Gemma makes a conjecture that the sum of an odd integer and itself is always an even integer. Which choice is the best proof of her conjecture?

A) Look at these different examples: 7 + 7 = 14, 13 + 13 = 26, 23 + 23 = 46. So the sum of an odd number and itself must be even
B) Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2. Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even.
C) Let n represent an odd number, and let n + n be an even number. Therefore, n + n = n + n, which shows that the sum of an odd number and itself is even.
D) Every time you add an odd number and itself, the sum is an even number.Every time you add an odd number and itself, the sum is an even number.

Answers

Answer 1

Answer:

Let 2n + 1 be an odd number......  B/2nd option

Step-by-step explanation:

Answer 2

The best choice is

Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2.

Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even.

What is Conjecture?

A hypothesis in mathematics is a conclusion or a proposition made tentatively without supporting evidence. Some conjectures, like the Fermat's Last Theorem or the Riemann hypothesis, have significantly influenced the development of new branches of mathematics.

First, Only three examples are given which is not appropriate at all.

Second, This is the best proof is

Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2. Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even.

Fourth, State the meaning of Title without proof.

Learn more about Conjecture here:

https://brainly.com/question/29153415

#SPJ2


Related Questions

8.
Which of the following is a negative
rational number that is not an integer?
А -pi
B -4.5
C -2
D 5 squared

Answers

The answer is B, 4.5
It is not an integer because it’s a decimal, it’s a rational number, unlike pi, and it’s negative, so it the answer is 4.5

Find the area of polygon ABCDE (shown below)
5
4
m
20

Answers

Answer:

The answer is 24

Step-by-step explanation:

Solve for x
I
(2x +1)° (5x +50°

Answers

Answer:

5 x + 1

Step-by-step explanation:

5 × + 50°

Any non - zero expression raised to the power of 0 equals 1

5 x + 1

Answer:

x = 12

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°

since this is a right triangle

90° + 2x + 1 + 5x + 5 = 180° add like terms

7x + 96 = 180 subtract 96 from both sides

7x = 84 divide both sides by 7

x = 12

HELP PLEASE IS FOR TODAY
20 points

•Segment A'B' is closer to point C than segment AB.

•Segment A"B'" is closer to point C than segment A'B'

•Segment A'B' is farther from point C than segment AB

•Segment A"B'" is farther from point C than segment AB.

•Segment A"B" is farther from point C than segment A'B'

Answers

Answer:

It's A. segment A"B" is closer to segment C than segment A"B".

Step-by-step explanation:

I need help

Indicate the quadrant in which the point belongs.
(-18, -12)

Answers

it will be in quadrant three

Answer:

3rd quadrant is where the point is

Write an equation of the line passing through point P(4,3) that is parallel to the line y = 12(x+4).

Answers

Answer:

y=12x-45

Step-by-step explanation:

First we want to get y=12(x+4) into Slope intercept form which is y=mx+b and we do that by multiplying 12 by x so we get 12x and multiplying 12 by 4 so we get 48.

Now we have:

y=12x+48

where the slope is 12.

Parallel lines have the same slope. so the line that goes through (4,3) will have the same slope.

Now that we have a slope and a point we want to write an equation in point-slope form: y-y1=m(x-x1)

Step 1 for this: y-3=12(x-4)

Step 2: we will distribute and solve for y so our answer is in slope intercept form.  

Step 3: we now have the equation y-3=12x-48 after distributing now we add 3 to -3 so it cancels out and we add 3 to -48 and we get -45

Our answer is y=12x-45

Hope this helps!

A cone has a diameter of 6 inches and a height of 8 inches. Find the volume of the both in terms of π and using 3.14 for π.

Answers

Answer

1- 61.95

2- 82.6  

Step-by-step explanation:

V=πr2h divided by 3

1/2 inch is equal to ____ /16 inch
a. 8
b. 2
c. 6
d. 4​

Answers

Answer:

a. 8

Step-by-step explanation:

hope you find it helpful

ps: mark as brainliest

Translate the equation into a verbal sentence 3y+8=32

Answers

Answer:

32 Is Eight More Than 3 Times A Number

Explanation:

32 Is Eight More Than: + 8 = 32

3 Times A Number: 3y

Put Everything Together: 3y + 8 = 32

Step-by-step explanation:

Hey there!

3y+8 = 32 --> The sum of thrice of a number and 8 is 32.

Reason:

When solving this word problem, we let "x" as variable as there is unknown number.After that as in word problem it says "thrice a number" it gives 3x.Then as there is "the sum of the unknown number and 8" it means 3x+8.Lastly the sum would be equal to 3x+8=32.

So, the word problem for this equation is " The sum of thrice of a number and 8 is 32.

Hope it helps...

Find the perimeter of $\triangle CDE$ . Round your answer to the nearest hundredth. A trapezoid A B C D is plotted on a coordinate plane. A D represents the longer base and B C represents the shorter base. Vertex A lies at ordered pair negative 5 comma 4. Vertex B lies at ordered pair 0 comma 3. Vertex C lies at ordered pair 4 comma negative 1. Vertex D lies at ordered pair 4 comma negative 5. A line is drawn from vertex B and intersects line A D at point F plotted at ordered pair negative 2 comma 1. A line is drawn from vertex C and intersects the line A D at point E plotted at ordered pair 2 comma negative 3. The perimeter is about units.

Answers

Answer:

The answer is below

Step-by-step explanation:

We are asked to find the perimeter of triangle CDE. The perimeter of a shape is simply the sum of all its sides, hence:

Perimeter of tiangle CDE = |CD| + |DE| + |CE|

Given that C(4, -1), D(4, -5), E(2, -3).

The distance between two points [tex]X(x_1,y_1)\ and\ Y(x_2,y_2)[/tex] is given as:

[tex]|XY|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Therefore the lengths of the triangle are:

[tex]|CD|=\sqrt{(4-4)^2+(-5-(-1))^2} =4\ units\\\\|DE|=\sqrt{(2-4)^2+(-3-(-5))^2} =2.83\ units\\\\|CE|=\sqrt{(2-4)^2+(-3-(-1))^2} =2.83\ units[/tex]

Perimeter of CDE = 4 + 2.83 + 2.83 = 9.66 units

If y is directly proportional to x. if y = 30 when x = -5, what is the value of y when x = 3?​

Answers

Answer:

the correct answer is -2. I hope this helped

Given h(x)=-2x-5, solve for x when h(x)=9 what is the answer someone help please

Answers

Answer:

-7

Step-by-step explanation:

[tex]h(x)=-2x-5\\h(x)=9\\so,\\-2x-5=9\\-2x=9+5\\-2x=14\\x=-7[/tex]

Simply replace h(x) with 9 because it is given in the question that h(x)=9

what Else would need to be congruent to show

Answers

Answer:

A

Step-by-step explanation:

20 POINTS AND BRAINLIEST
Two functions are shown.
What is the value of f(4) + g(3)?
f(x) = 64(0.5)*
g(x) = 20x + 12
Enter your response here:

Answers

Answer:

g(x) = 20x + 12

Step-by-step explanation:

can i plz have the brainleist

g(x)=20x+12 I’m my opinion it’s answer

45 + 15(n − 1) for n = 6

Answers

Answer:

120

Step-by-step explanation:

45 + 15 (6 -1)

45 + 15 (5)

45 + 75

120

is 42,260 a rational or irriational number

Answers

Answer:

rational

Step-by-step explanation:

it can be written as a ratio like 42260/1

brainliest?? please

Answer:

Rational

Step-by-step explanation:

This number is a whole, even number. It does not fit the criteria to be irrational because it can be written as a simple fraction

You have inherited a large collection of audio compact discs and decide to purchase a HiFi system to play them. At the retailer you find a choice of 4 CD players, 2 amplifiers and 3 sets of speakers. How many different HiFi systems are available to purchase from this retailer

Answers

Answer:

24

Step-by-step explanation:

Since at the retailer you find a choice of 4 CD players, 2 amplifiers and 3 sets of speakers. We have 4 different ways of selecting the CD players, we also have 2 different ways of selecting the amplifiers and 3 different ways of selecting the 3 sets of speakers.

So, the total number of different HiFi systems are available to purchase from this retailer is 4 × 3 × 2 = 24 .

So we have 24 different HiFi systems are available to purchase from this retailer

Davis used a drawing and a scale factor of 4 to design his triangular yard. The area of the yard is 400 ft². He wants to find the area of the scale drawing. A smaller triangle has an area of x. A larger triangle has an area of 400 feet squared. Davis knows that the original area times the square of the scale factor will equal the enlarged area. What is the area of the scale drawing? (Scale drawing)(Scale factor)2 = Enlarged Area (x)(4)2 = 400 16x = 400 x =

Answers

Answer:

25

Step-by-step explanation:

Answer:

it is 25 :)

Step-by-step explanation:

PLEASE HELP!!!! I HAVE TO TURN THIS IN IN 5 MIN!!!
ARE THE IMAGES IN THE CORRECT GROUPS????
(They have to be in groups of 3!)

Answers

Answer:

Orange with pink, Yellow with red, Purple with blue. Yellow should be 1x instead of 3x. Swotch the table under red with green aswell.

help show work
42,44,46,48,50
assig 9

Answers

Answer:  see below

Step-by-step explanation:

42)   11 < 3y + 2 < 20

      -2         -2    -2  

       9  <  3y      < 18

     ÷3   ÷3         ÷3  

      3 <    y      <  6

Graph:   o----------o

             3            6

44)   36 ≥ 1 - 5z >  -21

       -1     -1           -1    

       35 ≥     -5z >  -22

    ÷ -5 ↓  ÷ -5 ↓ ÷ -5

        7  ≤        z <  4.4

Graph:   o------------ ·

            4.4            7

 

46) 6b + 3 < 15    or    4b - 2 > 18

            -3   -3                 +2    +2

      6b       < 12           4b      > 20

    ÷6           ÷6         ÷4         ÷4  

         b      <  2    or     b     >   5

Graph:   ←--------o   o---------→

                        2    5

48)   8d < -64    and    5d > 25

      ÷8     ÷8                ÷5     ÷5

        d < -8      and       d > 5    

 there is no number that is both less than - 8 and greater than 5

                 No Solution

Graph:   (empty)

                       

50)  15x > 30    and    18x < -36

    ÷15     ÷15           ÷18     ÷18  

         x >   2      and       x < -2  

 there is no number that is both less than - 2 and greater than 2

                 No Solution

Graph:   (empty)

9. If one inch represents 14 feet,
what dimensions would you use
to make a scale drawing of a
building 84 feet by 126 feet?

Answers

Answer:

the answer would be 6in. by 9in.

Step-by-step explanation:

you have to divide 84 by 14 and 126 by 14

If mZ3 = 74°, find each measure.

Answers

Answer:

m<1 = 74

m<2 =  74

m<4 = 74

Step-by-step explanation:

Find the perimeter of the rectangle with points A(-1,4), B(3,4), C(-1,-2), D(3,-2).

Answers

hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

of two planes intersect is their intersection a point

Answers

If two planes intersect there’s alway going to be an intersection point where the two cross over

Once the child in the sample problem reaches the bottom of the hill, she continues sliding along the flat, snow-covered ground until she comes to a stop. If her acceleration during this time is -.392m/s^2 how long does it take her to travel from the bottom of the hill to her stopping point

Answers

Sample problem is;

A child slides down a steep, snow covered hill with an acceleration of 2.82 m/s². Her initial speed is 0.0 m/s² and her final speed is 15.5 m/s travelling from top to bottom of the hill.

Answer:

t = 39.54 s

Step-by-step explanation:

We are told that her acceleration is now -0.392 m/s²

Thus; a = -0.392 m/s²

From the sample problem, we have;. Initial velocity = 0 m/s

Final velocity = 15.5 m/s

However, in this question, we want to find the time from the bottom of the hill to her stopping point.

This means her initial velocity will now be; u = 15.5 m/s and final velocity since she will come to rest will be v = 0 m/s

To find the time it takes her to travel from the bottom of the hill to her stopping point, we will use Newton's equation of motion and so, we have;

v = u + at

making t the subject, we have;

t = (v - u)/a

t = (0 - 15.5)/(-0.392)

t = 39.54 s

9x + 3 = 6x - 12 + 3x

Answers

0=−15

Step-by-step explanation:

subtract 3 from both sides

9+3=9−12

9+3−3=9−12−3

simplify

9=9−15

subtract 9x from both sides

9=9−15

Simplify again and combine like terms and you should get  0=−15

calculate the distance travelled by a bus in 2 hrs which moves with a velocity of 22 m/s


Answers

Answer:

158400 meters

Step-by-step explanation:

multiply 3600 by 22 then multiply by 2

Solve for x:
(X+5)^1/2 = (5-2x)^1/4

Answers

Answer:

X = Negative 2 (-2)

At Al's Pizza they have the Expo Pizza, which is a 24-inch cheese pizza that costs $17.50. Each topping for the pizza costs $2.35. You order a pizza and get charged $29.25. Which equation represents the situation described?
A.29.25 = 17.50 +2.35x
B. 29.25 = 17.50x + 2.35
C. 2.35x = 29.25 + 17.50
D.17.50 +2.35 = 29.25x​

Answers

Answer:

Compare and contrast the to main candidates

Step-by-step explanation:

Help

HELP ME PLEASE!!! this is the recipe.

Answers

Answer:

Ok... hmmmmm

So im going to assume that this is an adding fractions question so for a half batch it would be 1 1/4 + 2 2/4 which is 3 3/4 cups and for a double batch it would be 15 cups because 10 + 5 is 15.

The first blank probably is 3 3/4

The second blank probably is 15

<3 I already answered this on the other question but I want points so tysm.

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