Let S be a set of ordered pairs of integers defined recursively by (a) Base step: (0,0) is element of S (b) Recursive step: If (a, b) is element of S, then (a 4, b 3) is element of S and (a 2, b 5) element of S. Use structural induction to show that a b is divisbile by 7 for any (a, b) is element of S

don't report but were is the digram

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

mrbilldoesmath!

answer: a parabola

steps:

(x-1)(x+4)   = x(x+4) - 1(x+4) = (x^2 + 4x) - (x+4)

                = x^2 +4x -x -4   = x^2 +3x -4

which is a parabola

mrb