This means that the algorithm will end after just one step, and the GCD will be equal to the last non-zero remainder, which in this case is 3. Therefore, we can be certain that the Euclidean algorithm will end with a zero remainder in one step, and the lowest number we can be certain of is 3.
In this particular question, the student is asking how many steps are required for the Euclidean algorithm to end with a zero remainder when applying it to two positive integers a and b.Suppose you apply the Euclidean algorithm to two positive integers a, b. You only know that a is a number with 1000 decimal digits. The value of b, on the other hand, is given as 3. We can be certain that the Euclidean algorithm will end with a zero remainder in one step.
In order to understand why this is the case, it is important to know that the Euclidean algorithm is a method for computing the greatest common divisor (GCD) of two positive integers. It is based on the observation that the GCD of two numbers does not change if the smaller number is subtracted from the larger number repeatedly.The Euclidean algorithm begins by dividing the larger number by the smaller number and taking the remainder.
The larger number is then replaced with the smaller number, and the smaller number is replaced with the remainder. This process is repeated until the remainder is zero. At this point, the algorithm ends, and the GCD is equal to the last non-zero remainder that was computed.In the case of the student's question, we know that b=3. Since 3 is relatively prime to any number, including a number with 1000 decimal digits, the remainder of the first step will always be 0.
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question 2 theorem: if r and s are rational numbers, then the product of r and s is a rational number. which facts are assumed in a direct proof of the theorem?
In a direct proof of the theorem "if r and s are rational numbers, then the product of r and s is a rational number," the following assumptions or facts are typically used:
Definition of rational numbers: A rational number is defined as any number that can be expressed as the ratio of two integers.Closure property of rational numbers under multiplication: When two rational numbers are multiplied, the result is always a rational number.Properties of integers: When two integers are multiplied, the result is always an integer.Properties of fractions: When two fractions are multiplied, the result is obtained by multiplying their numerators and denominators separately.Using these facts, a direct proof of the theorem can be constructed by assuming that r and s are rational numbers and then showing that their product is also a rational number. Specifically, we can express r and s as fractions with integer numerators and denominators, multiply their numerators together to obtain the numerator of the product.
Since the numerator and denominator of the product are both integers, and the denominator is nonzero, the product is a rational number.
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a sphere has a radius of 17 feet. the volume of the sphere is increasing at a rate of 562 cubic feet per minute. what is the rate of change of the radius, in feet per minute, when the radius is 5 feet?
When the sphere has a radius of 5 feet, the radius is increasing at a very slow rate of 0.018 feet per minute if volume is increasing.
The volume of a sphere formula, V = (4/3)r3, must be used to determine the rate of change of the radius.
Using this formula's derivative with regard to time t, we obtain:
[tex]dV/dt = 4r2(dr/dt)[/tex].
Here, r: radius of the sphere, and we need to determine dr/dt, the rate of change of the radius when r=5. dV/dt is the rate of change of the volume, which is provided as 562 cubic feet per minute.
When we enter the provided values, we obtain:
[tex]562 = 4\pi (17)^2(dr/dt)[/tex]
0.018 feet per minute is equal to[tex]dr/dt = 562 / (4(17)2)[/tex].
As a result, the radius changes at a rate of about 0.018 feet per minute when the radius is 5 feet.
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The table shows the dimensions of two fenced-in areas at the dog park. How many times greater is the area enclosed by the wood fence than the area enclosed by the metal fence
The area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence. So the correct answer is d. 7 3/4.
What is area?When measuring the area of a shape, we are determining the amount of surface the shape takes up.
To calculate the area enclosed by each fence, we must multiply the length and width of each.
The area enclosed by the wood fence is
6 1/2 x 2 1/4 = 14 7/8 square yards,
and the area enclosed by the metal fence is
2 3/4 x 2 1/2 = 6 7/8 square yards.
To determine how many times greater the area enclosed by the wood fence is than the area enclosed by the metal fence, we must divide the area of the wood fence by the area of the metal fence:
14 7/8 / 6 7/8 = 7 3/4.
This means the area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence.
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four cards are drawn from a deck without replacement. find the probability all cards are black cards.
The probability that all four cards drawn from a deck are black cards is 1/4165.
There are 26 black cards and 52 cards in a standard deck of cards. Therefore, the probability of drawing a black card from a standard deck of cards is 26/52 or 1/2. In the first draw, there are 26 black cards out of 52 cards, so the probability of drawing a black card is 26/52.
In the second draw, there are 25 black cards left out of 51 cards, so the probability of drawing a black card is 25/51. In the third draw, there are 24 black cards left out of 50 cards, so the probability of drawing a black card is 24/50. In the fourth draw, there are 23 black cards left out of 49 cards, so the probability of drawing a black card is 23/49.
Using the multiplication principle of probability, the probability that all four cards drawn from a deck are black cards is 26/52 × 25/51 × 24/50 × 23/49 = 1/4165.
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consider a data set of 900 values that exhibits a normal distribution in which the mean is 90 and the standard deviation is 8. how many values in the data set are between 86 and 98?
The data set which consists of 900 values that follow a standard normal distribution with a mean of 90 and a standard deviation of 8 has 480 values that lie between 86 and 98.
We need to determine how many values in the data set lie between 86 and 98. The formula for calculating the Z-score is as follows: Z = (X - μ) / σwhereX = the value of interestμ = the meanσ = the standard deviation
Using this formula, we can find the Z-scores for the lower and upper bounds of the range as follows:Z lower = (86 - 90) / 8 = -0.5Z upper = (98 - 90) / 8 = 1.0We can then look up these Z-scores in the standard normal distribution table to find the corresponding probabilities.
Using the table, the probability of a Z-score being less than -0.5 is 0.3085, and the probability of a Z-score being less than 1.0 is 0.8413. Therefore, the probability of a Z-score being between -0.5 and 1.0 is:0.8413 - 0.3085 = 0.5328
Finally, we can convert this probability to the number of values in the data set that lie between 86 and 98 by multiplying it by the total number of values in the data set:900 x 0.5328 = 479.52 values
Therefore, there are approximately 480 values in the data set that lie between 86 and 98.
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PLEASE HELP FAST (giving brainliest)
First one is 6
second one is 12
third one is -8
hope this helps
Answer:
Step-by-step explanation:
x=6
x=12
x=-8
the most recent census for a city indicated that there were 909,327 residents. the population of the city is expected to increase at an annual rate of 3.6 percent each year for the next 12 years. what will the population be at that time?
Option B) 1,390,072 is correct. The population of the city after 12 years can be calculated using the formula for compound interest.
To calculate the population of a city after 12 years using the formula for compound interest, we first need to identify the initial population (P0), the annual interest rate (r), and the number of years (n). We can then plug these values into the formula P = P0(1 + r/100)ⁿ. In this case, the initial population is given as 909327, the annual interest rate is 3.6%, and the number of years is 12. By substituting these values into the formula, we get P = 909327 * (1 + 3.6/100)¹² ≈ 1390072, which represents the population of the city after 12 years. Therefore, option B) 1,390,072 is the correct answer.
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Complete question:
The most recent census for a city indicated that there were 909,327 residents. the population of the city is expected to increase at an annual rate of 3.6 percent each year for the next 12 years. what will the population be at that time?
A) 1,491,958
B) 1,390,072
C) 1,440,114
Please HELP ME HELPPPPP
Answer:
bar chart
Step-by-step explanation:
you are right box plot, histogram and a circle graph aren't the right ones
Help me please please
The line of sight distance using the angle of depression 13° is derived to be 2222.71 m to the nearest hundredth meters.
What is an angle of depressionThe angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards.
Considering the right triangle formed by the height of the tower and the complementary angle 77°, we shall represent the line of sight distance for the television camera to the base of the stadium with x so that;
cos 77° = 500/x {adjacent/hypotenuse}
note that 90° - 13° = 77°
x = 500/ cos 77° {cross multiplication}
x = 2,222.7057.
Therefore, the line of sight distance for the television camera to the base of the stadium to the nearest hundredth meters is equal to 2,222.71. Using the trigonometric ratio of cosine for the angle 77° which is complementary to the angle of depression 13°
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your neighborhood fast food restaurant only sells chicken nuggets in packs of five or seven. what is the largest number of nuggets that is impossible to order?
The largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven.
The largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven. This is because the restaurant only sells nuggets in packs of five and seven. This means that if you wanted to order eleven nuggets, it would not be possible.
To explain this mathematically, eleven can be written as 5+5+1, 7+4, or 3+3+3+2. As none of these can be made with just five and seven packs of chicken nuggets, it is impossible to order eleven.
If the restaurant sold chicken nuggets in packs of three and seven, then it would be possible to order eleven nuggets (3+3+3+2).
In conclusion, the largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven.
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please help me with these questions plaese hurry need these today
For numbers 1-6, using the order of operations to evaluate each expression is given as follows:
[tex](8.15 x 4 + 5) x 3.2 = 120.32\\12 + 5 + 32 x 2.2 = 87.4\\17 + 8 x (2.7 + 6) - 3 = 83.6\\38.9 - 2.3 x 1.5 + 2.6 = 37.05\\0.2 x (5 - 0.7) + 1.8 + 2 = 4.66\\5 + (8.06 - 12.5 + 2) = 4.56[/tex]
Define pοlynοmial equatiοn.A pοlynοmial equatiοn is an equatiοn in which a pοlynοmial expressiοn is set equal tο anοther expressiοn οr tο zerο. It is an algebraic equatiοn that invοlves οne οr mοre terms in which the variables are raised tο a pοsitive integer pοwer and multiplied tοgether. The degree οf the pοlynοmial is the highest pοwer οf the variable in the pοlynοmial equatiοn.
(8.15 x 4/5) x 3.2
= (6.52) x 3.2 (Perfοrming multiplicatiοn befοre divisiοn)
= 20.86
2. 12/5+32 x 2.2
= 2.4 + 70.4 (Perfοrming multiplicatiοn befοre additiοn)
= 72.8
3. 17+8 x (2.7/6)-3
= 17 + 1.2 - 3.0 (Perfοrming divisiοn befοre multiplicatiοn and subtractiοn)
= 15.2
4. 38.9 - 2.3 x 1.5 + 2.6
= 38.9 - 3.45 + 2.6 (Perfοrming multiplicatiοn befοre subtractiοn)
= 37.05
5. 0.2 x (5 - 0.7) + 1.8 / 2
= 0.2 x 4.3 + 0.9 (Perfοrming subtractiοn inside the parentheses)
= 1.12
6. 21.5/5+(8.06-12.5/2)
= 4.3 + 1.53 (Perfοrming divisiοn befοre subtractiοn and additiοn inside the parentheses)
= 5.83
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Which of the cross sections described would result in a rectangle with a height of
inches (in.)?
A.A horizontal cross section through the center of a sphere with a radius of 4 in.
B. A horizontal cross section through the center of a cone with a radius of 4 and a height of 4 in.
C. A vertical cross section through the center of a cone with a radius of 4 and a height of 4 in.
D. A vertical cross section through the center of a cylinder with a radius of 4 and a height of 4 in.
Answer:B. A horizontal cross section through the center of a cone with a radius of 4 and a height of 4 in.
Step-by-step explanation:
Solve each of the given inequalities for z. Which of the inequalities has 5 as a solution?
Inequality 1 Inequality 2
(4(2.8z + 1.75) > - 26.6) (2(1.9z + 1.5) <= 18.2)
Answer: Inequality 1
Step-by-step explanation: Let's solve each inequality first.
4(2.8z+175 )>-26.6
let's distribute the 4.
4(2.8z)+4(175)
11.2z+700>-26.6
Now let's isolate the variable by subtracting 700 on each side.
11.2z>-726.6
Now let's divide both sides by 11.2
z>-64.875
Oh? This one already has 5 as a solution as 5 is more than -64.875!
How do I work this out?
a.) The mode for the chart is 24.
b.) The probability that the winning score will be 25 = 7/50
C.)The probability that the winning score will be 23 or more = 37/50.
How to calculate the probability of the selected outcomes?The number of times the game is played = 50 times
The number of games that showed the score of 25= 7
The probability of winning a score of 25 = 7/50
The scores that are 23 and above; 10+14+7+4+2= 37
The probability of winning a score of 23 and above = 37/50
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Find the value of x in the triangle
Answer:
x = 40
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
65 + 75 + x = 180
140 + x = 180 ( subtract 140 from both sides )
x = 40
Answer: x = 40
Step-by-step explanation:
In a triangle, all the angles add up to 180 degrees.
In this case, 65 + 75 + x = 180.
Add the 65 and 75 together using column addition:
65
+75
-------
140
Now, the equation is 140 + x = 180
Subtract 140 from both sides:
x = 40
Therefore, x is 40.
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
11, 18, 35, 39, 45, 45, 46, 47, 49, 49, 50, 50, 50, 50, 56, 57, 58, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 45.2 is the most accurate to use to show that they need more money.
The median of 49 is the most accurate to use, since the data is skewed.
The mean of 49 is the most accurate to use to show that they have plenty of money.
The mean of 45.2 is the most accurate to use, since the data is skewed.
The median of 49 is the most accurate to use, since the data is skewed.
What is distribution?Distribution refers to the pattern of variation in a dataset. Specifically, it refers to how the values in the dataset are spread out or clustered together.
According to question:The most appropriate measure of center to represent the data depends on the shape of the distribution. In this case, we can see from the histogram that the data is skewed to the right, with a longer tail of higher values.
In skewed distributions, the median is generally a more appropriate measure of center than the mean. This is because the mean can be influenced by extreme values in the tail of the distribution, whereas the median is more resistant to such outliers.Therefore, the correct answer is: the median of 49 is the most accurate to use, since the data is skewed. This represents the middle value of the data when it is arranged in order, and is less sensitive to the outliers at the high end of the distribution. Using the median can give a more accurate representation of the typical donations received by the charity.
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intelligence quotient (iq) scores are normally distributed with a mean of 100 and a standard deviation of 15. according to j.k rowling, there are about 1000 students at hogwart's school of witchcraft and wizardry. how many students would you expect to have an iq of 140 or above?
We would expect around 3 students to have an IQ of 140 or above at Hogwarts School of Witchcraft and Wizardry.
Based on the given information, we can use the normal distribution formula to calculate the number of students expected to have an IQ of 140 or above.
To explain this, we can use the following steps:
1. Calculate the z-score for an IQ of 140 using the formula: z = (x - μ) / σ where x is the IQ score, μ is the mean IQ score and σ is the standard deviation.
z = (140 - 100) / 15 = 2.672. Look up the probability of a z-score of 2.67 or above using a standard normal distribution table or calculator. This gives us the proportion of the population with an IQ of 140 or above.
P(z ≥ 2.67) = 0.00383. Multiply the proportion by the total number of students to get the expected number of students with an IQ of 140 or above.
Expected number = 0.0038 x 1000 = 3.8Since we cannot have a fraction of a student, we can round this to the nearest whole number to get the final answer.
Therefore, we would expect around 3 students to have an IQ of 140 or above at Hogwarts School of Witchcraft and Wizardry.
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a supply container dropped from an aircraft by parachute hits a target with a probability of 0.37. (a) what is the expected number of container drops needed to hit a target?
The given probability is 0.37 which is the probability of a supply container dropped from an aircraft by a parachute hitting a target. So the expected number of container drops needed to hit a target is approximately 2.7027.
To find out the expected number of container drops needed to hit a target, we can use the formula given below;
E(X) = (1/p) E(X)
= (1/0.37)E(X)
= 2.7027
Thus, the expected number of container drops needed to hit a target is approximately 2.7027.
An expected value is a statistical concept that represents the theoretical average value of a random variable. It is represented as E(X).
The expected value is calculated by multiplying each possible value of the random variable by its probability and then adding all of the products.
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the annual increase in height of cedar trees is believed to be distributed uniformly between seven and twelve inches. find the probability that a randomly selected cedar tree will grow more than 8 inches in a given year. round your answer to four decimal places, if necessary
The annual increase in height of cedar trees is believed to be distributed uniformly between seven and twelve inches. 0.8 is the probability that a randomly selected cedar tree will grow more than 8 inches in a given year.
The annual increase in height of cedar trees is believed to be distributed uniformly between seven and twelve inches.
To find the probability that a randomly selected cedar tree will grow more than 8 inches in a given year, the following steps should be followed:
Calculate the range of increase in height of cedar trees:
The range of increase in height is
(12 - 7) = 5 inches.
Calculate the probability that a cedar tree will grow more than 8 inches:
P(X > 8) = (12 - 8) / 5 = 0.8
where X is the annual increase in height of a cedar tree.
Round the answer to four decimal places:
Therefore, the probability that a randomly selected cedar tree will grow more than 8 inches in a given year is 0.8000 or 0.8 (rounded to four decimal places).
Probability can be defined as the measure of how likely an event is to occur.
The probability of an event ranges between 0 and 1, where 0 denotes that the event will not occur and 1 denotes that the event will certainly occur.
If a random variable X has a uniform distribution over an interval (a, b), then the probability of X falling between two values c and d is given by:
P(c < X < d) = (d - c) / (b - a)
In this problem, the annual increase in height of cedar trees is believed to be distributed uniformly between seven and twelve inches.
Therefore, the probability that a randomly selected cedar tree will grow more than 8 inches in a given year is: P(X > 8) = (12 - 8) / (12 - 7) = 4 / 5 = 0.8 (rounded to four decimal places).
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if you're good at quadratics...
Therefore, the correct answer is: [tex](x+10)^2=82[/tex]. ( right hand side of the equation).
What is equation?An equation is a mathematical statement that indicates that two expressions are equal. It typically contains variables, which are represented by letters, and may also include constants and operators. The general format of an equation is:
expression = expression
For example, the equation x + 2 = 6 means that the expression x + 2 is equal to the expression 6. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.
To solve the quadratic equation by completing the square, Jamie needs to follow the steps:
Move the constant term to the right-hand side of the equation:
[tex]x^2 + 20x = -18[/tex]
Add and subtract the square of half the coefficient of x to the left-hand side of the equation:
[tex]x^2 + 20x + (20/2)^2 - (20/2)^2 = -18[/tex]
[tex](x+10)^2 - 100 = -18[/tex]
Simplify the right-hand side of the equation:
[tex](x+10)^2 = 82[/tex]
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Can you help me with this and can you show the working
Step-by-step explanation:
Apply the power rule and multiply the exponents
Jarvis and his family are at the dine-in movies and wish to purchase some popcom. A large popcom costs $18 and a small popcom costs $12. Jarvis offered to pay for the popcom with $50 in his wallet.
Create an inequality in standard form that describes this situation.
Use the given numbers and the following variables.
• x = the number of large popcoms
• y = the number of small popcorn
Answer:
18x + 12y ≤ 50
Step-by-step explanation:
Let x be the number of large popcoms and y be the number of small popcoms.
The cost of a large popcom is $18, and the cost of a small popcom is $12. The total cost of purchasing x large popcoms and y small popcoms is given by:
Total cost = 18x + 12y
The problem states that Jarvis has $50 in his wallet to pay for the popcoms. Therefore, we can write the following inequality:
18x + 12y ≤ 50
This inequality represents the situation where Jarvis and his family want to purchase popcoms, and Jarvis has $50 to spend. The inequality ensures that the total cost of the popcoms does not exceed $50.
What are the solutions of the equation -3+sin(-3x)=-7/2 on the interval [0,π) ?
Answer:
We have the equation:
-3 + sin(-3x) = -7/2
Adding 3 to both sides gives:
sin(-3x) = -1/2
The solutions for sin(x) = -1/2 are x = 7π/6 and x = 11π/6 in the interval [0, 2π).
We need to find the solutions for -3x in the interval [0, π).
For x = 7π/18, we get -3x = -7π/6, which is not in the given interval.
For x = 5π/18, we get -3x = -5π/2, which is not in the given interval.
For x = π/18, we get -3x = -π/2, which is in the given interval.
Therefore, the solution to the equation in the given interval is:
-3x = -π/2
x = π/6
Gina Wilson All things Algebra Unit 10 Homework 6 answer key
Examining the figures of the circles, the values for x is calculated to be
11. x = 8
12. ED = 11
How to solve for xThe value of x in the two figure is solved using the relationship between secant and angle measures
11. The formula used here is
(2x + 7) = 0.5 * (78 - 32)
(2x + 7) = 0.5 * (46)
2x + 7 = 23
solving for x
2x = 23 - 7
2x = 16
x = 8
12.
11x - 9 = 0.5 ( (15x-39) - (9x-3) )
11x - 9 = 0.5 ( 15x - 39 - 9x + 3 )
11x - 9 = 0.5 ( 6x - 36 )
11x - 9 = 3x - 18
11x + 3x = -18 + 9
14x = -9
x = 14/9 = 1.56
solving for
ED = 9x - 3 = 9 * 14/9 - 3 = 14 - 3 = 11
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bethany used data of the money she earned over the past 5 years to estimate the amount she would earn 10 years from now. this is an example of: group of answer choices
Extrapolation is a useful tool for predicting future values based on past data
Bethany used a method of predicting future values from past values known as extrapolation. Extrapolation is a powerful tool for predicting future values, but it is important to remember that it only works if the underlying trend in the data does not change. In Bethany's case, she is making an assumption that her income over the next 10 years will follow the same trend as it did in the past 5 years.
In extrapolation, the assumption is that the data points that were observed in the past will continue in the same direction and with the same intensity into the future. Therefore, extrapolation can be used to make predictions about future values even when no new data points have been collected. It is important to remember, however, that any predictions made using extrapolation are only estimates and may not be accurate.
Extrapolation is used in many different fields, such as finance, economics, medicine, engineering, and even weather forecasting. For example, stock analysts may use extrapolation to make predictions about future stock prices based on past prices. Similarly, meteorologists may use extrapolation to make predictions about future weather conditions based on historical weather data.
Overall, extrapolation is a useful tool for predicting future values based on past data. However, it is important to remember that it only works when the underlying trend in the data does not change. Additionally, any predictions made using extrapolation are only estimates and may not be accurate.
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F(x)=x2-x3-4 What is the axis of symmetry of the following equation?
The axis of symmetry of equation f(x) = x² - x³ - 4 is x = 2/3.
The axis of symmetry is a vertical line that passes through the vertex of a parabolic function, which is the highest or lowest point on the graph depending on the direction of the parabola. The equation f(x) = x² - x³ - 4 is a cubic function that can be written in standard form as:
f(x) = -x³ + x² - 4
To find the axis of symmetry, we need to first find the x-coordinate of the vertex. This can be done by taking the derivative of f(x) and setting it equal to zero:
f'(x) = -3x² + 2x = 0
x(2-3x) = 0
x = 0 or x = 2/3
Since the coefficient of the x³ term is negative, the vertex of the cubic function is a maximum. Therefore, the axis of symmetry is the vertical line passing through the x-coordinate of the vertex, which is x = 2/3.
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ANSWER THIS WITHIN ONE HOUR OR ELSE I WILL BE DOOMED
mARKING BRAINLIEST
PS: FILL IN THE SHEET DONT JUST GIVE AN ANSWER
The prompt on fractions is given as follows:
1 ) (1/2) ÷ 4 = 1/8
2) ( 1/5) ÷ 2 = 1/10
3) (1/3) ÷ 5 = 1/15
4) (1/4) ÷ 4 = 1/16
5) The solution to the puzzle for (1/2) ÷ 3 is given below.
The calculations are given as follows;
1 )
= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]
= 1/8
2) (1/5) ÷ 2
= (1/5) x (1/2)
= 1/10
3)
(1/3) ÷ 5
= (1/3) x (1/5)
= 1/15
4) (1/4) ÷ 4
= (1/4) x (1/4)
= 1/16
5) Mary had 1/2 of a pie that she wanted to share with 3 of her friends. She decided to divide it equally among them. Each friend got 1/6 of the pie. To check, Mary multiplied 1/6 by 3 and got 1/2. This shows that (1/2)/3 equals 1/6, since dividing by 3 is the same as multiplying by its reciprocal, 1/3.
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Y is the midpoint of WX and WX ⟂ VY. Complete the proof that △VWY≅△VXY. V W X Y Statement Reason 1 Y is the midpoint of WX Given 2 WX ⟂ VY Given 3 ∠VYW≅∠VYX Additive Property of Length All right angles are congruent Definition of angle bisector Definition of equilateral triangle Definition of midpoint Vertical Angle Theorem 4 WY ≅ XY Definition of midpoint 5 VY ≅ VY Reflexive Property of Congruence 6 △VWY≅△VXY SSS CPCTC Definition of congruence SAS SSS
According to the Vertical Angle Theorem, two opposing vertical angles that are created when two lines cross one other are always equal to one another.
The opposing angles created by the junction of two lines are known as vertical angles or vertically opposed angles. A pair of angles that are vertically opposed to one another are always equal. Moreover, a vertical angle and the angle to which it is next are supplementary angles, meaning their sum is 180 degrees.
WH ⊥ VZ at y ,
Y is the midpoint of WX
Now since only one line can pass through W and Y ,
X must lie WH
Either W-Y-X-H of W-Y-H-X.
In any case W, Y, X and H are collinear.
Since, WH ⊥ VZ ⇒ WX ⊥ VZ at Y.
m∠VYW = m∠VYX = 90°
∠VYW ≅ ∠VYX = 90°.
Next,
Y is midpoint of WX
WY = XY
WY ≅ XY
Finally, VZ bisects ∠WYX
m∠WVY = m∠XVY
∠WVY ≅ ∠XVY
Using 1, 2, 3
ΔVWY ≅ ΔVXY by Right Hypotenuse side Congruency,
Alternatively ,
using 2, 3 and
VY ≅ VY
ΔVWY ≅ ΔVXY (by SSS congruence )
Using equations,
ΔVWY ≅ ΔVXY
by SAS congruence,
ΔVEY = ΔVXY by ASA Congruence
ΔVNY ≅ ΔVXY by AAS congruence
ΔVWY ≅ ΔVXY by AAS congruence.
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A spinner is divided into five colored sections that are not of equal size: red, blue,
green, yellow, and purple. The spinner is spun several times, and the results are
recorded below:
Spinner Results
Color Frequency
Red
Blue
Green
Yellow
Purple
14
6
12
4
16
Based on these results, express the probability that the next spin will land on purple
as a fraction in simplest form.
Answer: the answer is 21 percent
Step-by-step explanation:
when you have 16 of 52 which is all of the colors together then it will give you 21%
Answer:
21% or 4/13
Step-by-step explanation:
when you have 16 of 52 which is all of the colors together, then it will give you 21%
For fractions, you have 16 of 52, then you can simplify the fraction down to 4/13. Giving you the answer of a simplified fraction.
Find the quotient 9,280 divided by 32
Answer: 290.
Step-by-step explanation:
9,280
How many times can 32 go into 9? no times.
How many times can 32 go into 92? 2 times.
2880 remaining.
How many times can 32 go into 2? no times.
How many times can 32 go into 28? no times.
How many times can 32 go into 288? 9 times.
00 remaining.
Since there is an extra zero, you add a zero to your final answer.