Which value of x makes the equation 0.75( x + 20) = 2 + 0.5(x - 2) true?
1 answer:
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All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is
Multiply both sides by <em>r</em> :
Subtract the latter sum from the first, which eliminates all but the first and last terms:
Solve for :
Then as gets arbitrarily large, the term will converge to 0, leaving us with
So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18
Answer:
72 ft²
Step-by-step explanation:
Given :
Parallelogram ABCD with side AD parallel to side BC and side AB is parallel to side DC.
Point E is on side AB. AE is 3 feet. DC is 9 feet.
A dotted segment DE runs from point D to the opposite side AB and is perpendicular to side AB.
DE is 8 feet.
To Find: Area of parallelogram
Solution :
Refer the attached figure .
Since opposite sides of parallelogram is equal .
So DC=AB=9 feet
Area of parallelogram = base * height
= AB*DE
=9*8 = 72 ft²
Thus the area of garden in the shape of parallelogram is 72 ft²
