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lozanna [386]
3 years ago
14

Kayla is building a custom frame using reclaimed wood. She needs the frame to be 14 1/2 inches wide by 9 1/4 inches long. She ha

s two pieces of wood which are 18 inches long and two pieces which are 12 inches long. How much extra wood will she have?
Mathematics
1 answer:
Alborosie3 years ago
6 0

She will have 6 and 1/4 inches of wood left. 23 3/4 - 30 is 6 1/4.

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two terms of an arithmetic sequence are a6= 40 and a20= -16. write and explicit rule for the nth term
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Answer:

Tn = 64-4n

Step-by-step explanation:

The nth term of an AP is expressed as:

Tn = a+(n-1)d

a is the common difference

n is the number of terms

d is the common difference

Given the 6th term a6 = 40

T6 = a+(6-1)d

T6 = a+5d

40 = a+5d ... (1)

Given the 20th term a20 = -16

T20 = a+(20-1)d

T20 = a+19d

-16 = a+19d... (2)

Solving both equation simultaneously

40 = a+5d

-16 = a+19d

Subtracting both equation

40-(-16) = 5d-19d

56 = -14d

d = 56/-14

d = -4

Substituting d = -4 into equation

a+5d = 40

a+5(-4) = 40

a-20 = 40

a = 20+40

a = 60

Given a = 60, d = -4, to get the nth term of the sequence:

Tn = a+(n-1)d

Tn = 60+(n-1)(-4)

Tn = 60+(-4n+4)

Tn = 60-4n+4

Tn = 64-4n

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