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M3309-F10 Week 11.2 F G x + F(x) G(x) F(x) + G(x)

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Page 1: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 11.2

F

G

x

+

F(x)

G(x)

F(x) + G(x)

Page 2: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 11.2

F

G

6

+

24

18

42

6 24 18 42

Page 3: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 11.2

F

G

6

24

18

6 24 18 42 6 432

1.3

1.3

Page 4: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 11.2

F

G

k

+

4k

6 24 18 42 6 432 1.3

k

2k + 6

6k + 6

4k 2k + 6 6k + 6

Page 5: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 11.2

F

G

k 4k

6 24 18 42 6 432 1.3

k

2k + 6

4k – (2k + 6)

4k 2k + 6 6k + 6

–

2k – 6

Page 6: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 11.2

F

G

k 4k

6 24 18 42 6 432 1.3

k

2k + 6

4k(2k + 6)

4k 2k + 6 6k + 6 2k – 6

8k2 + 24k

Page 7: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 11.2

C(n)

R(n)

Page 8: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 11.2

C(n)

R(n)

P(n)

Page 9: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 11.2

C(n)

R(n)

P(n)

Page 10: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 11.2

2. Kenneth is planning to tile a rectangular area for his patio. He plans to use rectangular tiles but he wants the number of tiles on the longer side to be the same as the number of tiles on the shorter side. He plans to cover the center of the patio with an outdoor mat, leaving a border of 6 inches around the mat. The length and width of the mat, in number of inches, are given by functions L(x) = 12x – 12 and W(x) = 6x – 12 respectively, where the input x represents the number of tiles on each side.(The diagram represents a patio with 4 tiles on each side.)

6 in.

6 in.

a. Find L(15). Explain what L(15) represents.

b. Find W(15). Explain what the number 6 and the number 12 in W(x) = 6x – 12 represent.

Page 11: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 12.2

2. Kenneth is planning to tile a rectangular area for his patio. He plans to use rectangular tiles but he wants the number of tiles on the longer side to be the same as the number of tiles on the shorter side. He plans to cover the center of the patio with an outdoor mat, leaving a border of 6 inches around the mat. The length and width of the mat, in number of inches, are given by functions L(x) = 12x – 12 and W(x) = 6x – 12 respectively, where the input x represents the number of tiles on each side.(The diagram represents a patio with 4 tiles on each side.)

6 in.

6 in.

c. If Kenneth uses a total of 100 tiles, what is the area of the mat? Explain the steps you took to find the answer.

Page 12: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 12.2

x L(x) W(x) A(x)

01 0

02 0

L(x)

W(x)

Page 13: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 12.2

x L(x) W(x) A(x)

01 0

02 0

1.5 6 -3 -18

L(x)

W(x)

Page 14: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 12.2

x L(x) W(x) A(x)

01 0

02 0

1.5 6 -3 -18

2.2 14.4 1.2 17.28

0.8 -2.4 -7.2 17.28

L(x)

W(x)

Page 15: M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10 Week 12.2

x L(x) W(x) A(x)

01 0

02 0

1.5 6 -3 -18

2.2 14.4 1.2 17.28

0.8 -2.4 -7.2 17.28

L(x)

W(x)

L(x)W(x)


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