SHORT ANSWER: 84cm
Let width = w
Let length = w + 5
The area of a rectangle is found by multiplying its width by length and the problem states that the area is 84 cm2.
(Width)(Length) = 84
(w)(w + 5) = 84
w2 + 5w = 84
w2 + 5w - 84 = 0
(w + 12)(w -7) = 0
w + 12 = 0
w = -12
The width of a rectangle can't be NEGATIVE!!! Forget about that!
w - 7 = 0
w = 7
Now go back to naming the variables and replace the w with 7.
Length = w + 5 = 7 + 5 = 12
Width is 7 cm. Length is 12 cm.
Check it. Is 7 x 12 = 84? Yes.
The recursive formula for this sequence is
= -7;
=
+ 10
Step-by-step explanation:
The recursive formula of the arithmetic sequence is:
= first term;
=
+ d
is the first term in the sequence
is the nth term in the sequence
the term before the nth term - n is the term number
- d is the common difference
∵ The sequence is -7 , 3 , 13 , 23 , 33 , 43 , ........
∵ 3 - (-7) = 3 + 7 = 10
∵ 13 - 3 = 10
∵ 23 - 13 = 10
- There is a constant difference 10 between the consecutive terms
∴ The sequence is an arithmetic sequence
∵ The first term is -7
∴
= 7
∵ The common difference is 10
∴ d = 10
- Substitute in the formula above
by -7 and d by 10
∴
= -7;
=
+ 10
To check the formula find the second term
∵ n = 2
∴
= -7;
=
+ 10
∴
=
+ 10
∵
= -7
∴
= -7 + 10 = 3 which is right
The recursive formula for this sequence is
= -7;
=
+ 10
Learn more:
You can learn more about the sequences in brainly.com/question/7221312
#LearnwithBrainly
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