Question question
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32 and 5n + 2

Step-by-step explanation:

(a)

The pattern of the number of sticks is

7, 12, 17

There is a common difference of 5 between consecutive terms.

Thus to obtain the number of sticks in number 6 , add 5 to previous terms, that is

a₄ = 17 + 5 = 22

a₅ = 22 + 5 = 27

a₆ = 27 + 5 = 32

There are 32 sticks in pattern number 6

(b)

The sequence is arithmetic with n th term

= a₁ + (n - 1)d

Where a₁ is the first term and d the common difference

Here a₁ = 7 and d = 5 , then

= 7 + 5(n - 1) = 7 + 5n - 5 = 5n + 2

number of sticks in pattern number n is 5n + 2

b

step-by-step explanation:

given

- 2 (3x + 12y - 5 - 17x - 16y + 4 )

simplify the parenthesis by collecting like terms

= - 2 (- 14x - 4y - 1) ← distribute the parenthesis by - 2

= 28x + 8y + 2 → b

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x