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Zinaida [17]
3 years ago
13

If a rectangle is 2 meters more than its width, and the area of it is 80 square meters, what is the length and width?

Mathematics
1 answer:
bezimeni [28]3 years ago
6 0
Ok I think it means that the length l of the rectangle is 2 m more than is width w...
The area is A=l*w=(w+2)*w=80
so: w^{2} +2w-80=0
Solving this equation (using the quadratic formula) you get 2 solutons. The only acceptable is the positive one, i.e. w=8 m, the length will then be l=w+2=8+2=10m.
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9) tan(α) = opposite leg / adjacent leg = 1500√3 / 1500 = √3

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Use sigma notation to represent the sum of the first seven terms of the following sequence -4,-6,-8.....
lina2011 [118]

Answer:Answer:

\sum\left {{7} \atop {1}} \right -n(3+n)

Step-by-step explanation:

Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;

The sum of an arithmetic series is expressed as S_n = \frac{n}{2}[2a+(n-1)d]

n is the number of terms

a is the first term of the sequence

d is the common difference

Given parameters

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Required

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S_7 = \frac{7}{2}[2(-4)+(7-1)(-2)]\\\\S_7 =  \frac{7}{2}[-8+(6)(-2)]\\\\S_7 =  \frac{7}{2}[-8-12]\\\\\\S_7 = \frac{7}{2} * -20\\\\S_7 = -70

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S_n = \frac{n}{2}[2(-4)+(n-1)(-2)]\\\\S_n = \frac{n}{2}[-8+(-2n+2)]\\\\S_n = \frac{n}{2}[-6-2n]\\\\S_n =  \frac{-6n}{2} -  \frac{2n^2}{2}\\S_n = -3n-n^2\\\\S_n = -n(3+n)

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