PLEASE QUICKLY! A proof is a logical sequence of justified conclusions that lead from a hypothesis to a final conclusion. In your opinion, why are mathematical proofs important?

Suppose that a conclusion within a proof isn’t justified or is inaccurate. In geometry, what might be the consequences of the inaccuracy?

Now think about different kinds of proofs that take place outside the world of geometry, and list a few examples. What might be the consequences of having an unjustified conclusion surface in such proofs? Who might be affected and how?

Step-by-step explanation: Proofs are important because it help with  logically reasoning our problems and help us break the problem down and solve it based on assumed step that guarantee with our conclusion we are trying to prove. . Which is mathematics 101, and it helps us with logical arguments which is crucial for mathematics later down the line. Adding on to that that also means also it gives us different ways to solve problems.

In geometry, the consequences of being inaccurate is contradicting and not understanding the general properties, definitions, postulates, and theorems.

Most people use proofs for example, in court to prove whether someone is innocent or gulity.

They are very important, it's a part of geometry. Earlier scientists gave law and theory.

Everyone knows that law is true or false , hypothesis, postulated , or etc but today everything you want to be prove you can't give proof then your law and/or theory aren't acceptable. You could a fail a math assignment, or not do good on a project at work.

One example of using a proof is in court/law. By proving someone innocent or guilty you decide their fate. If you get it wrong, it's not like failing a math test, it is someone's life, you could put them away for something they didn't do.

Step-by-step explanation:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)