<p>1) tx+12y=-3</p>
<p>The equation above is the equation of a line in the xy-plane, and t is a constant. If the slope of the line is -10, what is the value of t?</p>
<p>2) n(t)=500(0.81)^t</p>
<p>The function above can be used to model the population of a certain endangered species living t DECADES after the year 1900, which of the following is true about the population of the species from 1900 to 1920.</p>
<p>A) increased by about 1000
B) increased by about 320
C) decreased by about 180
d) decreased by about 320
E) decreased by about 1000</p>
<p>3) In the figure above, a shaded polygon which had equal sides and equal angles is partially covered with a sheet of blank paper. If x+y=80, how many sides does the polygon have?</p>
<ol>
<li><p>12y = -tx - 3
y = -tx/12 + b (b arbitrary)
-t/12 = -10
t = 120</p></li>
<li><p>N(t) = 500(0.8)^t <– given
unknown –> N(0) - N(20) = ?
N(0) = 500(0.8)^0 = 500
N(2) = 500(0.8)^(2) = 320
Thus N(0) - N(2) = 500 - 320 = 180</p></li>
<li><p>You actually need to provide a figure for this question. But since I remember this question from a QAS…</p></li>
</ol>
<p>Let a stand for the measure of an interior angle of the polygon. In a quadrilateral the sum of all interior angles = 360. Therefore</p>
<p>x + y + 2a = 360
80 + 2a = 360
2a = 280
a = 140</p>
<p>Triangle’s sum of interior angles = 180//Each 60
Quadrilateral = 360//Each 90
Pentagon = 540//Each 108
Hexagon = 720//Each 120
Heptagon = 900//Each (not an integer)
Octagon = 1080//Each 135
Nonagon = 1260//Each 140</p>
<p>Therefore polygon is an equiangular nonagon, which has 9 sides</p>
<p>Thank you very much! But first explanation is a bit confusing. Where 3 is going? And why do you need to add b?
And what is decade? 1 year?</p>
<p>No problem! I heard that you are going to aim a high score with a current 750, and I am sure you will make at LEAST 750 if you keep up the good work!</p>
<p>
Yes, but my math power seems nothing in the landscape of yours…</p>
<p>I stated that b is arbitrary but will repeat my point of purpose: I just ignored 3 and put b because b is an unimportant constant. Although it would be more formal to solve the problem in this way:</p>
<p>12y = -tx - 3
12y/12 = -tx/12 - 3/12 …</p>
<p>we only need to compare the slope.
See below:
y = -tx/12 - 1/4</p>
<p>compare this with</p>
<p>y = mx + b where m is the slope and b is the y-intercept.
m = -t/12 = -10
t = 120</p>
<p>Note that the constant -1/4 is not used in the process of our problem-solving.</p>
<p>A decade is 10 years, by the way.</p>
<p>Thanks! I understand it now!</p>