Answer:
Check the explanation
Step-by-step explanation:
(a)Let p be the smallest prime divisor of (n!)^2+1 if p<=n then p|n! Hence p can not divide (n!)^2+1. Hence p>n
(b) (n!)^2=-1 mod p now by format theorem (n!)^(p-1)= 1 mod p ( as p doesn't divide (n!)^2)
Hence (-1)^(p-1)/2= 1 mod p hence [ as p-1/2 is an integer] and hence( p-1)/2 is even number hence p is of the form 4k+1
(C) now let p be the largest prime of the form 4k+1 consider x= (p!)^2+1 . Let q be the smallest prime dividing x . By the previous exercises q> p and q is also of the form 4k+1 hence contradiction. Hence P_1 is infinite
Solution for part A is where the red line and the red line meet, (2,-1)
solution for part B: any point on the blue red line is a solution. (2, -1), (0, 3), (3, -3), (-2, 7)
solution for part C is where the green curve and the blue line meet, (0,3)
Answer:
2/3
Step-by-step explanation:
The rate of change is the same thing as the slope of a line
Answer:
Just substitute each number into the expression:
5(5) - 6(3) + 20(1/4)/4(3)(1/4) = 25 - 18 + 5/3 = 7 + 5/3 = 26/3 or 8 and 2/3.
Step-by-step explanation:
Answer:
The correct option is;
An isosceles trapezoid with legs of length 8
Step-by-step explanation:
The correct option is an isosceles trapezoid with legs of length 8
The given properties of the quadrilateral are;
1) One pair of equal opposite sides
2) One pair of parallel opposite sides
From the given options, the two options which are not parallelograms are the kite and the trapezoid
However given that the option of the kite has a pair of adjacent side of length 8, with the given pair of equal length opposite side of length 8, we have that all the sides of the quadrilateral will be of length 8, and the figure cannot be a kite
An isosceles trapezoid of leg length 8 has one pair of equal length opposite sides of length 8 and one pair of parallel sides of unequal length
Given that the length of the lines that make up the pair of opposite parallel sides in the figure are not specified, the figure can be described by as being an isosceles trapezoid.
