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Zarrin [17]
2 years ago
8

How many counterexamples do you need to prove a conjecture to be false

Mathematics
1 answer:
Hoochie [10]2 years ago
3 0

Answer:

one , i guess....

because the conjecture is only true if it satisfies all the cases.

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Plzz anyone solve all answers plzzzzzzzz​
algol13

You posted a lot of problems here. In the future please only post one problem at a time. Thank you.

I'll do the first two problems to get you started. Hopefully it will help you finish off the rest of the questions.

==========================================

Problem 1

{18, a, b, -3} is an arithmetic sequence or arithmetic progression (AP).

This means we have some number d added on to each term to get the next term.

first term = 18

second term = first term + d = 18+d = a

third term = second term + d = (18+d)+d = 18+2d = b

fourth term = third term + d = (18+2d)+d = 18+3d = -3

----

Let's solve that last equation for d

18+3d = -3

18+3d-18 = -3-18

3d = -21

3d/3 = -21/3

d = -7

----

The value d = -7 tells us to add -7 to each term to get the next term. In other words, we subtract 7 from each term to get the next term

first term = 18

second term = first term + d = 18+d = 18+(-7) = 18-7 = 11

third term = second term + d = 11+d = 11+(-7) = 11-7 = 4

fourth term = third term + d = 4+d = 4+(-7) = 4-7 = -3

----

We see that a = 11 and b = 4 are the second and third terms respectively.

Therefore, a+b = 11+4 = 15

-------------

<h3>Answer: 15</h3>

==========================================

Problem 2

A multiple of 4 is in the form 4*n for some integer n, ie n is a whole number.

We want to know which values of 4*n are between 10 and 250.

----

Divide both 10 and 250 by 4 to get the following

10/4 = 2.5

250/4 = 62.5

If n = 2, then 4*n = 4*2 = 8 is not between 10 and 250; however n = 3 will make 4*n = 4*3 = 12 to be between 10 and 250. We see that n = 3 is the smallest possible allowed value.

If n = 62, then 4*n = 4*62 = 248 is between 10 and 250; while n = 63 will make 4*n too big because 4*63 = 252. The largest n can get is n = 62

----

The question posed in question 2 is equivalent to asking the following: "How many values are in the set {3, 4, 5, ..., 60, 61, 62}?"

You could count all of the values in the set, but that exercise is very tedious busywork. There's a much faster way. First lets consider the set below

{a, a+1, a+2, ..., b-2, b-1, b}

where a,b are integers. Basically this set starts at 'a', counts up until we get to 'b'. The handy formula

c = b-a+1

will provide the exact count of values in the set {a, a+1, a+2, ..., b-2, b-1, b}

----

In this case, a = 3 and b = 62, making

c = b-a+1

c = 62-3+1

c = 60

There are 60 values in the set {3, 4, 5, ..., 60, 61, 62}

There are 60 multiples of four that are between 10 and 250.

-------------

<h3>Answer: 60</h3>
4 0
3 years ago
Distance between (-3, 4/11) and (3, 4/11)
ELEN [110]

Answer:

6

Step-by-step explanation:

3 0
3 years ago
HELP ASAP!!! QUESTION IN PHOTO! MARKING BRAINLIEST
Norma-Jean [14]
What the question on
3 0
2 years ago
Line m is drawn so that it is perpendicular to two distinct planes, Q and R. What must be true about planes Q and R?
UNO [17]
B. are parallel.

<span>Line m is drawn so that it is perpendicular to two distinct planes, Q and R. Therefore, planes Q and R are parallel. 

Since it doesn't state that two planes intersect with each other, it is safe to assume that only line m is their connection. The planes are parallel with each other. </span>
7 0
2 years ago
SOMEONS PLEASE HELP ME I will mark brainliest!!!
tresset_1 [31]

Answer:

x=9

Step-by-step explanation:

because I asked my in-collage brother who told me

<h2>*<u><em>THIS USER HAS BEEN VERIFIED AND ACCEPTED AS AN OFFICIAL BRAINLY© USER, ALLOWING THAT YOU GOT LUCKY FOR HAVING A PRO ANSWER THIS QUESTION*</em></u></h2>
8 0
2 years ago
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