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ArbitrLikvidat [17]
3 years ago
14

Write an equation for the nth term of the geometric sequence 3584, 896, 224... Find the sixth term of this sequence

Mathematics
1 answer:
lions [1.4K]3 years ago
4 0

Answer:

Step-by-step explanation:

r = \frac{a_n}{a_{n-1}} = \frac{896}{3584} =  \frac{1}{4}

Using the geometric series formula for the <em>n</em>th term:

S_n = a \cdot \frac{1-r^n}{1-r} => S_{6} = 3584 \cdot \frac{1 - (\frac{1}{4})^{6} }{1 - \frac{1}{4} }  = 4777\frac{1}{2}

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Which number is a common factor of 84 and 144?
schepotkina [342]
Your answer would be 12
6 0
3 years ago
Find mPMA + mCMT. Please help..
juin [17]

PMA = 37

CMT =  101 - 54 =47

Total = 37 + 47 = 84

Answer: A. 84

8 0
2 years ago
A rectangle is twice as long as it is wide and has the same perimeter as a square whose area is 36 square feet larger than that
Korvikt [17]

Answer:

  • rectangle: 12 ft × 24 ft
  • square: 18 ft square

Step-by-step explanation:

You want the dimensions of a rectangle and square such that they have the same perimeter, but the square has an area of 36 more square feet. The rectangle is twice as long as wide.

<h3>Setup</h3>

Let x represent the side length of the square. Then its area is x², and the area of the rectangle is (x² -36).

This area is the product of length and width. The expression factors as ...

  rectangle area = x² -36 = (x +6)(x -6)

<h3>Solution</h3>

If we assume these factors are the dimensions of the rectangle, then the longer dimension is twice the shorter one:

  (x +6) = 2(x -6)

  18 = x . . . . . . . . . add 12-x to both sides

This is the side length of the square. The rectangle dimensions are ...

  x+6 = 18+6 = 24 . . . . feet long

  x -6 = 18 -6 = 12 . . . . feet wide

The rectangle is 12 feet wide and 24 feet long. The square is 18 feet on a side.

__

<em>Additional comment</em>

The perimeter in each case is 4x = 2((x+6) +(x -6)) = 72 ft.

The area of the rectangle is (12 ft)(24 ft) = 288 ft². The area of the square is (18 ft)² = 324 ft², a value that is 36 ft² more than the rectangle area.

<em>Alternate solution</em>

Using x for the width of the rectangle, the length is 2x and its area is x(2x) = 2x². The perimeter is 2(x +2x) = 6x, so the side length of the square is (6x)/4 = 3/2x and its area is (3/2x)² = 9/4x².

The difference is 36 square feet, so we have ...

  9/4x² -2x² = 36 = x²/4   ⇒   x = √(36·4) = 6·2 = 12 . . . . width of rectangle

8 0
1 year ago
Evaluate 6x – y if x = 5 and y = 8.<br> 3<br> 22<br> 43<br> 57
Anestetic [448]

Answer:

the answer is 22

Step-by-step explanation:

you just need to plug in the values of x and y so...

6(5)-8

30-8

=22

4 0
3 years ago
Forty-eight decreased by a number is the same as the difference of four times the number and seven. Find the number
vagabundo [1.1K]
Turn the text into an eqation:

48-x = 4x-7
5x = 55
x = 11
5 0
3 years ago
Read 2 more answers
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