Answers
Answer:
1. 4 tens 2 ones
2. 6 tens 5 ones
3. 3 tens 7 ones
4. 2 tens 6 ones
5. 7 tens 4 ones
6. 5 tens 9 ones
7. 8 tens 1 ones
8. 9 tens 9 ones
9. 1 tens 3 ones
Step-by-step explanation:
not sure if I did it right, lmk if im wrong. Think ur just suppsoed to count the number of boxes that make 10, and those that dont count up to 10, depending on the number, are seen as "ones".
Related Questions
someone please help with finding the greatest common factor, my teacher didn't explain it well
Answers
The greatest common factor is 2z^2
How you find it is first you find the greatest common factor of the two numbers, which is 2 (2 is the greatest number that can be multiplied into 2 and 10; 2 times 1 = 2 and also 2 times 5 = 10)
Then you find the greatest common factor of the variables, which is z^2.
(z^2 is the largest that can go into z^3 and z^2 because z^2 times z = z^3 and z^2 = z^2)
After that, you just multiply them together to get 2z^2
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 12 15 4 31
Female 9 8 16 33
Total 21 23 20 64
If one student is chosen at random, find the probability that the student was male GIVEN they got a 'C':
Answers
Answer:
To find the probability that a randomly selected student who received a "C" was male, we need to calculate the total number of male students who received a "C" and divide it by the total number of students who received a "C".
Total number of male students who received a "C": 12
Total number of students who received a "C": 20
Probability that the student was male:
12/20 = 0.6
Therefore, the probability that a randomly selected student who received a "C" was male is 0.6, or 60%.
find the probability that the student was male given they got a 'C', we need to use Bayes' theorem. Bayes' theorem states that:
P(A|B) = P(B|A) * P(A) / P(B)
where P(A|B) is the probability of event A given event B, P(B|A) is the probability of event B given event A, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.
In this case, event A is "the student is male" and event B is "the student got a 'C'". We are given the following information:
- P(A) = 31/64 (the prior probability of a student being male)
- P(B|A) = 4/31 (the probability of getting a 'C' given the student is male)
- P(B) = 20/64 (the prior probability of getting a 'C')
Using Bayes' theorem, we can calculate P(A|B) as:
P(A|B) = P(B|A) * P(A) / P(B)
P(A|C) = (4/31) * (31/64) / (20/64)
P(A|C) = 4/20
P(A|C) = 0.2
Therefore, the probability that the student was male given they got a 'C' is 0.2 or 20%.
what is the parallel line that passes through the point (-6, -3) for the line y= -5/3 x - 3
Answers
Answer:
y = -5/3 x - 13
Step-by-step explanation:
Parallel lines have the same slope. The slope will be -5/3
y = mx + b
We will substitute -3 for y (-6,-3).
We will substitute -5/3 for m.
We will substitute -6 for x (-6,-3)
-3 = -5/3(-6) + b
-3 = [tex]\frac{30}{3}[/tex] + b
-3 = 10 + b Subtract 10 from both sides
-3 - 10 = 10 - 10 + b
-13 = b
To write the equation, use -5/3 for m (the slope) and -13 for b (the y-intercept)
y = mx + b
y = -5/3 x - 13
Helping in the name of Jesus.
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #1
Answers
The end behavior of f(x) is described as follows:
As x -> -∞, f(x) -> ∞.As x -> ∞, f(x) -> 0.How to obtain the end behavior of a function?The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.
The function for this problem is given as follows:
f(x) = 4(5/7)^x.
It is an exponential function with base with absolute value less than 1, hence the end behavior is given as follows:
Increases to the left of the graph -> As x -> -∞, f(x) -> ∞.Approaches the horizontal asymptote y = 0 at the right of the graph -> As x -> ∞, f(x) -> 0.More can be learned about the end behavior of a function at brainly.com/question/1365136
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A football field is 300 feet long and 160 feet wide. To the nearest hundredth, how many acres are in a football field?
Answers
x = how many acres
keeping in mind that one yd² has 9 ft², and that an acre has 4840 yd²
[tex](300ft)(160ft)\implies 48000ft^2\implies \cfrac{48000}{9}\implies \cfrac{16000}{3}~yd^2 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} acre&yd^2\\ \cline{1-2} 1 & 4840\\[1em] x&\frac{16000}{3} \end{array} \implies \cfrac{1}{x}~~=~~\cfrac{4840}{ ~~ \frac{16000}{3} ~~ }\implies \cfrac{1}{x}=\cfrac{14520}{16000} \\\\\\ 16000=14520x\implies \cfrac{16000}{14520}=x\implies 1.10\approx x[/tex]
Assume that when human resource managers are randomly selected, 49% say job applicants should follow up within two weeks. If 7 human resource managers are randomly selected, find the probability that exactly 2 of them say job applicants should follow up within two weeks.
Answers
The probability that exactly 2 of them say job applicants should follow up within two weeks is 33.02%.
How to find the probability ?We can use the binomial probability formula:
P(x) = C ( n, x ) × p ^ x × ( 1 - p ) ^ ( n - x )
Solving then gives:
P ( 2 ) = C ( 7, 2 ) x 0.49 ^ 2 x ( 1 - 0. 49 ) ^ ( 7 - 2)
P ( 2 ) = 21 x 0. 49 ^ 2 x ( 1 - 0. 49) ^5
= 21 x 0. 2401 x 0. 078109
= 0. 3302
In conclusion, the probability that 2 of the 7 human resource managers say job applicants should follow up within two weeks is approximately 0.3302 or 33.02%.
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Lindsay sketches a right triangle with lengths f, g, and h as shown. She uses the Pythagorean Theorem to write the equation f2 + g2 = h2 to represent the triangle. How can Lindsay correct her error? Explain your reasoning.
Answers
It is a right triangle so f² = g² + h² not f² + g² = h²
What is the Pythagoras theorem?
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Here, we have
Given: Lindsay sketches a right triangle with lengths f, g, and h has shown. She uses the Pythagorean Theorem to write the equation f² + g² = h² to represent the triangle.
It is a right triangle.
∴ f² = g² + h² not f² + g² = h²
Hence, It is a right triangle. f² = g² + h² not f² + g² = h²
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A surveyor whose eye level is 5 feet above the ground determines the angle of elevation to the top of an office building to be 41.7°. If the surveyor is standing 40 feet from the base of the building, what is the height of the building to the nearest foot?
A.) 32ft.
B)50 ft
C)36ft
D.)41ft
Answers
The height of the building when the surveyor is standing that far is D.)41ft
How to find the height of the building ?The tangent function would be best to use to find the height because we would be able to use the adjacent and and opposite.
Assuming that 5 feet is the height and the angle of elevation is 41. 7 degrees, and the distance of 40 feet, we have :
tan ( A ) = (h - x) / D
tan ( 41. 7° ) = ( h - 5 ) / 40
h - 5 = 40 x tan ( 41. 7 ° )
h - 5 = 40 x 0.8895
h = 35.58 + 5
= 40.58
= 41 feet
The height of the building is 41 feet.
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I need help; please include an explanation!
Answers
We can see here that the equation that best models the situation is: B. 13 - (60h/23) = 10.
What is speed?Speed is a scalar quantity that describes how fast an object is moving, or the rate at which it covers distance. It is typically measured in units of distance per unit of time, such as miles per hour or meters per second.
Speed only tells us how fast an object is moving, without any information about the direction of motion or changes in direction.
We can see that if we find the time, h in hours, we will have:
h = (3 x 23)/60
Simplifying this expression gives us:
h = 69/60
Therefore, the equation is:
h = 1.15
(Note: 3 is gotten from 13 gallons - 10 gallons = 3 gallons that was used at that particular time and speed).
If we substitute h = 1.15 into our model equation, we will get the correct answer.
Thus, 13 - (60 × 1.15)/23 = 10.
∴ Option B is the correct answer.
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Find the total amount owed, to the nearest cent, for the following simple interest loans.
Answers
The total amount owed, to the nearest cent A = $ 3,283.44
What is simple interest?Simple interest is interest that is only calculated on the initial sum (the "principal") borrowed or deposited. Generally, simple interest is set as a fixed percentage for the duration of a loan. No matter how often simple interest is calculated, it only applies to this original principal amount.
A = P + I where
P (principal) = $ 2,950.00
I (interest) = $ 333.44
A = P(1 + r/n)^nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
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Correct question:
Find the total amount owed, to the nearest cent, for a simple interest loan with a principal of $2950, an interest rate of 7.4% and a time period of 1.5 years. Show
Can someone help me with this problem?
Answers
The measure of the arc angle is as follows:
m∠BAC = 228°
How to find arc angles?The central angle of an arc is the central angle subtended by the arc.
The measure of an arc is the measure of its central angle.
The Central Angle theorem states that the central angle subtended by
two points on a circle is twice the inscribed angle subtended by those
points.
Therefore, let's find m∠BAC
Hence,
m∠BC = Central angle
m∠BAC = 360 - 132
m∠BAC = 228 degrees
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The sector of a circle with a diameter of 8 feet has a central angle measure of 45°. What is the area of the sector?
A. π/2 ft²
B. π ft²
C. 2 π ft²
D. 8 π ft²
Answers
so, we know the diameter is 8, so that means its radius is half that, or 4.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =45 \end{cases}\implies A=\cfrac{(45)\pi (4)^2}{360}\implies A=2\pi ~ft^2[/tex]
Scott and Lana booked a cruise that departs from Seward, Alaska, but their flight flew into Anchorage, Alaska. The couple decided to travel from Anchorage to Seward on the Alaska Railroad's non-stop Coastal Classic route to enjoy the 117 miles of beautiful scenery. If the train had traveled 13 miles in 30 minutes, how long, in hours, was the non-stop train ride from Anchorage to Seward?
A. 4.5 hours
B. 18 hours
C. 3 hours
D. 9 hours
Answers
The answer is option A. That is, the time taken in hours if the train traveled 13 miles in 30 minutes is 4.5 hours.
What is the relation between distance travelled and time?The relation between distance traveled and time is given by the formula:
Distance = Speed x Time
where distance is the total distance traveled, speed is the rate at which the distance is covered, and time is the duration for which the distance is covered. This formula applies to any type of motion, whether it is linear or circular, and it is often used to calculate the distance covered by an object given its speed and the time it traveled. Alternatively, the formula can also be used to calculate the time required to travel a certain distance given the speed at which the object is traveling.
Given that the total distance = 117 miles. We need to find the time taken in hours if the train traveled 13 miles in 30 minutes.
For that we can use the equation, distance = rate x time
Now, rate = distance/time
Distance = 13 miles, time = 30 minutes = 30/60 hours = 0.5 hours
Therefore, rate = 13 miles / 0.5 hours = 26 miles per hour
Now to find the time it took to travel the entire 117 miles:
time = distance/rate
time = 117 miles/ 26 miles per hour
time = 4.5 hours
Therefore, the answer is (A) 4.5 hours.
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Milan took 3 1/4 hours to clean the bathroom. He took 1/8 hours to clean the bathroom. How much longer did it take Milan to clean the bathroom? Write your answer as a mixed number in simplest form.
Answers
The time it took Milan longer to clean the bathroom is 3 1/8 hours
How much longer did it take Milan to clean the bathroom?Time taken for Milan to clean the bathroom = 3 1/4 hours
Time taken for Milan to clean the kitchen = 1/8 hours
Time taken longer for Milan to clean the bathroom = 3 1/4 hours - 1/8 hours
= 13/4 - 1/8
= (26-1) / 8
= 25/8
= 3 1/8 hours
In conclusion, it took Milan 3 1/8 hours longer to clean the bathroom.
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1. What does the term inflation mean? If meat prices go up, does this auto-
matically mean that there is inflation? Explain your answer.
2. Give an example of who is hurt and who is helped by inflation. Briefly
explain how inflation affects each group you have named.
3. How is the Consumer Price Index used to measure the rate of inflation?
Answers
Inflation refers to the general increase in prices of goods and services in an economy over a period of time.
A rise in meat prices may be an indication of inflation, but it is not necessarily an automatic or definitive sign of inflation.
Inflation can hurt savers and fixed-income earners, such as retirees on a fixed pension, as the purchasing power of their savings and income decreases.
The Consumer Price Index (CPI) is used to measure the rate of inflation by tracking the average price change of a basket of goods and services commonly purchased by households, including food, housing, transportation, and medical care.
The CPI measures the percentage change in prices from a base period and is calculated by dividing the cost of the basket of goods and services in the current period by the cost of the same basket in the base period and multiplying the result by 100.
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If coto = 13 on top
6 on bottom
Then what is Seco
Remember to simplify and rationalize all answer
Answers
Answer:
√(205)/13
Step-by-step explanation:
Each marble bag sold by Eric’s Marble Company contains 3 red marbles for every 4 blue marbles. If a bag has 36 blue marbles, how many red marbles does it contain?
Answers
What is the value of x in both these questions
Answers
Answer:
x + 5 + 7x - 5 + x = 180
9x = 180
x = 20
So the measure of angle M is x + 5 = 20 + 5 = 25°
the Ponde family's Powerjet pumps 420 gallons of water per hour. At this rate, how many gallons of water will it pump in 45 minutes?
Answers
the number of gallons of water it can pump inn 45 minutes is
How to determine the amount of water?The given parameters that will help us to determine the quantity are
Powejet pumps 420 gallons of water per hour
how many gallons of water will it pump in 45 minutes = ?
1 hour = 60 minutes
This means = 450/60 = 7 gallons
Therefore in 45 minutes it can pump 7*45 = 315 gollons
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What is the value of x?
Answers
Answer:
12
Step-by-step explanation:
10x - 20 + 6x + 8 = 180
Supplementary angles
Answer:
x = 12
Step-by-step explanation:
The two given angles create a straight line (Definition of Straight Line). This means that:
[tex](10x - 20) + (6x + 8) = 180[/tex]
First, combine like terms. Like terms are terms that share the same amount of the same variables:
[tex](10x + 6x) + (8 - 20) = 180\\(16x) + (-12) = 180\\16x - 12 = 180\\[/tex]
Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, add 12 to both sides of the equation:
[tex]16x - 12 = 180\\16x - 12 (+12) = 180 (+12)\\16x = 180 + 12\\16x = 192[/tex]
Next, divide 16 from both sides of the equation:
[tex]\frac{16x}{16} = \frac{192}{16} \\x = \frac{192}{16}\\ x = 12[/tex]
12 is your answer.
~
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Joann's grandparents set up an investment account for her when she was born. They put $3000 in it when she was born and then add $300 to it twice a year. The money is invested in mostly bonds and earns an average of 4% each year. Her interest compounds semiannually. How much will she have when she turns 18?
Answers
When Joann turns 18, she will have approximately $41,551.20 in her investment account.
How to solve for the future valueFV = P * [(1 + r)^n - 1] / r
FV = future value
P = periodic payment ($300)
r = interest rate per period (0.04 / 2 = 0.02)
n = total number of periods (18 years * 2 = 36)
FV = 300 * [(1 + 0.02)^36 - 1] / 0.02
FV ≈ 300 * [2.3084] / 0.02
FV ≈ 34,626.00
Solve for inotial investment
FV_initial = PV * (1 + r)^n
FV_initial = 3000 * (1 + 0.02)^36
FV_initial ≈ 3000 * 2.3084
FV_initial ≈ 6,925.20
we have to add both future values
Total_FV = 6,925.20 + 34,626.00
Total_FV ≈ 41,551.20
When Joann turns 18, she will have approximately $41,551.20 in her investment account.
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#9
Identify an example of a solid from which a triangular, hexagonal, and trapezoidal cross section can be formed.
O cone
O sphere
O cylinder
O triangular prism
hexagonal prism
Answers
What kind of relationship does this table describe?
Answers
The table describes the relationship between membership status and attendance of classes under the principle of independence.
Option A is the correct answer.
We have,
This table describes the relationship between membership status and attendance of classes.
To determine if there is a relationship, we need to apply the principle of independence.
If the principle of independence holds, then the events "having a membership" and "attending one or more classes" are independent of each other, and similarly, the events "not having a membership" and "attending none of the classes" are independent of each other.
To check for independence, we can calculate the expected values for each cell assuming independence holds, and compare them to the observed values.
The expected value for "Have a membership" and "Attend one or more classes".
= (40/70) x (31/70) x 70
= 17.86
The expected value for "Have a membership" and "Attend none of the classes".
= (40/70) x (39/70) x 70
= 22.14
The expected value for "Do not have a membership" and "Attend one or more classes".
= (30/70) x (31/70) x 70
= 13.14
The expected value for "Do not have a membership" and "Attend none of the classes".
= (30/70) x (39/70) x 70
= 16.86
Comparing these expected values with the observed values, we see that they are reasonably close, indicating that the principle of independence holds.
Therefore,
We can conclude that this table describes the relationship between membership status and attendance of classes under the principle of independence.
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At a certain restaurant, the hourly wage for a waiter is 20 percent greater than the hourly wage for a dishwasher, and the hourly wage for a dishwasher is half as much as the hourly wage for a cook's assistant. If a cook's assistant earns $13.00 an hour, how much less than a cook's assistant does a waiter earn each hour?
Answers
At a certain restaurant, the hourly wage for a waiter is 20 percent greater than the hourly wage for a dishwasher, and the hourly wage for a dishwasher is half as much as the hourly wage for a cook's assistant. If a cook's assistant earns $13.00 an hour.
Let's break down the problem and use algebra to solve it step by step
1. Let x be the hourly wage for a dishwasher.
2. We know that the hourly wage for a waiter is 20% greater than the hourly wage for a dishwasher, so the hourly wage for a waiter is
x + 0.2x = 1.2x
3. We also know that the hourly wage for a dishwasher is half as much as the hourly wage for a cook's assistant, so
x = 1/2 * $13.00
x = $6.50
Therefore, the hourly wage for a dishwasher is $6.50.
4. We can substitute x = $6.50 into the expression we found for the hourly wage of a waiter
1.2x = 1.2 * $6.50
1.2x = $7.80
Therefore, the hourly wage for a waiter is $7.80.
5. Finally, we can calculate the difference in hourly wage between a cook's assistant and a waiter
Hourly wage difference = hourly wage for cook's assistant - hourly wage for waiter
Hourly wage difference = $13.00 - $7.80
Hourly wage difference = $5.20
Therefore, a waiter earns $5.20 less than a cook's assistant each hour.
In summary, we can use algebra to find that a dishwasher earns $6.50 an hour, a waiter earns $7.80 an hour, and a waiter earns $5.20 less than a cook's assistant each hour.
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For a confidence level of 80%, find the critical value. Round to 3 decimal places.
Answers
Answer:
Step-by-step explanation:
80.000
Dr. Rollins is both an anthropologist and archeologist. While excavating some ruins in South America, he discovered a scale drawing of a replica of a Mayan pyramid.
-The scale for the drawing to the replica was 1 inch : 2 feet.
- The scale for the replica to the actual pyramid was 1 foot : 14 feet.
If the height of the pyramid on the drawing was 3 1/2 inches, what was the height of the actual pyramid?
A. 98 feet
B. 49 feet
C. 91 feet
D. 196 feet
Answers
Correct answer is option A. If the height of the pyramid on the drawing was 3 1/2 inches, then the height of the actual pyramid is 98 feet
How do we compare inches to feet comparison on a replica?When a scale drawing or model is made, the actual object is typically much larger than the drawing or model. In order to represent the object in a smaller size, a ratio is used to scale down the dimensions. This ratio is can be in a fraction form or 'is to' form. We can use this ratio to easily calculate the dimensions of a replica from the actual object or vice versa.
To find the height of the actual pyramid, we need to use both scales given in the problem.
We can start by finding the height of the replica using the first scale:
1 inch on the drawing = 2 feet on the replica
So, 3.5 inches on the drawing = (3.5 * 2) feet on the replica = 7 feet on the replica
Now, using the second scale we can find the height of the actual pyramid:
1 foot on the replica = 14 feet on the actual pyramid
So, 7 feet on the replica = (7 * 14) feet on the actual pyramid = 98 feet
Therefore, the height of the actual pyramid is 98 feet.
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help math will give brainlist
Answers
Answer:
arc PTR = 277°
Step-by-step explanation:
PS is the diameter of the circle , then arc PS = 180°
arc PTR = PS + SR = 180° + 97° = 277°
Answer:
arc PTR = 277°
Step-by-step explanation:
PS is the diameter of the circle , then arc PS = 180°
arc PTR = PS + SR = 180° + 97° = 277°
P = $3000, r = 7%, t = 1 year
Calculate the simple interest earned. Round to the nearest cent.
Answers
Answer:
The interest earned in $210.00
Step-by-step explanation:
i = prt
i = 3000(.07)(1)
i = 210.00
Helping in the name of Jesus.
find the values of variables then find the lengths of the sides of each quadrilateral
Answers
4 , 7 , 2 are the values of variables then find the lengths of the sides of each quadrilateral .
What do math quadrilaterals mean?
Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional form. Concave and convex are the two most common forms. The vertices on them total four. The sides of them are four. 360 degrees is the total number of interior angles.
There are two diagonals between them. A polygon having four sides is referred to as a quadrilateral. A line segment whose endpoints are the opposing vertices of a quadrilateral is said to be the diagonal of the quadrilateral.
2X + 2 = 4
2X = 4 -2
2X = 2
X = 1
2x + 2 = 2 * 1 + 2 = 4
4x + 3 = 4 * 1 + 3 = 7
2x = 2 * 1 = 2
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4 , 7 , 2 are the values of variables then find the lengths of the sides of each quadrilateral .
What do math quadrilaterals mean?
Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional form. Concave and convex are the two most common forms. The vertices on them total four. The sides of them are four. 360 degrees is the total number of interior angles.
There are two diagonals between them. A polygon having four sides is referred to as a quadrilateral. A line segment whose endpoints are the opposing vertices of a quadrilateral is said to be the diagonal of the quadrilateral.
2X + 2 = 4
2X = 4 -2
2X = 2
X = 1
2x + 2 = 2 * 1 + 2 = 4
4x + 3 = 4 * 1 + 3 = 7
2x = 2 * 1 = 2
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Solve for x
x = 1+2+3+4..... Infinity
Answers
Answer:
x = -1/12
Step-by-step explanation:
It is actually a rather simple proof. Before we get to that, it’s important to understand a couple of other things. Let’s consider the following infinite summation:
X = 1 - 1 + 1 - 1 + 1 - 1 ...
Rearranging the above equation a little bit, we get:
X = 1 - (1 - 1 + 1 - 1 + 1 - 1 ...)
If you look at the term inside the brackets, it in fact equals X. So let’s substitute that:
X = 1 - X
2X = 1
X = 1/2
Now let’s consider another sum.
Y = 1 - 2 + 3 - 4 + 5 - ...
Writing it in another way, we get:
Y = 0 + 1 - 2 + 3 - 4 + 5 + ...
Adding the above two equations:
Y + Y = (1 - 2 + 3 - 4 + 5 ...) + (0 + 1 - 2 + 3 - 4 + 5 ...)
Grouping the corresponding terms within the brackets, we get:
2Y = 1 + 0 - 2 + 1 + 3 - 2 - 4 + 3 + 5 - 4 ...
2Y = 1 - (2-1) + (3-2) - (4-3) + ...
2Y = 1 - 1 + 1 - 1 + 1 - 1 ...
But the summation on the right hand side is X. Let’s substitute it:
2Y = X
2Y = 1/2
Y = 1/4
Finally, let’s consider our original question at hand i.e. the sum of all natural numbers:
S = 1 + 2 + 3 + 4 + ...
We defined Y earlier as:
Y = 1 - 2 + 3 - 4 + ...
Subtracting Y from S:
S - Y = 1 - 1 + 2 + 2 + 3 - 3 + 4 + 4 + ...
S - Y = 4 + 8 + 12 + 16 + ...
We just calculated the value of Y to be 1/4. So let’s substitute it:
S - 1/4 = 4 x (1 + 2 + 3 + 4 + ...)
S - 1/4 = 4S
3S = -1/4
S = -1/12