 1, 2, 37, 74 4 is a square number

29)
Answer:
7 weeks of work -> $30 and the bike 4 weeks of work -> $3 and the bike 3 weeks of work -> $27 $27/3weeks = $x/4weeks x = $36 $36 = $3 + bike bike = $33

30)
Answer:
2m * 3m * 2 * 10^-1m = 1.2m³ 1m³ = 1000kg 1.2m³ = 1000kg + .2(1000kg) 1.2m³ = 1200kg 1200kg + 1 kg = 1201kg

31)
Answer:
4*(2¹⁹⁹⁶) 2²*(2¹⁹⁹⁶) 2^{1996 + 2} 2¹⁹⁹⁸

32)
Answer:
The sum of the two sides = 300 + 200 = 500 The sum of the two sides of a triangle has to be greater than the third side. Therefore, the piece of land was a line, not a triangle and had no area!!

33)
Answer:
40% contain two or more people 60% contain one person 25% of 60% contain a male 15% of total contain a male. 45% of houses contain single females.

34)
Answer:
Let x = the number of eligible voters 542 + 430 + 130 = 1102 .9 * x = 1102 x = 1224 There were 1224 eligible voters.

35)
Answer:
B

36)
Answer:
a + 3 = b - 3 = 3c = d/3 Let k equal the number all of them equal k = a + 3 k = b - 3 k = 3c k = d/3 a = k - 3 b = k + 3 c = k/3 d = 3k k - 3 + k + 3 + k/3 + 3k = 64 5k + k/3 = 64 16k/3 = 64 k = 12 a = 12 - 3 = 9 d = 3(12) = 36 36 - 9 = 27

37)
Answer:
x + 5 2x - 3, x + 2, x + 5, 2x + 1, x - 3

38)
Answer:
28 5(5) + 3 = 28 12 21 13 22 14 23 15 24 11 25

39)
Answer:
Mark: $4.50 J.M.: $3.00 Mark spends 2x J.M spends x 2(4.50 - 2x) = 3.00 - x 9.00 - 4x = 3.00 - x 3x = 6.00 x = 2.00 Jean-Martin spends $2.00 and has $1.00 left. Mark spends $4.00 and has $0.50 left

40)
Answer:
60km/hr * 1.25hr = 75km = distance the motorcycle travelled 50km/1.25hr = 40km/hr The average speed of the truck is 40km/hr

41)
Answer:
19.5 * 26 = 507 7.5 * 10 = 75 18 * 24 = 432 432 + 75 = 507
The sum of the areas of the rectangles on the legs equals the area of the rectangle on the hypoteneuse. Relates to the Pythagorean Theorem.

42)
Answer:
Pr = 30 units PB = 19.84 30² = 15² + x² 30² - 15² = x² 675^1/2 = x 675^1/2 / 2 = BA (675^1/2 / 2)² + 15² = 4² 393.75^1/2 = 4 19.84 = 4

43)
Answer:
1/3 * x = 8 x = 24 2/3 (24) = 16 * .15 = $2.40

44)
ANSWER:
C of Clock = 2Pi (6) = 12Pi (1/2)12Pi = 6Pi (1/12)12Pi = Pi Therefore 6Pi + Pi = 7Pi cm

45)
ANSWER:
3(x-3)/x+7 = 3/2 2(3x-9) = 3(x+7) 6x - 18 = 3x+21 3x = 39 x = 13 10/13

46)
ANSWER:
100 in 5 days. x <- st day x+6 <- 2nd day x+12 <- 3rd day x+18 <- 4th day x+24 <- 5th day x + x+6 + x+12 + x+18 + x+24 = 100 5x + 60 = 100 5x = 40 x = 8 1st day he ate 8

47)
ANSWER:
2² * 2 + 2 = 10 10² * 2 + 2 = 202 202² * 2 + 2 = 81610

48)
ANSWER:
CI VI L

49)
ANSWER:
42 | 35 | 40 ----+----+---- 37 | 39 | 41 ----+----+---- 38 | 43 | 36

50)
ANSWER:
Six Faces -> LENGTH OF SQUARE A = 8^1/2 * 8^1/2 = 8 Therefore 6 * 8 = 48 Triangles Height? (8^1/2)² = (8^1/2/2)² + x² 8 = 2 + x² 6 = x² x = 6^1/2 Area Of One Triangle 1/2 * 6^1/2 * 8^1/2 = (48^1/2)/2 = 4 * (48^1/2) Answer: 48 + 4 * (48^1/2)