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140 Answered Questions for the topic Proofs



Proving using induction. Polygons and (n-2)*(180)

Show that if n > 2 points are spread round a circle and are connected in order to form a polygon, then the interior anglesof the polygon add up to (n − 2) × 180◦ Basis: let n=3 3>2 which is... more


M<TUV=90, m<XWV=90, m<1=m<3

It’s about proofs M<TUV=90, m<XWV=90, m<1=m<3


Prove: triangle ABC is congruent to triangle DCB

Given: Line AB is congruent to line CD           Line AB is parallel to line CD

True or False: If false, give a counter example if true write a proof. Discrete Math

For all positive integers m and n, with m<n if m divides (35n) then either m divides 35 or m divides n


Prove this relation:

if 3x5y=325, then x=2 and y=1 

Prove that gcf(p,q) = gcf(p+q,lcm(p,q))?

Prove that gcf(p,q) = gcf(p+q,lcm(p,q))?
Proofs Trigonometry


Prove that Cos(2x) = -Sin(x)

Took a quiz in precal and this question completely stumped me to the point of writing it down to try and figure it out later. I know you would start with the left side but that’s as far as I have... more


What's the proof bu induction of the( summation from i=1 to 2k-1 of (x^i/(x^i+x^k)) )= k-1/2

let x be a positive real number let k be a positive integer prove  by induction that: 2k-1 ∑       xi / (xi +xk)      = k- (1/2) i=1


Geometry proof should

Given:<DBE is congruent to <EBF Prove: <ABE is congruent to <CBE


Well Ordering Principle Question

You are given a series of envelopes, respectively containing 1, 2, 4, , , , , 2m dollars.Definition:Property 1: For any nonnegative integer less than 2m+1 there is a selection of envelopes whose... more


Proving BIjection

Suppose thata + b + c = d;where a, b, c, d are nonnegative integers.Let P be the assertion that d is even. Let W be the assertion that exactly one amonga, b, c are even, and let T be the assertion... more


how do you prove that the derivative of x^n is nx^n-1

how do you prove that the derivative of x^n is nx^n-1


Discrete math: proving by contradiction. . .

Prove by contradiction: If an integer n has the form 3K+1, then it does not have the form 9L+5.


How do I prove this statement? sin^-1(sin Ø) = Ø

I can't figure out how to prove that statement. Any help would be great. 


If both pairs of opposite sides of quadrilateral ABCD are congruent, prove that △ABC is congruent to △CDA

The picture is a quadrilateral with point A on the bottom left corner, point B on the bottom right corner, point D on the top left corner, point C on the top right corner, with a diagonal line from... more


I did half of this question but am stuck on the second part of it.(a) Prove that a divides bc+2 (b) Does a necessarily divide bc-2? Why?

2 Let a and b be integers such that a divides b+2 and a divides c-1.(a) Prove that a divides bc+2Let a, b and c be integers such that a divides b and a divides c. Let x and y be integers. Then... more

Write a plan to prove that the midpoins of the sides of a rhombus determine a rectangle using coordinate geometry.

Full Question: The coordinates for a rhombus are given (2a, 0), (0, 2b), (-2a, 0), (0,-2b). Write a plan to prove that the midpoints of the sides of a rhombus determine a rectangle using... more
Proofs Calculus Proof


Prove (x^5)+(e^x)=0 has at most 1 real root

I know to like assume that (x^5)+(e^x)=0 has two distinct roots and then find the contradiction. But am stuck.  


Given: line WXY, m<WXZ = 135°. Prove: m<ZXY = 45°

Statements line WXY m<WXY = 180° m<WXZ = 135° m<WXY = m<WXZ + m<ZXY 180° = 135° + m<ZXY 45° = m<ZXY m<ZXY = 45°   Reasons  Given Defintion of supplementary... more


Prove using a paragraph proof.

** Will need 3 steps.   If m<1 = 40° and m<2 = 50°, then the angles are complementary. 


Prove using a paragraph proof.

Statements:  9 = 4x - 3(x - 2)  9 = 4x - 3x + 6  9 = x + 6  3 = x  x = 3   Reasons: Given          Proofs : Fill in the reasons (4) for the statements provided


Given: m ⊥ l, n ⊥ l. Prove m || n

Statements: m ⊥ l, n ⊥ l <1 is a right angle <2 is a right angle <1 =~ <2 m || n    Reasons: Given           Proofs : Fill in the reasons (4) for the statements... more


Given: AL = SK ; Prove: AS = LK

Could you prove and explain how you did it/ what properties you used.     A____L_________S____K    <---- Line Segment

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