The number of quadrilaterals that can be formed with the vertices of a regular pentagon is given by:
5.
How to obtain the number of quadrilaterals?The number of vertices for each polygon is given as follows:
Quadrilateral: 4 vertices.Pentagon: 5 vertices.Hence, to build the quadrilaterals, four vertices are taken from the set of five vertices of the pentagon.
The formula to be used is given as follows:
Permutation formula -> order of the vertices is not relevant.Combination formula -> order of the vertices relevant.The order of the vertices is not relevant, hence the combination formula is used, given as follows:
[tex]C_{n,x} = \frac{n!}{x!(n - x)!}[/tex]
Which gives the number of different combinations of x elements from a set of n elements.
Hence, in the context of this problem, the number of quadrilaterals is obtained as follows:
[tex]C_{5,4} = \frac{5!}{4!1!} = 5[/tex]
Translation
The problem asks for how many quadrilaterals can be formed with the vertices of a regular pentagon.
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Evaluate the algebraic expression for the given values of the variables.
x²-13(x-y), for x = 7 and y=4
When x = 7 and y=4, x² - 13(x - y) =
The answer to the algebraic expession is 10.
What is algebraic expression?
An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression.
Main Body:
We have to find the value of x²-13(x-y) at x=7 and y=4
Now substitute the value of x,y in the expression
=(7)²-13(7-4)
= 49-13(3)
= 10
Hence the answer is 10.
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Evergreen Landscaping bought 7 tons of topsoil, 6 tons of mulch, and 3 tons of pea gravel for $3270. The next week the firm bought 5 tons of topsoil, 5 tons of mulch, and 5 tons of pea gravel for $3015. Pea gravel costs $28 less per ton than topsoil. Find the cost per ton for each item.
The cost of topsoil per ton would be $48.
The cost of pea gravel per ton is $20.
The cost of mulch per ton is $479.
What is the linear equations in two variable?
A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equation.
We have,
7 tons of topsoil, 6 tons of mulch, and 3 tons of pea gravel for $3270.
5 tons of topsoil, 5 tons of mulch, and 5 tons of pea gravel for $3015.
Let,
cost of topsoil per ton = x
cost of pea gravel per ton = x - 28
cost of mulch per ton = m
7x + 6m + 3(x - 28) = 3270
7x + 6m + 3x - 84 = 3270
10x + 6m = 3270 + 84
10x + 6m = 3354 -------------(i)
5x + 5m + 5(x - 28) = 3015
5x + 5m + 5(x - 28) = 3015
10x + 5m = 3015 - 140
10x + 5m = 2875 -----------(II)
Subtracting equation (II) from (I), we get
10x + 6m = 3354
- 10x + 5m = 2875
Solving we get
m = 479
Put m = 479 in equation(I), we get
10x + 6m = 3354
10x + 6(479) = 3354
10x = 480
x = 480/10
x = 48
Hence,
The cost of topsoil per ton would be = x = $48.
The cost of pea gravel per ton = x - 28 = 48 - 28 = $20.
The cost of mulch per ton = m = $479.
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How many reflection symmetry does an eight pointed star have ? How many rotational symmetry does an eight pointed star have ?
An eight pointed star have 8 rotational symmetry and 8 reflection symmetry
What is rotational symmetry?The rotational symmetry of a shape explains why an object's shape remains unchanged when rotated about its own axis.
The eight pointed star while standing on any of the edges will be symmetrical.
What is reflection symmetry?Symmetry with respect to reflections is known as reflection symmetry. Mirror or line symmetry are other names for reflection symmetry.
For a reflection symmetry to be in a figure, the figure must at least have one line dividing it into two parts, one of which is the mirror image of the other,
Each of the peak and crest in the star will make 8 reflection symmetry
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HELP.
This item has two parts: Part A and Part B. Use the function to complete Part A and Part B.
f(x) = (x – 5)(x + 3)(x – 1)2
Which of the following statements CORRECTLY identifies the degree and number of unique zeros of the function?
degree: 3; number of unique zeros: 4
degree: 4; number of unique zeros: 3
degree: 4; number of unique zeros: 4
degree: 3; number of unique zeros: 3
Part B
What is the end behavior of the function?
as x → –∞, f(x) → ∞ and as x → ∞, f(x) → –∞
as x → –∞, f(x) → ∞ and as x → ∞, f(x) → ∞
as x → –∞, f(x) → –∞ and as x → ∞, f(x) → ∞
as x → –∞, f(x) → –∞ and as x → ∞, f(x) → –∞
The degree and number of unique zeros of f(x) = (x – 5)(x + 3)(x – 1)² is:
Degree: 4; number of unique zeros: 3.
The end behavior of the polynomial is:
As x → –∞, f(x) → ∞ and as x → ∞, f(x) → ∞.
How to obtain the degree of the function?The degree of the polynomial function is given by the sum of the multiplicities of the roots.
These roots are given as follows:
x = 5 with a multiplicity of 1.x = -3 with a multiplicity of 1.x = 1 with a multiplicity of 2.Hence the degree is:
1 + 1 + 2 = 4.
The unique zeros are the roots, hence there are three unique zeros, which is the same number of linear factors of the function.
What is the end behavior of the function?The end behavior is the limit of the function as x goes to negative infinity and to positive infinite, hence:
lim x -> -∞ f(x) = lim x -> -∞ x^4 = (-∞)^4 = ∞.lim x -> ∞ f(x) = lim x -> ∞ x^4 = (∞)^4 = ∞.Learn more about the end behavior of a function at brainly.com/question/1365136
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A patient is using a bicycle as part of their physiotherapy routine. The diameter of the bicycle’s wheel is 590 mm. While in session, the wheel is rotating at a speed of 82 rpm (revolutions per minute). If the patient is riding the bicycle for 1 h and 10 minutes, determine the number of kilometres the patient has travelled. Round to the nearest tenth.
The total distance traveled by the patient in 1 hour and 10 minutes is 10.6 kilometers.
What is the distance?The distance is the length from one point to the end.
For our purpose, distance represents the product of speed and time.
Diameter of the bicycle's wheel = 590 mm
Speed (Revolutions) per minute = 82 rpm
Time riding the bicycle = 1 hr and 10 minutes = 70 minutes
1 Kilometer = 1,000,000 Millimeters
Distance per rotation = pi x diameter
= 3.14 x 590
= 1,852.6 mm/minute
Total distance traveled in kilometers = (1,852.6 x 82 x 70) ÷ 1,000,000
= 10,633,924 ÷ 1,000,000
= 10.6 kilometers
Thus, we can conclude that the patient traveled 10.6 kilometers by bicycling for one hour and 10 minutes.
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ax+by=cd
solve for b
Answer:
b=(cd-ax)/y
Step-by-step explanation:
b=(cd-ax)/y
Glass cases how many gumballs are in the gumball machine one student guesses 456 counting it was determined that they were actually 408 gumballs in the machine what is the percent error of the guess
According to the solving the percent error = 11.764%
What does "percent mistake" mean?The percent error is the distinction between the estimated value and the real value in relation to the actual value. In those other words, the relative error is multiplied by 100 to calculate the percent error.
What does a high percent error rate mean?The difference between an approximate number and an exact value is measured in percent error. The bigger the percentage error, the further your estimated value deviates from the known value; conversely, the smaller the percentage error, more closer your approximation to the true value.
According to the given data:Actual value = 408
Expected value = 456
We know that the percent error :
= (expected value - actual value)/actual value.
= (456 - 408)/ 408
= 48/408
= 11.764
= 11.764%
According to the solving the percent error = 11.764%
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Jackson had 5/6 yard of ribbon. He used 2/6 yard to decorate a present.
How many yards does he have left?
Step-by-step explanation:
Jackson had 5/6 yard of ribbon. He used 2/6 yard to decorate a present. How many yards does he have left?
5/6 - 2/6 = 3/6
3/6 reduces to 1/2 yards left
The lifetimes of batteries created by a company are normally distributed with a
mean of 105 hours and a standard deviation of 12 hours. What percentage of these batteries will last between 90.6 and 109.8 hours?
Answer:
84.6
Step-by-step explanation:
Fabian has $700 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $387.10. He buys 3 bicycle reflectors for $4.43 each and a pair of bike gloves for $12.36. He plans to spend some or all of the money he has left to buy new biking outfits for $45.81 each. What is the greatest number of outfits Fabian can buy with the money that's left over?
6.) One clothing Store has a dress for $6.20
and a belt for $3.50. Customers
buy 3 dresses for $15.20. How much
would be saved by buying 3 dresses
Than by buying per piece?
1. Which graph best represents y = 4* - 1? (1 point)
Answer:
a little confused, but it should just be a horizontal line on -4 because of 4 times negative 1 = -4
Step-by-step explanation:
In the first five math quizzes, Patty had an average score of 8. She got a 7 and a 5 on the next two quizzes. After the eighth quiz, her
average stood at 7.5. What was her score on the eighth quiz?
*
Answer:
SHe got a 8 on the 8th quiz
Step-by-step explanation:
The score for eighth quiz is 8.
What is Algebra ?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
The average for 5 quiz marks is 8.
So, total quiz point = 8 x 5
= 40
Now, for next two the score are 7 and 8
The Total quiz point= 40 + 7+ 8= 55
let x be score on the 8th quiz
55+ x /8= 7.5
52 + x = (7.5)(8)
x = 60 - 52
x= 8
Hence, the score for eighth quiz is 8.
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If a = 4, then a³ + a=
I know the answer but can someone explain step by step
Answer:
D) 16
Step-by-step explanation:
A=4
[tex]a^3[/tex]/a=?
[tex](4^3)[/tex]/(4)=?
64/4=16
The total cost of a plane ride, C, is given below as a function of the time flown, m, in minutes.
C = $33.00 + $1.20m
If a customer spends $267.00 on a plane ride, how many minutes does the ride last?
A. 250
B. 195
C. 223
D. 325
The number of minutes is 195 minutes when the customer spends $267.00. The correct option is B.
How to calculate the time?From the information, the total cost of a plane ride, C, is given as a function
C = $33.00 + $1.20m
where n = number of minute
Since the customer spends $267.00 on a plane ride, this will be:
C = = 33.00 + $1.20m
33 + 1.2m = 267
Collect like terms
1.2m = 267 - 33
1.2m = 234
Divide
m = 234 / 1.2
m = 195
Minutes used is 195 minutes
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Karen is waiting for a pot of soup to cook off before serving it. After 4 3/4 min the soup has cooled from 100°C to 78° C. What was the average change in temperature each minute.
Answer:
Karen is waiting for a pot of soup to cool off before serving it. After 4 min the soup has cooled from 100°C to 78°C. What was the average change in temperature each minute?
✓ Answer:It went down 5.5°C a minute.Step-by-step explanation:You have to look for the difference of 100 and 78, which is …
Children at nutrition are either playing or sitting down resting. The ratio of kids playing to resting is 3:1. If there are 8 children resting, then how many are playing?
Answer: 24 kids playing
Step-by-step explanation: Since the ratio of the kids playing and resting is 3:1, and there are 8 kids resting, replace the 1 with 8, and multiply the 3 with 8 to make the equation balanced. 24:8!
His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas
mileage in his new car?
The Xavier is not getting better mileage with his new car .
In the question ,
it is given that
distance travelled by Xavier's new car in 25 gallons = 528 miles
the mileage can be calculated using the formula = (distance travelled)/( gallons of fuel used) .
So , mileage of the new car = 528/25 = 21.12 miles per gallon ,
the milage of Xavier's former car = 20.28 miles per gallon .
From the above data , we can see that the mileage of former car is greater than new car .
Therefore , The Xavier is not getting better mileage with his new car .
The given question is incomplete , the complete question is
Xavier's new car uses 25 gallons for 528 miles , His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas mileage in his new car?
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A dairy farmer wants to mix a 80% protein supplement and a standard 55% protein ration to make 1400 pounds of a high-grade 60% protein ration. How many pounds of each should he use?
If the dairy farmer wants to mix a 80% protein. The amount of pounds of each that he should use is 80% 280 pounds and 55% 1120 pounds.
How to find the number of pounds?Protein I 80% = x pounds
Protein II 55% = 1400 - x pounds
Mixture 60% = 1400
Hence,
80% x + 55% ( 1400 - x ) = 60% × 1400
80 x + 55 ( 1400 - x ) = 84000
80 x + 77000 - 55 x = 84000
Combine like terms
80 x - 55 x = 84000 - -77000
25 x = 7000
Divide both side by 25x
x= 7000/25
x =280 pounds ( Protein I)
Protein II
1400 - x pounds
1400 -280
= 1120 pounds
Therefore the farmer should use 280 pounds and 1120 pounds.
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Find an equation for the perpendicular bisector of the line segment whose endpoints are (4,6) and (8,-6)
The equation of the perpendicular bisector for the line is y = 1/3(x) - 2
How to determine the equation of the perpendicular bisector?
Given: the endpoints of the line (4,6) and (8,-6)
The bisector of the line will divide the line into two i.e. the bisector will be at the point of the line.
The coordinate of the midpoint can be calculated using the formula below:
Xm = (X1 +X2)/2 and Ym = (Y1 +Y2)/2
Where X1 = 4, Y1 =6 and X2= 8, Y2= -6
Xm = (4+8)/ 2 = 12/2 = 6 and Ym = (6+(-6))/2 = 0/2 = 0
Thus, midpoint(6, 0)
slope = y2-y1 / x2-x1
Thus, the slope of the line segment (m₁) = -6-6 / 8-4 = -12/4 = -3
When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ × m₂ = -1
where m₁ and m₂ represent the slope of the lines
Let the slope of the bisector be m₂
-3 × m₂ = -1
m₂ = 1/3
Equation of perpendicular bisector with coordinate (6,0):
y - 0 = 1/3(x-6)
y = 1/3(x-6)
y = 1/3(x) - 2
Therefore, the equation for the perpendicular bisector of the line segment is y = 1/3(x) - 2
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2. Sketch a list or tree diagram to represent
the sample space of flipping a penny, a nickel,
and a dime one time each.
There are total 8 possible outcomes if we flip penny , nickel , dime together. We can show these outcomes by the Tree diagram or by listing each outcome separately.
The one way to create an organized list to represent the sample space
Penny NICKEL DIME
H H H
H H T
H T H
H T T
T H H
T H T
T T H
T T T
The another way to create an organized list to represent the sample space is to make a tree diagram .
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Fill in the blank, rounding the result to exactly three significant digits when necessary
81 m = ___ ft
95 POINTS
2. Millicent's password for a website is a 5-digit number. The digits are the prime factors of 2,205 listed from least to greatest. What is Millicent's password?
33577
D 35577
B 33557
A 33357
Answer: 33577
Step-by-step explanation:
3x3x5x7x7 = 2205
I need help with an orthocenter of a triangle question. Brainly is having a problem uploading my picture so here is the question: Find the coordinates of the orthocenter of the triangle with the given vertices: P(-1,2), Q(5,2), R(2,1). My Textbook has horrible step by step instructions and I really want to understand this process. Thanks!
The orthocenter of the triangle with vertices P(-1,2), Q(5,2), R(2,1) is
(2, 5)How to find orthocenterOrthocenter is calculated by
finding the slope of a side and the slope of the line perpendicular to the side finding the equation of the perpendicular line passing through the third side of the trianglerepeat step 1 and 2 for another sideWith two equations, solve for the two unknowns (x, y)this gives the coordinate of the orthocenterformula for slope is
m = (y₂ - y₁) / (x₂ - x₁)
slope of the perpendicular = -1/m
Using side PR P(-1,2) R(2,1) ,
m = (1 - 2) / (2 - -1)
m = 1 / 3
slope of the perpendicular = -1/m = - 1 / (1/3) = -3
using point-slope formula for equation of line passing through Q (5, 2)
point slope formula
(y - y₁) = m (x - x₁)
(y - 5) = -3 (x - 2)
y - 5 = -3x + 6
y = -3x + 6 + 5
y = 11 - 3x
Using side PQ P(-1, 2), Q(5, 2)
m = (2 - 2) / (5 - -1)
m = 0
slope of horizontal line is zero for horizontal line the perpendicular is a vertical line
using point-slope formula for vertical line passing through R (2, 1)
point slope formula
(y - y₁) = m (x - x₁)
0 = (x - 2)
x = 2
The two equations are
y = 11 - 3x
x = 2
solving both equations with x already known
y = 11 - 3 * 2
y = 11 - 6
y = 5
Therefore the orthocenter is (2, 5)
The triangle is attached
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which is the correct answer ????
Please help me with this thank you :)))
Answer:
Step-by-step explanation:
Which statement is most likely to be true for this distribution?
O A. The mean is less than the median.
• B. The mean is greater than the median.
• C. The mean is the same as the median.
The statement that is most likely correct for the negatively skewed data distribution given is B. The mean is less than the median.
What is a Negatively Skewed Data Distribution?
A negatively skewed data distribution has the tail to the left of the number line, and therefore its median is usually greater than its mean.
The dot plot shows a data distribution that is negatively skewed. Therefore, the statement that is most likely to be true is B. The mean is less than the median.
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Select the expression that is equivalent to (x - 1)².
OA. 2²-2x+1
OB. x² - 2x+2
OC. x²-x+1
OD. x²-x+ 2
SUBMIT
Answer:
hi, I think the answer is x^2-2x+1 I don't see that option there but I'm guessing that was suppose to be option OA.
explanation:
(x-1)^2 is basically
(x-1)×(x-1)
rest of the explanation is in the photo
hope this helps
Suppose that $1900 is invested at an interest rate of 3.25% per year, compounded continuously. After how many years will the initial investment be doubled?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
The time that initial investment be doubles is 20 year.
What is compound interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
Compound interest = principal (1+r/100)^n
compound interest = 3800.
3800 = 1900(1+3.5%)^n
3800/1900 = 1.035^n
taking natural log
ln(2) = n ln(1.035)
n = ln(2)/ln(1.035)
n = 20.15
Hence, time is 20 years.
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what percent of factors of 21! are odd?
Step-by-step explanation:
here's the answer, all of them