Our initial assumption that for every vertex u in T, the distance between u and v is greater than (n-1)/2 must be false. Thus, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.
To prove that there exists a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can use a proof by contradiction.
Assume that for every vertex u in T, the distance between u and v is greater than (n-1)/2.
Since T is a tree with n vertices, it has n-1 edges. We can select a longest path P in T, which has a length of at least n-1. Let's denote the endpoints of this path as u and w, where u is the starting vertex and w is the ending vertex.
Now, consider the distance between u and v. Since we assumed that the distance between any vertex u and v is greater than (n-1)/2, the distance between u and v must be greater than (n-1)/2.
However, let's consider the distance between w and v. Since the path P is the longest path in the tree, the distance between w and v must be greater than or equal to the length of path P, which is at least n-1.
Now, let's consider the total number of vertices in the tree, which is n. Since n is an odd integer, (n-1)/2 is an integer as well.
If the distance between w and v is greater than or equal to n-1, and (n-1)/2 is an integer, then there must be a contradiction. This is because the distance between w and v is greater than (n-1)/2, violating our assumption.
Therefore, our initial assumption that for every vertex u in T, the distance between u and v is greater than (n-1)/2 must be false. Thus, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.
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Can anyone help please asap, I need the work shown for this too. I don’t understand
Based on the given values, the value of A is given as 5
How to solveTo find the value of A, we need to solve the equation for the expected value, E(X) = 5.75, using the provided probabilities and x values.
The expected value formula is:
E(X) = Σ[x * P(x)]
Plugging in the given values:
5.75 = (4 * 0.15) + (A * 0.55) + (8 * 0.3)
To solve for A, we can first simplify the equation:
5.75 = 0.6 + 0.55A + 2.4
Now, combine constants and subtract from the left side:
2.75 = 0.55A
Finally, divide by 0.55 to find the value of A:
A = 2.75 / 0.55 ≈ 5
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Find the area of the shaded region. Round to the nearest tenth if necessary.
A. 332.1 cm
B. 210 cm
C. 201.3 cm
D. 205.8 cm
The area of the shaded region, obtained by finding the area of the composite figure is the difference between the area of the square and the area of the triangle and semicircle composite figure.
5. The area of the shaded region is about 205.8 cm squared. The correct option is therefore;
D. 205.8 cm squared
What is a composite figure?A composite figure is a figure that is composed two or more regular figures.
The area of the shaded region can be found by considering the unshaded region as a composite figure consisting of a triangle and a semicircle.
The area of the unshaded semicircle = π × 24²/8 = 72·π
The area of the triangular part of the unshaded region = (1/2) × 24 × 12 = 144
Area of the square = 24 × 24 = 576
Therefore, the area of shaded region = 576 - (72·π + 144) ≈ 205.8
The area of the shaded region ≈ 205.8 cm squared
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On the first day of the month, Sandra starts to read a 420-page book. She is determined to read 30
pages each night. The function P (d) = 420-30d specifies the number of pages P remaining
after Sandra does her reading on day d of the month.
Which equation offers a solution giving the day of the month Sandra finishes, and what day of the
month is that?
OP(d)=0; day 21
OP(d)-30; day 21
OP(d) = 420; day 21
OP(d) = 420; day 14
OP(d) = 0; day 14
OP (d)-30; day 14
Answer:
P(d) = 0; 14 days
Step-by-step explanation:
First part of answer: Setting P(d) = 0 would allow us to find the day Sandra finishes since P represents the pages remaining the book will be finished when there are 0 pages left to read.
Second part of answer: We can solve the equation P(d) = 0 = 420 - 30d to see how it would take 14 days to finish the book and have 0 pages left to read:
Step 1: Subtract 420 from both sides:
(0 = 420 - 30d) - 420
-420 = -30d
Step 2: Divide both sides by -3 to solve for d:
(-420 = -30d) / -30
14 = d
If your heart beats 48 times in 40 seconds, which proportion could be used to make the best estimate for the number of beats in 60 seconds? A. 48/40 = 60/x B. 40/60 = 48/x C. 48/40 = 60/x D. 48/60 = 40/x
Given statement solution :- The correct proportion to make the best estimate for the number of beats in 60 seconds is:
A. 48/40 = 60/x
To make the best estimate for the number of beats in 60 seconds, we need to find the proportion that relates the beats per second in the given scenario to the desired duration of 60 seconds.
Let's set up the proportion using the given information:
Heart beats per second (beats/sec) = 48 beats / 40 seconds
We want to find the number of beats in 60 seconds (x beats / 60 seconds).
The correct proportion would be:
48 beats / 40 seconds = x beats / 60 seconds
Therefore, the correct proportion to make the best estimate for the number of beats in 60 seconds is:
A. 48/40 = 60/x
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65 POINTS!!!!!! PLEASE ANSWER QUICK
The probabilities are: 1a) P(A) = 12, 1b)P(B) = 1.055 + 1,160 = 1,161.055 . 1c) P(A and B) = P(AB) = 1.055
How to find the probabilitiesP(A) = 12
P(B) = 1.055 + 1,160 = 1,161.055
P(A and B) = P(AB) = 1.055
To determine if the events A and B are independent, we need to check if P(A and B) = P(A) * P(B).
P(A) * P(B) = 12 * 1,161.055 = 13,932.66
Since P(AB) = 1.055 is not equal to P(A) * P(B) = 13,932.66, the events A and B are not independent.
P(A | B) = P(AB) / P(B) = 1.055 / 1,161.055 ≈ 0.0009098
To convert this probability to a percentage, we multiply by 100:
Percentage chance = P(A | B) * 100 ≈ 0.0009098 * 100 ≈ 0.091%
Therefore, the company should report a percentage chance of approximately 0.091% to the person as an estimate of their risk of developing the disease based on the study.
The reasoning behind this estimation is that among those who have the genetic variation (B), the probability of having the disease (A) is approximately 0.0009098, which corresponds to 0.091% when expressed as a percentage.
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Pls can someone help me?
I’m pretty sure the value of a->60
b-> 110
c->80
What do i write for the reasons of them tho? Pls help! thanks
The values of the angles a, b and c are 60°, 110° and 80° respectively.
Given is a figure we need to find the measure of the angles given,
a, b, c.
So,
70° + 50° + a = 180° [making linear pair angles]
120° + a = 180°
a = 60°
50° + a = b [corresponding angles between parallel lines]
b = 50° + 60°
b = 110°
a + 40° + ∠HFE = 180° [angle sum property of a triangle]
60° + 40° + ∠HFE = 180°
∠HFE = 80°
∠HFE = c [alternate angles between parallel lines]
c = 80°
Hence the values of the angles a, b and c are 60°, 110° and 80° respectively.
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here is my algebra 13 homework, can someone please help me quick!
The decreasing interval of function is (-∞ , 0) .
The decreasing interval in the function is said to be when the value of the derivative f' (x) ≤ 0 .
Decreasing interval is when f(x) is decreasing as x is increasing.
Here the graph is of a parabola the equation of a upper parabola is
f(x) = x²
Now doing derivation of the parabola equation, we get
f'(x) = 2x
As for decreasing interval we will put
f'(x) ≤ 0
Putting the value of f'(x) in the equation
2x ≤ 0
x ≤ 0
Decreasing interval (-∞ , 0)
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The dot plot displays data from 14 random samples, each consisting of 30 middle school students. Each dot represents the mean number of sports played per year by students in the sample.
Which number best represents the mean number of sports played by middle school students? Write your answer as a decimal to the nearest tenth.
__ sports
Part B
Find and interpret the variability in the distribution. Round the MAD to the nearest hundredth.
The MAD is about_____ sport(s). The majority of the sample means are within ______ sport(s) of the mean. This means our estimate is likely not far off from the true mean.
The best representation of the mean number of sports played by middle school students is 2.75 sports and the MAD is about 0.84 sports.
To find the best representation of the mean number of sports played by middle school students, we need to calculate the median of the given data.
The median represents the central tendency of the data and is less affected by extreme values.
Arranging the means of the samples in ascending order, we have:
1, 1, 2, 2.5, 3, 3, 3.5, 4
Since there are eight values, the median will be the average of the fourth and fifth values:
(2.5 + 3) / 2 = 2.75
Variability in the Distribution
Summing up the absolute deviations:
1.75 + 1.75 + 0.75 + 0.25 + 0.25 + 0.25 + 0.75 + 1.25 = 6.75
To find the MAD, we divide the sum of the absolute deviations by the total number of data points:
MAD = 6.75 / 8 = 0.84
Therefore, the MAD is about 0.84 sports.
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What is the equation, in point-slope form, of the line that
is perpendicular to the given line and passes through the
point (-4,-3)?
y + 3 = -4(x + 4)
y + 3 =(x+4)
Y + 3 = ¹/(x+4)
y + 3 = 4(x + 4)
An equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4,-3) is: C. y + 3 = 1/4(x + 4) .
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-3 - 1)/(0 + 1)
Slope (m) = -4
m₁ × m₂ = -1
-4 × m₂ = -1
m₂ = -1/-4
Slope, m₂ = 1/4
At data point (-4, -3) and a slope of 1/4, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 3 = 1/4(x + 4)
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
What are the first two steps in solving the radical equation below?
√x+1-4 = 8
A. Square both sides and then subtract 1 from both sides.
B. Add 4 to both sides and then subtract 1 from both sides.
C. Square both sides and then add 4 to both sides.
D. Add 4 to both sides and then square both sides.
SUBMIT
The first two steps in solving the radical equation, √x+1-4 = 8 is D. Add 4 to both sides and then square both sides.
How do we solve the radical equation?We can solve the radical equation by adding 4 to both sides and then squaring both sides.
Given equation: √x+1 - 4 = 8.
The First step: add 4 to both sides of the equation:
√x+1 - 4 + 4 = 8 + 4
Simplifying the equation:
√x+1 = 12
The Second step: square both sides of the equation to eliminate the square root:
(√x+1)² = 12²
Squaring both sides gives:
x + 1 = 144
Finally, subtract 1 from both sides to isolate x:
x + 1 - 1 = 144 - 1
x = 143
So, adding 4 to both sides and then squaring both sides are the first two steps in solving the equation.
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5. A movie is made of a series of still images called frames. A standard rate for a movie is 24 frames per second. Two movies, A and B, each last 100 minutes. Movie A was filmed at the standard rate. Movie B was filmed at 30 frames per second. Movie B has what percent more frames than movie A? Movie B has what frames than movie A.
Movie B has approximately 25% more frames than Movie A.
For Movie A the duration is 100 minutes
Frame rate: 24 frames per second
Total frames in Movie A:
Total frames in Movie A = 100×60×24
Movie B:
Duration: 100 minutes
Frame rate: 30 frames per second
Total frames in Movie B:
Total frames in Movie B = 100 × 60 × 30
To find the percent more frames in Movie B compared to Movie A, we can use the following formula:
Percent more frames = ((Total frames in Movie B - Total frames in Movie A) / Total frames in Movie A) × 100
Total frames in Movie A = 100 × 60× 24
Total frames in Movie B = 100 ×60 × 30
Percent more frames = ((Total frames in Movie B - Total frames in Movie A) / Total frames in Movie A) × 100
Percent more frames = ((100 × 60× 30) - (100 × 60×24)) / (100 × 60× 24)×100
Percent more frames = (180,000 - 144,000) / 144,000 * 100
Percent more frames = 36,000 / 144,000 * 100
Percent more frames = 25%
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14. All of the following are advantages of a 401(k), EXCEPT... *
1 point
A.You don't pay taxes on your investments' growth each year
b.You can invest your 401(k) into a wider variety of asset types than you can with
an IRA
c.Your employer may match some of your 401(k) contributions
d.You can contribute more money into a 401(k) than into an IRA
Except You can invest your 401(k) into a wider variety of asset types than you can with an IRA. All are the advantages. Option B
A) You don't pay taxes on your investments' growth each year: One of the main advantages of a 401(k) plan is the tax advantage it provides.
Contributions to a traditional 401(k) are made on a pre-tax basis, meaning that the money you contribute is not subject to income tax. Additionally, the growth of investments within the 401(k) account is tax-deferred until you make withdrawals in retirement.
C) Your employer may match some of your 401(k) contributions: Many employers offer a matching contribution to their employees' 401(k) plans. This means that for every dollar you contribute to your 401(k), your employer will contribute a certain percentage, up to a specified limit.
D) You can contribute more money into a 401(k) than into an IRA: 401(k) plans generally allow for higher contribution limits compared to Individual Retirement Accounts (IRAs).
In 2021, the annual contribution limit for a 401(k) is $19,500 (with an additional $6,500 catch-up contribution for individuals aged 50 or older).
In contrast, the annual contribution limit for an IRA is $6,000 (with an additional $1,000 catch-up contribution for individuals aged 50 or older). The higher contribution limits of a 401(k) allow individuals to save more for retirement on a tax-advantaged basis.
In summary, the correct answer is B. The ability to invest in a wider variety of asset types is not an advantage of a 401(k) plan. However, the other options listed (A, C, and D) are all advantages of a 401(k) plan.
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In AEFG we know that m/F = 75° and m/G=45°. Which of the following is the measure
of E? Show how you found your answer.
(1) 40°
(2) 55°
(3) 60°
(4) 70°
Answer:
(3) 60°
Step-by-step explanation:
You want the measure of the third angle (E) in triangle EFG, given that two of the angles have measures 75° (angle F) and 45° (angle G).
Angle sum theoremThe angle sum theorem tells you the sum of angles in any triangle is 180°. This means ...
E + F + G = 180
E + 75 + 45 = 180
E = 60 . . . . . . . . . . . . . subtract 120 from both sides and simplify
The measure of angle E is 60°.
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(30 de puncte) SUBIECTUL al III-lea. Scrieți rezolvările complete. 1. Denisa are cu 27 de ani mai puțin decât mama ei, care are cu un an mai puţin decât tatăl fetei. Denisa este de cinci ori mai tânără decât tatăl său. a) Cu câți ani este mai tânără Denisa decât tatăl ei? b) Determină vârsta fetei. (2p) (3p) (Sp)
Answer:
Să rezolvăm această problemă pas cu pas. Să denotăm vârsta Denisei ca D, vârsta mamei sale ca M și vârsta tatălui ei ca F. Din informațiile date, putem scrie următoarele ecuații:
M = D + 27 (Denisa are cu 27 de ani mai puțin decât mama ei) F = M + 1 (mama Denisei are cu un an mai puțin decât tatăl ei) F = 5D (Denisa este de cinci ori mai tânără decât tatăl ei)
a) Din ultima ecuație, putem vedea că Denisa este F - D cu ani mai tânără decât tatăl ei. Înlocuind F cu 5D, înțelegem că Denisa este 5D - D = 4D cu ani mai tânără decât tatăl ei.
b) Pentru a determina vârsta Denisei, putem rezolva sistemul de ecuații. Din prima ecuație, obținem acel M = D + 27. Înlocuind acest lucru în a doua ecuație, obținem acel F = D + 27 + 1 = D + 28. Înlocuind acest lucru în a treia ecuație, obținem acel D + 28 = 5D. Rezolvând pentru D, obținem acel D = 7.
Deci Denisa are 7 ani.
Answer:
Denisa are 7 ani
Step-by-step explanation:
the coldest temperature ever recorded on earth was -89.2
The statement that "the coldest temperature ever recorded on earth was - 89. 2 ° " is True.
What was the coldest temperature recorded ?The Soviet Union's Vostok Station in Antarctica recorded the coldest temperature ever observed on Earth, measuring at -89.2°C on July 21, 1983 via satellite and weather station data.
This natural occurrence saw a temperature that presents significant risks to animal and human life due to poor insulation available against such extreme colds. Without suitable warming tools, survival is near impossible.
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A top travels 8 centimeters each time it is spun. if it is spun 7 times what distance does it travel?
If a top travels 8 centimeters each time it is spun and it is spun 7 times, the total distance it travels is 56 centimeters.
How the total distance is determined:The total distance is determined by multiplication of the distance traveled per spin and the number of spins.
Multiplication involves the multiplicand, the multiplier, and the product.
The traveling distance per spun = 8 centimeters
The number of spinning of the top = 7 times
The total distance = 56 centimeters (8 x 7)
Thus, using multiplication, the total distance the top travels after the 7th spin is 56 centimeters.
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Which shows all the exact solutions of 2sec²x-tan^x=-1? Give your answer in radians.
0+
O +k and+k
0+ -2k* and 5+2K*
3
7%
5+28
4
○ 주 +2kx3+2kx +2kx, and 7+2kx
+kr2+ks 4*k* and 5+k
47
+ K
Kx
Answer:
Step-by-step explanation:
The exact solutions for the equation 2sec²x - tan²x = -1 in radians are:
x = π/4 + πk, where k is an integer
x = 3π/4 + πk, where k is an integer
These solutions represent all the values of x that satisfy the given equation.
100 Points! Geometry question. Identify the similar triangles. Then find each measure. Photo attached. Please show as much work as possible. Thank you!
The similar triangles for this problem are given as follows:
RST and VUT.
Then the measure VT is given as follows:
VT = 5.4 units.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.Hence the similar triangles for this problem are given as follows:
RST and VUT.
The proportional relationship for the side lengths is given as follows:
6/14 = (x + 2)/(4x - 1).
Applying cross multiplication, the value of x is obtained as follows:
14(x + 2) = 6(4x - 1)
14x + 28 = 24x - 6
10x = 3.4
x = 3.4.
Then the length VT is given as follows:
VT = 3.4 + 2
VT = 5.4 units.
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The figure below can be used to prove the Pythagorean Theorem. Use the drop-down menus to complete the proof. b Click the arrows to choose an answer from each menu. The expression Choose.. represents the area of the figure as the sum of the area of the shaded triangles and the area of the white square.
The expression 2ab + [tex]c^2[/tex] represents the area of the figure as the sum of the area of the shaded triangles and the area of the white square.
The equivalent expression [tex]a^2 +b^2+2ab[/tex] use the length of the figure to represent the area.
[tex]2ab +c^2=a^2+b^2+2ab[/tex]
Subtracting 2ab from both sides
[tex]c^2=a^2+b^2[/tex]
Figure of a square with some shaded triangles.
Area of the triangle formula is 1/2 times base times height
base =a and height =a
Area of one triangle = 1/2ab
There are 4 shaded triangles
Area of 4 shaded triangles = 4 x 1/2ab
Area of the square = side times side
Now we find the area of outer square. side length is a+b
Area of outside square = (a + b)(a + b) = [tex](a+b)^2[/tex] = [tex]a^2 +b^2+2ab[/tex]
Using the length of the figure to represent the area.
Thus, now set both the areas equal to each other.
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Your question seems incomplete, the probable complete question is
PLEASE HELP
Triangle ABC is similar to triangle XYZ.
Solve for p.
Answer:
Step-by-step explanation:
What is the definition of postulate? A. an assumption, presumed to be true, that is used as the basis for a logical argument B. a statement that has been shown to be false by logical argument C. a statement that has been shown to be true by logical argument D. a statement, known to be false, that is used as the basis for a logical argument
Postulate is an assumption, presumed to be true, that is used as the basis for a logical argument.
We have,
A postulate is a statement or proposition that is accepted as true without proof.
It is an assumption or starting point in a logical argument that is considered to be self-evident or evident based on previous experience or observation.
In mathematics,
Postulates are used to define the basic concepts and axioms that form the foundation of a particular system of thought.
They are often used as the starting point for deriving other mathematical concepts and theorems.
Postulates are also known as axioms or assumptions.
Thus,
Postulate is an assumption, presumed to be true, that is used as the basis for a logical argument.
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What’s the answers to this?
The vector representing the radius at the given position is -13i - j - 5k.
The magnitude of the radius vector is 13.96 units.
What is the vector representing the radius?
The vector representing the radius at the given position is calculated as follows;
center of the sphere = (11, 5, 2)
The point of the radius = ( -2, 4, -3 )
The radius vector = ( - 2 - 11) , ( 4 - 5), ( -3 - 2)
r = ( -13, - 1, - 5)
r = -13i - j - 5k
The magnitude of the radius vector is calculated as follows;
| r | = √ x² + y² + z²
where;
x, y, z are the various component of the radius| r | = √[ ( -13²) + ( -1)² + ( -5 )² ]
| r | = √ ( 169 + 1 + 25 )
| r | = √ ( 195 )
| r | = 13.96 units
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The number 1.3 is both a(n) __________ and a(n) __________ number.
The number 1.3 is both a rational and an irrational number.
What is the number 1.3?The number 1.3 is a rational number because it can be expressed as the quotient of two integers, namely 13/10.
The number 1.3 an irrational number because it cannot be expressed as the ratio of two integers, without repeating or terminating decimals, and its decimal representation goes on forever without repeating.
So we can conclude that the number 1.3 is both rational and irrational number.
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Can a triangle be formed with side lengths 4,8,11? Explain
No because 11-8<4
Yes because 11-4<8
No because 4+8>11
Yes because 4+8>11
Directions: For A and B, use the given rules to write the first five terms in each
sequence. Then, use the terms to create ordered pairs for each numerical pattern.
A. Rule 1: Add 3 starting from 13.
Rule 2: 25-2x, where x is equal to 5, 6, 7, 8, 9.
Sequence 2
Sequence 1
B. Rule 1: Multiply by 3, then add 2, starting from 1.
Rule 2: Multiply by 2, then add 3, starting from 6.
Sequence 1
Sequence 2
Ordered Pair
Ordered Pair
OFFERING 50 POINTS
In solving the sequence using the provided rules, we have:
A) Sequence 1: 13, 16, 19, 22, 25.
Sequence 2: 15, 13, 11, 9, 7.
Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7)
B) Sequence 1: 1, 5, 17, 53, 159.
Sequence 2: 6, 15, 33, 69, 141.
Ordered Pair: (1, 6), (5, 15), (17, 33), (53, 69), (159, 141).
How to solve the sequence?Using the given rules, we can solve the sequence as follows:
A. Rule 1: Add 3 starting from 13
The first five terms in Sequence 1 would be:
13, 13 +3 = 16, 16 +3 = 19, 19 + 3 = 22, 22 + 3 = 25.
13, 16, 19, 22, 25
Using Rule 2: 25-2x, where x is equal to 5, 6, 7, 8, 9
The first five terms in Sequence 2 would be:
25 - 2(5) = 25 - 10 = 15
25 - 2(6) = 25 - 12 = 13
25 - 2(7) = 25 - 14 = 11
25 - 2(8) = 25 - 16 = 9
25 - 2(9) = 25 - 18 = 7
The ordered pairs for each numerical pattern would be:
(13, 15), (16, 13), (19, 11), (22, 9), (25, 7)
B. Rule 1: Multiply by 3, then add 2, starting from 1
The first five terms in Sequence 1:
1, (1 * 3) + 2 = 5, (5 * 3) + 2 = 17, (17 * 3) + 2 = 53, (53 * 3) + 2 = 159
Using Rule 2: Multiply by 2, then add 3, starting from 6
The first five terms in Sequence 2:
6, (6 * 2) + 3 = 15, (15 * 2) + 3 = 33, (33 * 2) + 3 = 69, (69 * 2) + 3 = 141
The ordered pairs for each numerical pattern would be:
(1, 6), (5, 15), (17, 33), (53, 69), (159, 141)
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11. Descartes is thinking of a number that when he multiplies it by 9, he gets the number he is thinking of. What number is Descartes thinking of? brainly
Descartes must be thinking of the number 0.
Now, Let's call the number Descartes is thinking of "x".
Hence, According to the problem, if Descartes multiplies "x" by 9, he gets "x" back. In other words, 9 times "x" is equal to "x".
So we can write this as an equation:
⇒ 9x = x
Now we need to solve for "x". We can start by subtracting "x" from both sides of the equation:
⇒ 9x - x = 0
⇒ 8x = 0
divide both sides by 8 to get:
⇒ x = 0
Thus, Descartes must be thinking of the number 0.
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Given that ΔA′B′C′ is a dilation of ΔABC, how are the angles and side lengths of the preimage and image related?
A. The angles are congruent and the side lengths are congruent.
B. The angles are congruent and the side lengths are proportional.
C. The angles are proportional and the side lengths are congruent.
D. The angles are proportional, and the side lengths are proportional.
When a dilation is performed on a triangle, the angles and side lengths of the preimage and image are related in a specific way. The correct answer is B. The angles are congruent, and the side lengths are proportional.
In a dilation, each corresponding angle of the preimage and image triangles is congruent. This means that if an angle in the preimage triangle measures 60 degrees, the corresponding angle in the image triangle will also measure 60 degrees.
However, the side lengths of the preimage and image triangles are not necessarily congruent. Instead, they are proportional. This means that the ratio of corresponding side lengths remains constant throughout the dilation. For example, if one side of the preimage triangle is twice as long as another side, the corresponding side in the image triangle will also be twice as long as its corresponding side.
It's important to note that the center of dilation and the scale factor determine the specific proportions between the side lengths. The scale factor represents the ratio of corresponding side lengths in the preimage and image triangles.
Therefore, in a dilation, the angles are congruent, and the side lengths are proportional.
The right answer is B. The angles are congruent and the side lengths are proportional.
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what is the area,in square centimeters
Answer:
11.9 sq cm, answer choice C.
Step-by-step explanation:
Area of a parallelogram = base x height.
The base is 4.25 cm, and the height is 2.8 cm. The other measurement is not needed.
area = 4.25 x 2.8 = 11.9 sq cm, answer choice C.
Mrs.Stacey's class has 5 pieces of artwork on their bulletin board.each piece of artwork is 8.5 by 11 inches. The bulletin board is 48 inches by 48 inches.How much of the bulletin board is NOT covered with art work?
Answer:
1836.50 square inches of the bulletin board is NOT covered with art work.
Step-by-step explanation:
The question focuses on the area covered by the paintings and the board, since area is defined as: the amount of space enclosed within the boundaries of a flat, two-dimensional shape, such as a square, circle, or rectangle.
Step 1: First, we need to know the total area of the five paintings.
We can assume that every piece of artwork is a rectangle since the dimensions are different and only two dimensions are given. Thus, we can find the total area by multiplying the area of one piece of artwork by 5:The formula for area of a rectangle isA = lw, where
A is the area in square units, l is the length,and widthWe can allow 8.5 to be the length and 11 to be the width:
A = 8.5 * 11
A = 93.5 square inches
Multiplying 93.5 by 5 shows us the the total area covered by the five pieces of artwork is 467.50 square inches as 93.5 * 5 = 467.50
Step 2: Now we need to find the area of the bulletin board.
We can assume that the board is a square since the dimensions are the same and only two dimensions are given.The formula for area of a square isA = s^2, where
A is the area in square units,and s is the side48 is s in the area formula:
A = 48^2
A = 2304 square inches
Thus, the area of the bulletin board is 2304 square inches.
Step 3: Finally, subtracting the total area of the five pieces of artwork from the area of the bulletin board will tell us how much of the bulletin board is NOT covered with art work:
2304 - 467.50 = 1836.50 square inches
Thus, 1836.50 square inches of the bulletin board is not covered with art work.
The diagram shows a right-angled triangle.
24 cm
18 cm
_Not to scale
Calculate the value oft. Give your answer correct to 1 decimal place.
Answer:
can i have a photo, please?
Step-by-step explanation: