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Answers:</h3>
The first ordered pair is ( -4 , -3 )
The second ordered pair is ( 8, 3 )
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Explanation:
The first point is (x,-3) where x is unknown. It pairs up with y = -3 so we can use algebra to find x
x-2y = 2
x-2(-3) = 2 ... replace every y with -3; isolate x
x+6 = 2
x = 2-6
x = -4
The first point is (-4, -3)
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We'll do something similar for the other point. This time we know x but don't know y. Plug x = 8 into the equation and solve for y
x-2y = 2
8-2y = 2
-2y = 2-8
-2y = -6
y = -6/(-2)
y = 3
The second point is (8, 3)
Answer:
100 people
Step-by-step explanation:
<em>Population</em><em> </em><em>Of</em><em> </em><em>People</em><em>=</em><em>1</em><em>1</em><em>5</em><em>Percentage</em><em>ncrease</em><em>=</em><em>1</em><em>5</em><em>%</em>
<em>The</em><em> </em><em>New</em><em> </em><em>Population </em><em>corresponds </em><em>to</em><em> </em><em>1</em><em>1</em><em>5</em><em>%</em>
<em>(</em><em>That</em><em> </em><em>is</em><em> </em><em>1</em><em>0</em><em>0</em><em>+</em><em>1</em><em>5</em><em>)</em>
<em>We</em><em> </em><em>want</em><em> </em><em>to </em><em>find</em><em> </em><em>the</em><em> </em><em>popula</em><em>tion</em><em> </em><em>that</em><em> </em><em>corresponds</em><em> </em><em>to </em><em>100%</em><em> </em><em>that </em><em>is </em><em>the</em><em> </em><em>original</em><em> </em><em>population</em><em>.</em>
<em>Therefore</em><em> </em><em>Original </em><em>Population</em><em>;</em>
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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
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Answer:
y=-3x
Step-by-step explanation:
The meaning of direct proportion is that the ratio remains the same, and the ratio will only remain the same if y= a constant number into x