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4vir4ik [10]
3 years ago
7

The length of a rectangle is 8 feet more than it's width. The area of the rectangle is 84 square feet. Find it's length and widt

h.
Mathematics
1 answer:
S_A_V [24]3 years ago
3 0

Length of the rectangle is 14 ft and width is 6 ft

Step-by-step explanation:

  • Step 1: Let the width of the rectangle be x, then length = 8 + x. Find dimensions if area = 84 ft²

⇒ Area of the rectangle = length × width

⇒ 84 = x(8 + x) = 8x + x²

⇒ x² + 8x - 84 = 0

⇒ x² + 14x - 6x - 84 = 0 (Using product sum rule to factorize)

⇒ x(x + 14) - 6(x + 14) = 0

⇒ (x + 14)(x - 6) = 0

⇒ x = -14, +6 (negative value is neglected)

∴ x = 6 and x + 8 = 14

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Calculate the sum of the first 36 terms of the arithmetic sequence defined in which a36=14 and the common difference is d=1/8
user100 [1]

Answer:

425.25


Step-by-step explanation:

Since we are given 36th term as 14 and we know common difference is \frac{1}{8}, it means that from the first term, we add \frac{1}{8} to each and get 14 on the 36th term. To figure out the first term, thus, we have to subtract \frac{1}{8} 35 times from 14. Let's do it to get first term:

14-35(\frac{1}{8})=\frac{77}{8}=9.625

The sum of arithmetic sequence formula is:

S_{n}=\frac{n}{2}[2a+(n-1)d]

Where,

  • S_{n} is the sum of nth term (we want to figure this out for first 36 terms)
  • a is the first term (we figured this out to be 9.625)
  • n is the term number (36 for our case)
  • d is the common difference (given as \frac{1}{8})

Substituting all the values, we get:

S_{36}=\frac{36}{2}[2(9.625)+(36-1)(\frac{1}{8})]\\S_{36}=18[19.25+4.375]\\S_{36}=18[23.625]\\S_{36}=425.25

First answer choice is right.


7 0
2 years ago
Read 2 more answers
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Answer:

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Step-by-step explanation:

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Zina [86]

Answer:

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Step-by-step explanation:

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It is given that point P partitions the directed line segment from A to B in 3:4. It means 3 parts are before P and 4 partes are after P.

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From the below figure we can say that point S is closest to point B.

It is also written as

A

A

Therefore option 4 is correct.

6 0
2 years ago
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AlexFokin [52]

Answer: 10

Step-by-step explanation:

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