A triangle has exactly three sides. Prove the conditional by proving the contrapositive. If a polygon has more than three sides, then it is not a triangle. Contrapositive: If _____, then _____. Since ______, the contrapositive is _____, the original statement must be _____.

Answers

Answer 1

Answer:

If a polygon is a triangle, then it has exactly three sides

Since as have been presented above, the contraposition is true, the original statement must be true

Step-by-step explanation:

The contrapositive statement; If a polygon has more than three sides, then it is not a triangle

We have that the definition of a triangle = A polygon with exactly three sides

Therefore;

A polygon with more than three sides is not a triangle and has (n - 1)/2×180 degrees interior angle, where n = The number of sides

Therefore, when n > 3, (n - 2)/2×180 > 180°

The sum of interior angles of a triangle = 180°

Therefore, the contrapositive statement, if a polygon has more than three sides, then it is not a triangle is true

Therefore, we have;

If a polygon is a triangle, then it has exactly three sides

Since as have been presented above, the contraposition is true, the original statement must be true


Related Questions


Six identical circles fit inside the rectangle as shown below. If the rectangle has a width of 15
units and a height of 10 units, what is the radius of each circle?

Answers

Answer:

The radius of each circle is 2.5 units

Step-by-step explanation:

Width of the rectangle = 15 units

Height of the rectangle = 10 units

6 identical circles fit inside the rectangle,

Two circles fit along the height of the rectangle.

Therefore, diameter of both the circles = Height of the rectangle

2d = 10

d = 5

Since, radius of a circle = [tex]\frac{\text{Diameter}}{2}[/tex]

                                       = [tex]\frac{5}{2}[/tex]

                                       = 25. units

Therefore, Option (4) will be the correct option.

Learn more,

https://brainly.com/question/20188113

arrange in ascending order
31/40;78%;0,7

Answers

Ascending order (smallest time biggest)
0.7 = 70%
31/40 = 77.5%
78% = 78%
Hope this is what you were looking for...

Solve the system below by substitution. Give your answer as an ordered pair.
y = 6r + 23
2x + 5y = -13​

Answers

Work:
2x+5(6x+23)=-13
2x+30x+115=-13
32x=-128
x=-4

y=6(-4)+23
y=-24+23
y=-1

The answer is (-4,-1)

Hopefully this helps!

Point a(10,9) and point b(-2,3). What are the coordinates of the point of the way from a to b?

Answers

Answer:.

....

Step-by-step explanation:

Please help my answering this hurryy

Answers

Answer:

where is the question i do not see a question but if you provide me with one i will be more than happy to help you!

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

It is A because A can type 50 words in a minute and B only types 40 words in a minute and 50 words > 40 words

I need help fast please​

Answers

Answer:

K= 18

Step-by-step explanation:

1 and 8 are exact opposites so they equal eachother

so

3k-7=5k+29

subtract 3k to 5k and add 7 to 29

2k=36

then divide 36 by -2

so K = 18

You received $112 in all selling paintings. You sold one painting for $27
and the rest for $ 17 each. Solve the equation below to find .x, the number
of $17 paintings you sold.
17x + 27 = 112

Answers

Answer:

The answer is 5 paintings

Step-by-step explanation:

112 = 27 + 17x  

112 - 27 = 85

85/17 = 5

5 paintings

Hopefully this helps you

pls mark brainlest

Answer:

5

Step-by-step explanation:

17x=112-27; 17x=85; x=85÷17; x=5

what is 5 + 5 I need help on question 5 + 5 + 6 + 7 - 8 - 5 ​

Answers

Answer:

10

Step-by-step explanation:

Answer:

5+5=10

Step-by-step explanation:

use addition to add 5 and 5

The lengths of the two diagonals of a rhombus are 6 cm and 8 cm. Find the length of its perimeter (in
cm)

Answers

Answer:

The perimeter of the rhombus is 20 cm

Step-by-step explanation:

Perimeter of a Rhombus

Given the lengths of the two diagonals of a rhombus, let's call them a and b,  the perimeter of the rhombus is given by:

[tex]P=2\sqrt{a^2+b^2}[/tex]

The values of the diagonals provided by the question are a=6 cm, b=8 cm, thus the perimeter is:

[tex]P=2\sqrt{6^2+8^2}[/tex]

[tex]P=2\sqrt{36+64}[/tex]

[tex]P=2\sqrt{100}=2*10[/tex]

[tex]P=20\ cm[/tex]

The perimeter of the rhombus is 20 cm

Select the conic section that represents the equation. y = 2x^2 + 7​

Answers

Answer:

x intercept: none

y intercepts: (0, 7)

Step-by-step explanation:

Answer:

Parabola

Step-by-step explanation:

What is the slope between the points (-10, 15) and (-13, 5)? What is the equation of the line in point slope form?

Answers

Answer:

y-15=-10/3 (x+10)

Step-by-step explanation:

Find the value of x. 2(3x - 5) = 8

Answers

Answer:

3

Step-by-step explanation:

2(3x - 5) =8

6x - 10 =8

6x =8 +10

6x =18

x=18 :6

x=3

pLeAsE hElP
ASAPPP
:/
*Will give 25 points and Brainliest...*

Answers

Step-by-step explanation:

I agree with Trevon because the number and letters are used in different forms but can probably be solved in the same way

pls help me pls! thanks! will give brainliest

Answers

Answer:

4.5 is the range

Step-by-step explanation:

Ok, so it's asking for range, Range means The Highest number minus the smallest number.

What is the highest number? it's "2.3"

What is the lowest number? it's "-2.2"

so subtract those numbers and you get your answer!

Wait... why is the range 4.5? well, you do 2.3-(-2.2) when there are 2 minuses, you switch it to a + sign. so, 2.3+2.2=4.5!

-3 1/2 - 15/6 helpppppppppp

Answers

answer: will be -6 to that question

An infinite geometric series contains consecutive terms 262.4, 209.92, 167.963 and the sum is 1640. What is the first term?​

Answers

Answer:

328

Step-by-step explanation:

[tex]\frac{a}{1-r}[/tex] is the equation for the sum of an infinite geometric series, where [tex]a[/tex] is the first term of the infinite geometric series, and r is the common ratio between the terms. Here, we can find the common ratio between any consecutive terms. [tex]\frac{209.92}{262.4} = \frac{4}{5}[/tex]

Therefore, [tex]\frac{a}{1-\frac{4}{5}} = 1640[/tex].

This simplifies to [tex]5a = 1640[/tex]

Therefore, [tex]a = 328[/tex]

What is the rise and run of the line D

PLEASE HELPPPP ANSWER this QUESTION WITH PROPER EXPLAINATIONNNN BRainliest will be givennn

Answers

Answer:

rise: 1

run: 2

rise over run 1/2

Step-by-step explanation:

to find slope move up one over 2 to the left

the price of a share of stock was $23 on Monday and $19 on Tuesday. what is the difference in price of those two days. write an integer represent the change in price of the stock

Answers

Answer:

.

Step-by-step explanation:

true or false
A number that has values on the left and the right of the decimal point is called a "decimal mixed number.

Answers

the imposter the answer is true

Which equation represents a line that passes through (5, 1) and has a slope of StartFraction one-half EndFraction?

y – 5 = y minus 5 equals StartFraction one-half EndFraction left-parenthesis x minus 1 right-parenthesis.(x –1)
y – y minus StartFraction one-half EndFraction equals 5 left-parenthesis x minus 1 right-parenthesis. = 5(x –1)
y – 1 = y minus 1 equals StartFraction one-half EndFraction left-parenthesis x minus 5 right-parenthesis.(x –5)
y – 1 = 5y minus 1 equals 5 left-parenthesis x minus StartFraction one-half EndFraction right-parenthesis

Answers

Answer:

y - 1 = 1/2(x -5)

Just took the test, hope this helps!

Answer:

above is correct the letter answer is C on edg2020

Step-by-step explanation:

edg2020

How many hectograms are in 45 centigrams?

Answers

Answer:

0.0045 hectograms are in 45 centigrams

Step-by-step explanation:

Triangle MNO has vertices with coordinates (–8, 2), (–5, 5), and (5, – 2).





Which of these equations represents the line that passes through point N and is perpendicular to the line passing through points O and M?
y = x + 3

y = x - 3

y = -x + 3

y = -x - 3

Answers

Answer:

i think its c

Step-by-step explanation:

The equation of a straight line is represented as: [tex]y = mx + c[/tex]

The equation of the line is: [tex](c)\ y = -x +3[/tex]

The coordinates are given as:

[tex]M = (-5,5)[/tex]

[tex]N = (5,-2)[/tex]

[tex]O = (-8,2)[/tex]

First, we calculate the slope of line MO using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{2-5}{-8--5}[/tex]

[tex]m = \frac{-3}{-3}[/tex]

[tex]m = 1[/tex]

The line that passes through N is perpendicular to MO.

This means that, the slope (m2) of the line is:

[tex]m_2 = -\frac 1m[/tex]

So, we have:

[tex]m_2 = -\frac 1{1}[/tex]

[tex]m_2 = -1[/tex]

The equation of the line is then calculated as:

[tex]y = m_2(x - x_1) + y_1[/tex]

Where:

[tex]m_2 = -1[/tex]

[tex]N = (5,-2)[/tex] --- [tex](x_1,y_1)[/tex]

So, we have:

[tex]y = -1(x -5) - 2[/tex]

[tex]y = -x +5 - 2[/tex]

[tex]y = -x +3[/tex]

Hence, the equation of the line is: [tex](c)\ y = -x +3[/tex]

See attachment for the graph of the lines

Read more about equations of straight lines at:

https://brainly.com/question/21627259

URGENT!!
1. Given the equation 3x – 4y = 24.
a) Find two solutions to the equation. Write your answer as coordinates.





b) Using your answers from part a, what is the slope of the given equation.





c) Convert the given equation into slope-intercept form.

Answers

Answer:

(0, -6) and (8, 0)

[tex]\dfrac{4}{3}[/tex]

[tex]y=\dfrac{3}{4}-6[/tex]

Step-by-step explanation:

(a) [tex]3x-4y=24[/tex]

Let [tex]x=0[/tex]

[tex]0-4y=24\\\Rightarrow y=-6[/tex]

Let [tex]y=0[/tex]

[tex]3x-0=24\\\Rightarrow x=8[/tex]

Two coordinates are (0, -6) and (8, 0)

(b) Slope is given by

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\\Rightarrow m=\dfrac{0-(-6)}{8-0}\\\Rightarrow m=\dfrac{3}{4}[/tex]

The slope of the equation is [tex]\dfrac{4}{3}[/tex]

(c)

[tex]3x-4y=24\\\Rightarrow 4y=3x-24\\\Rightarrow y=\dfrac{3}{4}-6[/tex]

The slope intercept form of the equation is [tex]y=\dfrac{3}{4}-6[/tex]

please help At a bake sale there were 50 items sold total. If 5 of the items sold were cookies and the rest were brownies what is the ratio of brownies sold to cookies sold?

Answers

Answer:

45:5 or 45 to 5

Step-by-step explanation:

If 5 of them were cookies then that leaves the rest of them (which is 45) to be brownies. So it would be brownies to cookies which equals 45:5

Are all perfect cubes also multiples of 3?
Are all multiples of 3 also perfect cubes?

Answers

Answer:

See below

Step-by-step explanation:

I'm not positive that this is right, but I'll try.

No, and no. 6 is not a perfect cube, and that is a multiple of 3.

8 is a perfect cube that is not a multiple of three.

I hope this helps, sorry if I'm wrong.

which of the following shows why 6 1/3 is equivalent to

Answers

Answer:

equivilent to what?

Step-by-step explanation:

fidn the slope of the line.,,,,,free brainliest to who answers first

Answers

Answer:

do I get brainliest?

Step-by-step explanation:

cause you said you'd give brainliest

✧・゚: *✧・゚:*  Answer:  *:・゚✧*:・゚✧

✅ This question is highly inappropriate!

~ ₕₒₚₑ ₜₕᵢₛ ₕₑₗₚₛ! :₎ ♡

~

please help! will give brainliest!! financial lit.!! it's a choose all that apply kind of question btw!!

Answers

Answer:

:) hey kaydence

Step-by-step explanation:

It's B and D.

Hope this helps.

What is a number with exactly 2 factors and what is a number with more than 2 factors

Answers

A number with more than two factors is called a composite number. The number 1 is neither prime nor composite. It has only one factor, itself. A prime number is a counting number greater than 1 whose only factors are 1 and itself.

idk if this helped but lmk if it didn’t

144 students enter a spelling bee, but only \frac{1}{6}
​6

​1
​​ of the group will make into the semi-final round, and only \frac{2}{3}
​3

​2
​​ that group will make into the final round. How many students will enter the final round of the spelling bee?

Answers

Answer: 16 students will enter the final round of the spelling bee.

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