Might have to experiment a bit to choose the right answer.
In A, the first term is 456 and the common difference is 10. Each time we have a new term, the next one is the same except that 10 is added.
Suppose n were 1000. Then we'd have 456 + (1000)(10) = 10456
In B, the first term is 5 and the common ratio is 3. From 5 we get 15 by mult. 5 by 3. Similarly, from 135 we get 405 by mult. 135 by 3. This is a geom. series with first term 5 and common ratio 3. a_n = a_0*(3)^(n-1).
So if n were to reach 1000, the 1000th term would be 5*3^999, which is a very large number, certainly more than the 10456 you'd reach in A, above.
Can you now examine C and D in the same manner, and then choose the greatest final value? Safe to continue using n = 1000.
Answer:
To graph this line, move one of the points to positive three on the horizontal (side to side) line and negative six on the vertical (up and down) line. To get a slope of negative 1/2 you move down one point and right two points, and you continue until you reach the edge of the graph. Then you do the opposite on the way up (up one and left two).
Hope this helps!
We know that
The Euler's formula state that, the number of vertices, minus the number of edges, plus the number of faces, is equal to two
V - E + F = 2
clear F
F=2-V+E
in this problem
V=8
E=14
F=?
so
F=2-8+14
F=8
the answer is8 faces
For part A, if P is the center of that triangle, then PR and PT have the same length; therefore, triangle RPT is isosceles. For part B, by the definition of an incenter...if P is an incenter, then it is the place where all the angle bisectors meet. Therefore, angles SRP and PRT are congruent, as are angles STP and PTR. Since the vertex angle measures 64, then each of the base angles by the isosceles triangle theorem measure 58. Half of 58 makes the base angles within the smaller triangle measure 29. And if both of those measure 29, by the triangle angle-sum theorem, 180-29-29 = 122 And that's the measure of angle RPT. Eek.
(0,-5) and (3,-4) Hope this helps
