Total 816 triangles that can be formed using diagonals from a common vertex of a 21-gon.
What are Diagonals?In mathematics, a diagonal is a line joining two vertices of a polygon or solid whose vertices do not lie on the same edge. Diagonals are generally defined as oblique lines or slanted lines connecting the vertices of a shape. A diagonal is defined as a horizontal shape with sides/edges and corners.
Solution of the given problem:
Firstly, choose 3 vertices of 21-gon which are not adjacent to each other.
Secondly, connect all three vertices to a common vertex.
Now, there are 18 vertices that are not adjacent to common vertex and there are now 18 diagonals that can be drawn to the common vertex up to these vertices.
To form a triangle using these diagonals, we need to choose 3 of these 18 vertices, this can be calculated using the binomial coefficient formula:
18 choose 3 = 18! / (3! * (18 - 3)!) = (18 * 17 * 16) / (3 * 2 * 1) = 816
Thus, total 816 triangles can be formed.
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∠A and ∠B are vertical angles. If m∠A=(7x−18) ∘ and m∠B=(6x−8) ∘ , then find the measure of ∠A.
The measure of angle A is 52 degree.
What is the measure of angle A?Vertical angles are angles that are opposite of each other when two lines crosses, they are congruent.
Given that;
Angle A = ( 7x - 18 )∘Angle B = ( 6x - 8)∘Since vertical angles are congruent,
Angle A = Angle B
Plug in the given values
( 7x - 18 ) = ( 6x - 8)
Solve for x
7x - 18 = 6x - 8
7x - 6x = -8 + 18
x = -8 + 18
x = 10
Hence, angle A will be;
Angle A = 7x - 18
Plug in x = 10
Angle A = 7( 10 ) - 18
Angle A = 70 - 18
Angle A = 52°
Therefore, angle A is 52 degree.
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a park in the shape of a rectangle 2.5 miles long and 1.25 miles wide if you walk diagonally across the park how many miles will you walk
Answer: You will walk 2.795 miles
Step-by-step explanation:
You can solve this using the Pythagorean theorem which is a^2 + b^2 = c^2
Plug in your numbers so you have 2.5^2 + 1.25^2 = c^2
Simplify that down to 6.25 + 1.5625 = c^2
Add 7.8125 = c^2
Find the square root of each of them. 2.795 = c
I don't know how you want me to round the answer so I just did it to the nearest thousandths.
SOMEONE PLS HELPP FAST
picture below
The graph representing the association will be a negative linear association. Then the correct option is C.
What is the association?The form, direction, confidence, and outliers of an association (relationship) between two quantitative variables can be used to describe it. • A positive association exists when one variable increases as the other dependent variable.
There is no boundary and all the dots are widely dispersed if there is no association. Variational individuals who are part that the dots are close together but not in a straight line.
From the graph, the slope of the best line will be negative.
The graph representing the association will be a negative linear association. Then the correct option is C.
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Find three consecutive even integers such that the sum of the three integers is 90
Unknowns: Let x=first even integer
____= second consecutive even integer
____= third consecutive even integer
Equation:
Solve:
Answer: 28, 30, 32
Step-by-step explanation: The first integer is 28, the second is 30, and the third is 32. The difference from the first integer and the last integer should be 4. x is the first integer, so the equation is:
x+x+2+x+4=90
The first integer plus the second integer(x+2) plus the third integer(x+4) equals 90. Now solve.
x+x+2+x+4=90
3x+6=90
-6 -6
3x=84
/3 /3
x=28
So the first integer is 28, second is 30, third is 32.
Hope this helps!
Simplifier chacune des expressions suivantes et identifier la nature du nombre obtenu.
= 2 +
2
3
; =
2
5
+ 7; = (√3 + 1)(√3 − 1) ; = (√5 + 1)²
Answer:its 5
Step-by-step explanation: cuz
If it takes 4 people 6 hours to build a wall how long will it take 3 people to complete the same task
A college student is paying for tuition through private loans. Two lenders have approved the student for a $25,000 loan. Offer 1: 5.99% annual simple interest, with a total account balance of $32,487.50 after a 60-month term Offer 2: 3.75% annual interest compounded monthly for a 66-month term Assuming no payments are made, what is the difference in the account balances at the end of the loan terms? Round your answer to the nearest penny. $1,245.00 $1,770.87 $2,964.36 $3,319.94
Answer:
$1770.87
Step-by-step explanation:
Formula; Simple Interest(I) = P × R × T/100
= $1770.87
Erika has a baking company and needs to purchase 17 2/5 pounds of flour for her cakes. The Baking Goods Store sells two different-sized bags of flour. The table shows the amounts of flour in the bag, the number of bags at the store, and the cost per bag of flour.
The number of small ball bags she will need is 7 small bags, the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given that;
Need of flour for cakes= 17 2/5 pounds
Now,
There are 4 large bags, and each one has 4 pounds.
She buys all of the large bags, she already has;
4x4=16
16 pounds. So, she only needs
17 2/5 -16= 1 2/5
=5/5+2/5
=7/5
1 2/5 pounds more, this fraction is equals to 7/5 pounds.
The small bags only contains 1/5 pounds of flour so,
7/5/1/5
=7*5/1*5
=7
Therefore, by algebra the answer will be 7 bags
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The complete question is;
Erika has a baking company and needs to purchase 17 pounds of flour for her cakes. The Baking Goods Store sells two different-sized bags of flour. The table shows the amounts of flour in the bag, the number of bags at the store, and the cost per bag of flour. Size Pounds 1 Bags for Sale 75 Cost per Bag Small $0.84 5 Large 4 4 $16.80 If Erika buys all of the large bags, how many small bags will she need? A. 7 small bags B. 12 small bags C. 28 small bags D. 71 small bags
Keith's bookshelf has 5 shelves. If he has 262 books, estimate the number books he can put on each shelf by rounding the larger number to the neare hundred.
Answer:
52.40
Step-by-step explanation:
Given that,
Keith's bookshelf has 5 shelves.
He has 262 books.
To find the number of books he can put on each shelf.
[tex]required \\ number = \frac{Total Books}{Total Shelves}\\\\= \frac{262}{5} = 52.40[/tex]
Hence 52.40 is the right answer.
Answer:
you in BBC FDA's in BBC FDA's in just had not had not had not had on under end
Step-by-step explanation:
no exception
PLEASE HELP! And show all steps!
Answer:2y32 is the answer u the graph line and some o f the sqaures to count it
Step-by-step explanation:
A student is walking to school and sees a mirror on the ground.
She stops a short distance from the mirror to practice her Geometry.
She knows her own height and the height of the school. She also knows the distance from the mirror to the school from previous Geometry activity. She would like to calculate the distance she is standing from the mirror.
The height of the school is 30 ft.
The distance from the school to the mirror is 50 ft.
The height of the student is 6.3 ft.
What is the distance d between the student and the mirror?
The distance d between the student and the mirror is given by the similar triangles are d = 10.5 feet
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the triangles be represented as ΔABC and ΔCDE
Now , they are similar triangles
The measure of AB = height of the school = 30 feet
The measure of BC = distance from the school to the mirror = 50 feet
And ,
The measure of DE = height of the student = 6.3 feet
The measure of CD = distance d between the student and the mirror
So , the corresponding sides of similar triangles are in the same ratio
On simplifying the equation , we get
BC / AB = CD / DE
And , 50 / 30 = d / 6.3
Multiply by 6.3 on both sides , we get
d = ( 5/3 ) x 6.3
d = 31.5 / 3
d = 10.5 feet
Hence , the distance d between the student and the mirror is 10.5 feet
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help pls
1. Use the relationship PV = nRT to find the number of moles in an amount of gas when the
temperature is 299 K, the pressure is 3 atmospheres, and the volume is 5 liters
(R = 0.0821).
The number of moles is given by the equation n = 0.611 moles
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
PV = nRT be equation (1)
Divide by RT on both sides of the equation , we get
n = PV / RT
Now , when temperature T = 299 K
The value of pressure P = 3 atm
The value of volume V = 5 Liters
The universal gas constant R = 0.0821
Substituting the values in the equation , we get
n = ( 3 x 5 ) / ( 0.0821 x 299 )
On simplifying the equation , we get
n = 15 / 24.5479
n = 0.611 moles
Therefore , the number of moles is 0.611 moles
Hence , the equation is n = 0.611 moles
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Using the picture below, which trig function can be used to find the length of x?
The length of the base is approximately 8.71 units.
What is triangle ?
Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
Let's call the two legs of the right triangle a and b, and the hypotenuse c. The hypotenuse is the side opposite the right angle, so in this case, we have c = 29. We also know that one of the acute angles is 71 degrees.
Using trigonometry, we can use the tangent function to find the length of the base:
tan(71) = a/b
We can solve for b by multiplying both sides by b:
b tan(71) = a
Now we can substitute c = 29 and solve for b:
b = c / tan(71)
b = 29 / tan(71)
b ≈ 8.71
Hence, The length of the base is approximately 8.71 units.
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Write the following ratio in simplest form: 32 min : 36 min (1 point) a. 8 : 9 b. 8 : 36 c. 32 : 9 d. 128 : 144
The simplest form of the given ratio 32 min : 36 min is equal to
option a. 8 : 9.
Ratio is equal to
32 min : 36 min
Factors of 32 are = 1, 2, 4, 8, 16, 32
Factors of 36 are = 1, 2, 3, 4, 6, 9, 12, 18, 36
Greatest common factor of 32 and 36 is equal to 4
Simplest form of the given ratio is equal to
32 min : 36 min
= ( 8 × 4 ) min : ( 9 × 4 ) min
'4' get cancelled with other we get,
= 8 min : 9 min
Therefore, the simplest form of the given ratio by taking out common factors is equal to option a. 8 : 9 .
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A global denim brand announced in 2010 that it is launching a new collection of jeans which are made with reduced consumption of water during the manufacturing process. While usual manufacturing of a pair of jeans requires approximately 42 litres of water, this collection would reduce the water usage by a minimum of 28%. Do you think this initiative by the company is beneficial for water conservation? How much water can be conserved in litres, on a pair of jeans?
The number of liters of water that can be conserved will be 11.76 liters. The initiative by the company is beneficial for water conservation.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The number of liters of water that can be conserved is given as,
⇒ 28% of 42
⇒ 0.28 x 42
⇒ 11.76 liters
The number of liters of water that can be conserved will be 11.76 liters. The initiative by the company is beneficial for water conservation.
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Find the area of the composite figure:
Please hurry!!
Figure ABCD is a square. If AC+BD=56, what is the length of AX?
Figure ABCD is a square. If AC+BD=56, the length of AX is 28.
How did we get the value?Since ABCD is a square, all sides have the same length, let's call it "x".
We know that the sum of the diagonals of a square is equal to twice the length of a side, so AC + BD = 2x.
Therefore, 56 = 2x, and x = 28.
So the length of AX (or any side of the square) is 28 units
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the sensitivity range for an objective function coefficient is the range of values over which the profit does not change.True or False
Answer:The answer to your question “the sensitivity range for an objective function coefficient is the range of values over which the profit does not change.True or False” Is FALSE.
Write an equation in slope-intercept form for the line that passes through the points (0, 5) and (1, 3)?
Answer:
Step-by-step explanation:
y= -2x + 5
sketch a graph for days 0-9
According to the information in the table, the graph would look like the one in the attached image.
How to graph the information in the table?To graph the information in the table we must carefully observe the information. In this case, the relationship is decreasing because the number of infected is decreasing as time increases. In accordance with the above, the curve that shows this relationship is a decreasing curve.
In this case, we must locate the time on the x axis and the infected on the y axis and mark a point in the areas where the data coincide. Later we must graph a line that joins the points and our graph would be finished.
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what is the probability of three or fewer heads on four flips of a fair coin. enter the answer to four decimal places?
The probability of three or fewer heads on four flips of a fair coin is 0.375. This can be determined by calculating the probability of zero, one, two and three heads, which are 0.0625, 0.25, 0.375 and 0.25 respectively. The total of these probabilities is 0.375.
The probability of zero heads on four flips of a fair coin is 0.0625 (1/16).
The probability of one head on four flips of a fair coin is 0.25 (4/16).
The probability of two heads on four flips of a fair coin is 0.375 (6/16).
The probability of three heads on four flips of a fair coin is 0.25 (4/16).
The total probability of three or fewer heads on four flips of a fair coin is 0.375 (1/4).The probability of three or fewer heads on four flips of a fair coin is 0.375. This can be calculated by determining the probability of zero, one, two and three heads. The probability of zero heads is 0.0625, the probability of one head is 0.25, the probability of two heads is 0.375, and the probability of three heads is 0.25. When these probabilities are added together, the total probability of three or fewer heads on four flips is 0.375. This means that the probability of getting three or fewer heads on four flips of a fair coin is 0.375.
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PLEASE HELP NEED SOON!!!!!!!!!!!! WILL GIVE BRAINLIEST TO BEST ANSWER!
do the following calculations
1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9 2. 11 > -2 Add 3 to both sides, then add 3, then add (-4) 3. -2 = -2 Subtract 6 from both sides, then 8, and then 2 4. -4 < 8 Divide both sides by -4, then by -2 5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
The expressions are evaluated below
How to evaluate the expressionsExpression 1: 4 < 7
Multiplying both sides by 3, 2, 4, and 9 respectively:
3 * 2 * 4 * 9 * (4 < 7)
864 < 1515
Expression 2: 11 > -2
Adding 3 to both sides, then adding 3, then adding (-4) respectively:
3 + 3 - 4 + (11 > -2)
13 > 0
Expression 3: -2 = -2
Subtracting 6 from both sides, then adding 8, then adding 2 respectively:
-2 + 6 + 8 + 2 = -2 + 6 + 8 + 2
14 = 14
Expression 4: -4 < 8
Dividing both sides by -4, then by -2 respectively:
-4/(-4 * -2) < 8/(-4 * -2)
-1/2 < 1
The operations performed on the inequalities in each question did not affect the inequality sig.
The truth of the inequality was also not affected by the operations in all cases.
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how to tell if an integral is convergent or divergent
: CC> Chapter 9: Mean> Section Exercises 9.2 > Exercise 13
13
Complete these two different sets of data so that they each have six values and a mean of 21.
20, 20.5, 20.5, 21.5, 21.5,
20, 21, 21, 21, 21,
Answer:
To complete the first set of data so that it has six values and a mean of 21, you can add the following values: 20, 20.5, 20.5, 21.5, 21.5, 21.
The mean of this set is calculated as follows: (20 + 20.5 + 20.5 + 21.5 + 21.5 + 21) / 6 = 21.
To complete the second set of data so that it has six values and a mean of 21, you can add the following values: 20, 21, 21, 21, 21, 22.
The mean of this set is calculated as follows: (20 + 21 + 21 + 21 + 21 + 22) / 6 = 21.
A student is walking to school and sees a mirror on the ground.
She stops a short distance from the mirror to practice her Geometry.
She knows her own height and the height of the school. She also knows
the distance from the mirror to the school from a previous Geometry activity.
She would like to calculate the distance she is standing from the mirror.
The height of the school is 30 ft.
The distance from the school to the mirror is 50 ft.
The height of the student is 5.1 ft.
What is the distance d between the student and the mirror?
Show all your work
The distance between the student and the mirror is apprοximately 29.41 feet.
What do you mean by Distance?Distance is a numerical measurement of hοw far apart or how far away objects or lοcations are from each other. It is a physical quantity that is usually expressed in units such as meters, kilοmeters, miles, οr feet. Distance is a scalar quantity, meaning it οnly has magnitude and nο direction.
To sοlve the problem, we can use the similar triangles prοperty of geometry. Let's denοte the distance between the student and the mirrοr as d. Then, we can set up the follοwing proportion:
(student height + height of mirrοr) / distance frοm student to mirror = height of schοol / distance from mirrοr to school
Plugging in the given values, we get:
(5.1 + 0) / d = 30 / (50 + d)
Simplifying and sοlving for d, we get:
5.1d + 0 = 150
d = 29.41
Therefοre, the distance between the student and the mirrοr is apprοximately 29.41 feet.
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HELP ASAP!!
Simplify the expression.
the expression negative one fifth j plus three fourths minus the expression five halves j plus seven eighths
The simplified expression is given as follows:
-27j/10 - 1/8.
How to simplify the expression?The expression for this problem is defined as follows:
-j/5 + 3/4 - (5j/2 + 7/8).
The negative sign means that every term in the parenthesis has the signal exchanged, hence:
-j/5 + 3/4 - 5j/2 - 7/8.
Then the expression is simplified combining the like terms, as follows:
With j: -j/5 - 5j/2 = -2j/10 - 25j/10 = -27j/10.Constant: 3/4 - 7/8 = 6/8 - 7/8 = -1/8.Meaning that the expression is of:
-27j/10 - 1/8.
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select the statement which is true about the functions over the interval [1,2]
The true statement is (b) Function 2 has the lowest average rate
How to determine the true statementWe start by calculating the average rates of each function
The interval is given as [1, 2]
For Function 1
We have
f(1) = -3
f(2) = 3
The average rate is then calculated as
Average rate = [f(2) - f(1)]/[2 - 1]
Average rate = (3 + 3)/1
Average rate = 6
For Function 2
We have
f(1) = (1/4)^1 + 4 = 4.25
f(2) = (1/4)^2 + 4 = 4.0625
The average rate is then calculated as
Average rate = [f(2) - f(1)]/[2 - 1]
Average rate = (4.0625 - 4.25)/1
Average rate =-0.1875
For Function 2
We have
f(1) = -2
f(2) = 0
The average rate is then calculated as
Average rate = [f(2) - f(1)]/[2 - 1]
Average rate = (0 + 2)/1
Average rate = 2
The lowest average rate is -0.1875 for function 2
Hence, function 2 has the least rate
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A 2020 study showed that the presence of male pattern baldness and a severe reaction to COVID-19 had a strong association, so some suggested that having male pattern baldness might somehow cause a person to have a severe reaction to COVID-19 (since they had been bald before catching COVID-19, so that the disease could not have caused their baldness). Which option below was most likely a lurking variable?
Age
Diet
Height
Weight
If a 2020 study showed that the presence of male pattern baldness and a severe reaction to COVID-19 had a strong association: A. Age is the most likely lurking variable in this scenario.
What is a lurking variable?In this case, the relationship between male pattern baldness and severe COVID-19 reactions may be influenced by age, as older individuals are more likely to experience both male pattern baldness and severe COVID-19 symptoms.
Age could also affect other factors such as overall health and immune system function, which may contribute to the severity of COVID-19 symptoms.
Diet, height, and weight may also be related to overall health and immune system function, but they are less likely to be related specifically to male pattern baldness
Therefore, age is the most likely lurking variable in this scenario.
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How do I find the value of two numbers if their sum is 12 and their difference is 4?
Answer:
The value of two numbers if their sum is 12 and their difference is 4 are 8 and 4.
Step-by-step explanation:
I hope this helped
By rounding to one significant figure estimate the answer to 59 divided by 25
Answer:2
Step-by-step explanation:
59 to 1 sig. fig= 60
25 to 1 sig fig = 30
Therefore, 60/30 =2
Hope this helps :)
Answer:
2
Step-by-step explanation:
divide the numbers. then find the left furthest critical number.
count to the rifht by desired sig fig. use decimal to mark a place of significant zeros.