A line segment can be drawn from each vertex of a polygon to every other vertex, forming the sides and
diagonals of the polygon. A square, for example, has 4 sides and 2 diagonals. Using combinations, write
an expression that would give you the total number of sides and diagonals for a polygon with
sides.
Answers
Answer:
n(n - 3)/2
Step-by-step explanation:
We are told that;
A square has 4 sides and 2 diagonals.
Now, a pentagon will have 5 sides and 5 diagonals
A hexagonal when drawn will have 6 sides and 9 diagonals
Thus, we see that;
When n = 4, d = 2
When n = 5, d = 5
When n = 6, d = 9
Using combination, we will find number of pairs of 2 vertices that can possibly be formed from n-vertices. Thereafter we will subtract n from that since it's neighboring vertices can't combine with the current one.
Thus, we have;
C(n, 2) - n
This gives s;
(n(n-1)/2) - n
Simplifying this gives;
(n(n - 1) - 2n)/2
>> (n² - n - 2n)/2
>> (n² - 3n)/2
>> n(n - 3)/2
Related Questions
Can someone pleaseeee help and if you’re correct i’ll give brainliest
Answers
Answer:
35
Step-by-step explanation:
Rows: 7+7+7+7+7=35
Columns: 5+5+5+5+5+5+5=35
Please help me this could help my grade in math!!! I will mark!
Answers
Answer:
I believe it is three
Step-by-step explanation:
Good luck!
Answer:
It is 3! I am 100% sure!
Step-by-step explanation:
Marking brainliest , help pls
Answers
Answer:
the answer is c) 5,2 hope this helped
Answer:
(5,2)
Step-by-step explanation:
its the only one in the purple
find the image of B(4,7) reflected in the y-axis
Answers
find the next three terms of the arithmetic sequence 39 50 61 72
Answers
Answer:
83, 94, 105Step-by-step explanation:
d = 50 - 39 = 11
Therefore:
the 5th: 72 + 11 = 83
the 6th: 83 + 11 = 94
the 7th: 94 + 11 = 105
Which of the following is not a factor of the polynomial p(x) = x³ - 23x² + 142x - 120?
Options :
A(x - 1)
B(x - 10)
C(x - 5)
D(x - 12)
no spam answers and explain how you got the solution.
Answers
Answer:
The correct answer is C- (X-5)Solution
Given -
polynomial p(x) = x³ - 23x² + 142x - 120
Now see the coefficients
coefficient of x³ is 1 x² is -23 x is 142 and then -120
when you'll add this coefficients
i.e.
1-23+142-120=0
When sum of the coefficient turn out 0 then x = 1
using x=1, x-1 = 0
devide the given polynomial p(x) = x³ - 23x² + 142x - 120 by x-1 you'll get rest two factors hence
Answer is option C
algebra 1 chapter 10
Answers
Answer:
wheres the question ?
Step-by-step explanation:
Please help I’ll make you the brainiest
Answers
Answer:
B is the right answer
Step-by-step explanation:
1(z^8-20)
=1/z^12
Answer:
1/z¹² (3rd answer choice)
Step-by-step explanation:
z0(z2z−5)4
=
z8/z20
=
1/z¹²
A family wants to remodel a house and spend at most $135,000 total for the entire project. a)If the builder wants to make a 15% profit on the value of the project, what is the largest amount the family can spend on hard costs (materials, labor, engineering, designing, permits) to be able to pay the builder his profit while staying under the $135,000 budget? b)What is the builder's profit? (Hint: You cannot simply take 15% of $135,000 because the $135,000 includes the builder's profit. Just like in our commission problems, you don't make commission on commission. The percentage is applied to the value of goods and services provided.)
Answers
Michael boards an elevator at the 23rd floor. She travels up 14 floors, and then down 7 floors.
What floor did she finally end up on?
Answers
my grades not looking to well if you guys can help me with some problems i will give points and brainliest i need this problem and a few more done
Answers
Answer:
8 unitsStep-by-step explanation:
Parallel lines cut the transversals into proportional segments:
ST / UT = SR / QRST / 16 = 18/ 36ST / 16 = 1/2ST = 16/2ST = 8ST be x
Apply Thales theorem
x/16=18/36=1/2x=16/2ST=8unitwPlease help !! 25 points
(No links or ill report you, just reply the answer) thanks
Use the general form of the equation for a circle to help write equations for the circles described below:
a) Center (2, -1) and radius 4
b) center (-2, 2) and radius 3
Answers
Step-by-step explanation:
a. (x-2)^2 + (y+1)^2 = 16
b. (x + 2)^2 + (y-2)^2 = 9
Marking brainliest
Can you give me an example on why it’s not foolish to fear ?
Answers
Answer:
It is not foolish to fear—it is a matter of survival. The physical responses we have to objects or situations that we fear are often grouped together and characterized as a “fight or flight” instinct. Something alarms you, and instantly your brain causes a number of chemicals to be released into your bloodstream.
Answer:
Fear is already a part of human nature. In fact, fear is used as a defense mechanism of our ancestors long time ago. They used to live on caves, jungles, and not so sturdy shelters that would make them vulnerable enough to different predators. Thus having the feeling of fear saves them by backing down and to retreat unto safer places. Therefore I can say that it's not foolish to fear since it's already a part of us human beings. Even the bravest persons in the world have their own fears too. We can't just separate it from ourselves and let's just embrace it and try to do something to lessen it.
(this is just my opinion)
Write the equation of the line in fully simplified slope-intercept form.
Answers
Answer:
y = -6x - 8
Step-by-step explanation:
Two points on this line are (-3, 10) and (0, -8). Moving from the first to the second, we see that x increases by 3 and y decreases by 18. Thus, the rise and run are -18 and 3 respectively, so that the slope of this line is m = -6.
Adapt the slope-intercept form y = mx + b to this particular situation. Recognize that the given (0, -8) is the y-intercept and that the slope, m, is -6.
The equation of this line is thus
y = -6x - 8
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answers
Answer:
first step is to add the both angles that are given =78+46
=124
second step is to minus 124 from 180 =180-124
=56 . I used 180 because that is the sum of all the angles in a triangle . so x =56
The function f(x) has a vertical asymptote at x= [blank].
Answers
Answer:
The vertical assymptote is at x = 0
Step-by-step explanation:
Vertical assymptote are simply defined as lines that correspond to the points where the denominator of a rational function is zero.
From the graph, we can see that the curve remains on the y - axis at x = 0
Thus, the vertical assymptote is x = 0
Cindy is buying a new car and wants to learn how the value of her car will change over time. Insurance actuaries predict the future value of cars using depreciation functions. One such function is applied to the car whose declining value is shown at the right. Write an exponential function for it.
Answers
Answer:
[tex]C=10000(0.852)^t[/tex]
Step-by-step explanation:
Let the exponential function be,
[tex]C=a(b)^t[/tex]
Here, C = cost of the car
t = Duration or period in years
From the given table,
Two points representing cost of the car and time are (10000, 0) and (8520, 1),
For (10000, 0),
[tex]10000=a(b)^0[/tex]
a = 10000
For (8520, 1)
8520 = [tex]10000(b)^1[/tex]
[tex]b=\frac{8520}{10000}[/tex]
b = 0.8520
Therefore, exponential equation will be,
[tex]C=10000(0.852)^t[/tex]
The graph of y = ½ x2 − x − 4 is shown below. What are the zeros of the quadratic?
Answers
Answer:
x = - 2, x = 4
Step-by-step explanation:
The zeros are the values of x on the x- axis where the graph crosses
The graph crosses the x- axis at (- 2, 0 ) and (4, 0 )
Then the zeros are x = - 2 and x = 4
multiply:5a(2apower2-3)
Answers
Answer:
5a(2a²-3)10a³-15aHOPE IT HELPS.
STAY SAFE HEALTHY AND HAPPY.Diego is selling raffle tickets for $1.75 per ticket.
a. Complete the table to show how much money he would earn if he sold each number of tickets.
b. How many tickets would Diego need to sell to earn $140? Explain your reasoning.
need ASAP
Answers
Answer:
The answer is 80
Step-by-step explanation:
Four more than six multiplied by a number is seven
Answers
Answer:
4+6n=7
n=1/2
Step-by-step explanation:
put the numbers in and n= a number
name this slope please
Answers
Answer:
-5/4
Step-by-step explanation:
Part B:
Louis wants to buy skis that have a regular price of $328. They have been marked down 25% off the regular price. Louis calculates the new total price including tax.
How much money will Louis save on the total cost because of the markdown?
Answers
Answer:
Part ACalculate sale price and add sales tax:
20% off $339 add tax ⇒ $339*0.8*1.085 = $294.25 ≤ $30015% off $310 add tax ⇒ $310*0.85*1.085 = $285.90 ≤ $30025% off $365 add tax ⇒ $365*0.75*1.085 = $297.02 ≤ $30020% off $300 add tax ⇒ $300*0.8*1.085 = $260.40 ≤ $300Each price is acceptable as less than $300
Part BMarkdown with tax added:
25% off $328 add tax ⇒ $328*0.75*1.085 = $266.91Without discount, the price with the tax added:
$328*1.085 = $355.88The difference is the amount Luis has saved:
$355.88 - $266.91 = $88.97Can u please help me ??
Answers
Answer:
Please post a more clear pictah.
Step-by-step explanation:
-6<3x+12` and 3x+12<21
Answers
Answer:
x>−6 and x<3 which is (-6,3)
Step-by-step explanation:
Find each unit rate. Round to the nearest hundredth if necessary/
$312 for 12 tickets (show work)
Answers
after this, we get 26. we know that unit rate is price PER 1 ticket.
Therefore, we get:
$26/ticket
I need helppp.....?????
Answers
Answer:
G is the answer
Step-by-step explanation:
EASY- Han has to build the figure below, which will serve as a counterweight, for his robotics project. Find the VOLUME of the finished object assuming it is empty inside.
Answers
Given:
A combined figure of a triangular prism and a cuboid.
To find:
The volume of the finished object assuming it is empty inside.
Solution:
From the given figure it is clear that the dimensions of the cuboid are 6 cm, 8 cm and 5 cm.
So, the volume of the cuboid is:
[tex]V_1=length\times width\times height[/tex]
[tex]V_1=6\times 8\times 5[/tex]
[tex]V_1=240[/tex]
The volume of the cuboid is 240 cubic cm.
The area of a triangle is:
[tex]Area=\dfrac{1}{2}\times base\times height[/tex]
Thus, the base area of the triangular prism whose base is 8 cm and height 4 cm, is:
[tex]B=\dfrac{1}{2}\times 8\times 4[/tex]
[tex]B=16[/tex]
The volume of a triangular prism is:
[tex]V_2=Bh[/tex]
Where, B is the base area and h is the height of the prism.
The base area of the triangular prism is 16 square cm and the height is 5 cm. So, the volume of a triangular prism is:
[tex]V_2=16(5)[/tex]
[tex]V_2=80[/tex]
Now, the volume of the given figure is:
[tex]V=V_1+V_2[/tex]
[tex]V=240+80[/tex]
[tex]V=320[/tex]
Hence, the volume of the finished object is 320 cubic cm.
Anybody know 8×1/2 (FRACTIONS AGAIN) (Maybe giving brainliest.)
Answers
Answer: 16
Step-by-step explanation:
8/2 •1/2 = 1/16 = 16
Write the product using exponents. (1/3.(1/3)(1/3) Using exponents, the product is
Answers
Answer:
The answer is 1/3 to the power of 3
Step-by-step explanation: