The simplification of each sum or difference of given expression [tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}[/tex] is equal to (-3)(2y+1)/ (2y-1). Restriction on the variables is given by y ≠1/2.
As given in the question,
Given expression is [tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}[/tex]
Simplify the expression by taking the least common multiple
[tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}\\\\= \frac{-5y-y-3}{2y-1}\\ \\= \frac{-6y-3}{2y-1}\\ \\= \frac{-3(2y+1)}{2y-1}[/tex]
Restriction on the variables is given by y ≠1/2.
Therefore, the simplification of each sum or difference of given expression [tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}[/tex] is equal to (-3)(2y+1)/ (2y-1). Restriction on the variables is given by y ≠1/2.
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Unit Test, Part 2: Working with Data
Answer the questions. When you have finished, submit this assignment to your teacher by the due date for full
credit
Fy
Total score: of 20 points
Answer:
Styles
(
(Score for Question 1: of 9 points)
1. The data set shows the fuel efficiencies, in miles per gallon, of the vehicles featured in a car-buying guide.
26 31 40 28 19 23 35 38 43 46 28 30
(a) What is the five-number summary of the data set?
(b) What is the range of the data set? Show your work
(c) What is the interquartile range (IQR) of the data set? Show your work.
The data set's interquartile range (IQR) is 12 and the data set's range is expressed as a five-number summary at 46.
Interquartile range: what is it?The interquartile range is a measure of statistical dispersion, or the spread of the data, in descriptive statistics. The middle 50%, fourth spread, or H-spread are further names for the IQR.The discrepancy between a data set's 75th and 25th percentiles.
ACCORDING TO GIVEN STATEMENT;
Firstly, arrange the data.
19 23 26 28 28 30 31 35 38 40 43 46
a) 5 number summary
-min value = 19
- Q1= (26+28/2) = 27
- Q2/ Median = (30+31/2)= 30.5
- Q3= (38+40/2)= 39
- Max value= 46
b) range= max value-min value
∴46-19= 21
c)interquartile range = Q3-Q1
= 39-27
=12
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Francisco’s game involves a bag of 3 green, 2 yellow, 4 red, and 3 black marbles. andrew wants to increase the likelihood of selecting a yellow marble. how can the game be modified to make drawing a yellow marble more likely? select all that apply. andrew should add more green marbles to the bag. andrew should add more yellow marbles to the bag. andrew should remove from the bag 1 green, 1 black, and 2 red marbles. andrew should add more black marbles to the bag. andrew should triple the number of yellow marbles in the bag.
From the options given, the options that can increase the likelihood of selecting a yellow marble can be determined by finding out the probability of selecting the yellow marble.
Probability is method of determining a numerical occurrence of a outcome from the set of all possible outcomes of an events. The value is expressed from zero to one.
Probability (Event)= Favorable Outcomes(x)/Total Outcomes(n)
Hence,
n=total number of marbles=3+2+4+3=12
x=no of yellow marbles=2
Probability=2/12=1/6
In order to increase the probability of choosing a yellow marble, let consider the options.
Andrew should add more green marbles to the bag.
Increasing green by say 2
Probability=2/14=1/7<1/6
Andrew should add more yellow marbles to the bag.
Increasing yellow by say 3
Probability=5/15=1/3>1/6
Andrew should remove from the bag 1 green, 1 black, and 2 red marbles.
Decreasing the said marbles
Probability=2/8=1/4>1/6
Andrew should add more black marbles to the bag.
Increasing black by 2
Probability=2/14=1/7<1/6
Andrew should triple the number of yellow marbles in the bag.
Increasing yellow marble by 2x3=6
Probability=6/16=3/8>1/6
Hence, the options of making the likelihood of yellow drawing more would be Andrew should add more yellow marbles to the bag, Andrew should remove from the bag 1 green, 1 black, and 2 red marbles and Andrew should triple the number of yellow marbles in the bag.
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Please help me understand this problem!
Answer:
30 degrees.
Step-by-step explanation:
I included a picture to solve for X. Once you have X, we know that angle a=A= x + 39.
Doing the math on the paper, we know that X= - 9, therefore - 9 + 39 = 30.
Thus, angle A is equal to 30 degrees.
I NEED HELP THIS IS DUE TODAY
Answer:
B is the correct answer:)) explanation up top
Solve each equation. 3(2 z+1)=35
The solution of the given linear equation in one variable 3(2z +1) = 35.
According to the given question.
We have a linear equation in one variable 3(2z + 1) = 35.
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Therefore, the solution of the given linear equation in one variable is given by
3(2z + 1) = 35
⇒ 6z + 3 = 35 (by distributive rule)
⇒ 6z = 35 - 3 (subtracting 3 from both the sides)
⇒ 6z = 32
⇒ z = 32/6 (dividing both the sides by 6)
⇒ z = 16/3
Hence, the solution of the given linear equation in one variable 3(2z +1) = 35.
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Emma and Ben each have some money.
Hafid has no money.
Emma gives £8 to Hafid.
Ben gives £3 to Hafid.
Now they all have the same amount of money.
How much did Emma have to begin with
Emma initially had £19 as the amount of money she initially had at the beginning
How to calculate the amount of money that Emma has ?Emma gives £8 to Hafid
Ben gives £3 to Hafid
The total amount of money that Hafid can be calculated by adding Emma and Ben's money together.
= 3 + 8
= 11
They all have the same amount of money.
Emma initial amount can be calculated by adding 11 and the amount of money Emma gives to Hafid
= 11+8
= 19
Hence Emma initially had £19
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You are designing a house with three 3-foot windows across the back. There are 4 feet
between the edge of the house and the end windows. The total width of the house is 33
feet. How far apart are the windows?
The windows of house are 8 feet apart distance.
As we are provided with the the total width of house is 33 feet and 4 feet distance between the edge of the house and the end windows
So the space available for the windows is total width of the house minus the distance between the edge of the house and the windows from both the sides = 33 - 2(4) = 33-8 = 25 feet
The length of the windows to be inserted is the product of number of windows and their side = 3 × 3 = 9 feet
The total distance between the windows can be find out by reducing the distance covered by windows from the area available for windows = 25feet - 9 feet = 16 feet
There are three windows, so there will be only 2 gaps whose length is 16 feet / 2 = 8 feets
Hence, the windows of the house are 8 feet apart
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The local gym holds two 45-minute workout sessions and four 30-minute sessions each week. Judy attended all of the sessions this week but left 5 minutes early during the 30-minute sessions and 10 minutes early during the 45-minute sessions. How many total minutes did Judy work out for the week?
170 minutes
190 minutes
65 minutes
75 minutes
Answer: 75
Step-by-step explanation:
The total number of minutes Judy worked out for the week was 170 minutes. The correct option is the first option 170 minutes
Calculating timeFrom the question, we are to determine the total number of minutes Judy worked out for the week
From the given information,
The gym holds two 45-minute workout sessions and four 30-minute sessions each week
Thus,
The total number of minutes the gym holds workout sessions is
2 × 45 + 4 × 30
= 90 + 120
= 210 minutes
Also, from the information,
Judy left 5 minutes early during the 30-minute sessions and 10 minutes early during the 45-minute sessions
The total number of minutes Judy didn't attend is
2 × 10 + 4 × 5
= 20 + 20
= 40 minutes
Then,
The total number of minutes Judy worked out for the week was
210 minutes - 40 minutes
= 170 minutes
Hence, the total number of minutes Judy worked out for the week was 170 minutes. The correct option is the first option 170 minutes
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A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.
a. Suppose two trials of this experiment are conducted. Are the events independent or dependent? Explain.
Both can be seen as individual events. thus the events are independent.
Which pair of events are called independent events?When one event's occurrence or non-occurrence doesn't affect occurrence or non-occurrence of other event, then such events are called independent events.
Symbolically, we have:
Two events A and B are said to be independent iff we have:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Given that; A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.
The probability of selecting the chip is green;
= 5/20
= 1/4
The probability of selecting the chip is brown;
= 4/20
= 1/5
the probability that the first chip is green and the second is brown
= 1/4 x 1/5
= 1/20
Both can be seen as individual events. thus the events are independent.
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Find the mean of the data summarized in the given frequency distribution. compare the computed mean to the actual mean of miles per hour. speed (miles per hour) 4245 4649 5053 5457 5861 frequency
47.4 is the mean of the data summarized in the given frequency distribution.
What is a frequency distribution?
The number of times a value appears in a dataset is its frequency. The pattern of frequencies for a variable is known as a frequency distribution. The frequency with which each potential value of a variable appears in a dataset.speed m f m*f
42-45 43.5 22 957
46-49 47.5 14 665
50-53 51.5 7 360.5
54-57 55.5 4 222
58-61 59.5 2 119
Total 49 2323.5
mean = 2323.5/49 = 47.4
The computed mean is not close to the actual mean because the difference between the means is more than 5%.
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Does anyone know the answers to these?
The results for each case of congruence are listed below:
9) Congruent
10) No congruent
11) No congruent
12) Congruent
13) Congruent
14) No congruent
Are two line segments congruent to each other?
There are several ways to determine if two line segments are congruent to each other. One form consists in finding the vector associated with each line segment and the length is found by the Pythagorean theorem:
Now we proceed to show how to apply the vector criterion:
9) AB = (- 4, 8) - (- 4, 5) = (0, 3), CD = (2, 0) - (2, - 3) = (0, 3).
AB = 3, CD = 3. Congruent
10) AB = (1, - 1) - (6, - 1) = (- 5, 0), CD = (4, - 3) - (2, - 3) = (2, 0).
AB = 5, CD = 2. No congruent
11) AB = (- 1, 3) - (8, 3) = (- 9, 0), CD = (5, 3) - (5, 10) = (0, - 7).
AB = 9, CD = 7. No congruent
12) AB = (6, 1) - (6, - 8) = (0, 9), CD = (- 2, - 2) - (7, - 2) = (- 9, 0).
AB = 9, CD = 9. Congruent
13) AB = (- 5, - 1) - (- 5, 6) = (0, - 7), CD = (3, 3) - (- 4, 3) = (7, 0).
AB = 7, CD = 7. Congruent
14) AB = (3, - 4) - (10, - 4) = (- 7, 0), CD = (- 1, 5) - (- 1, 2) = (0, 3).
AB = 7, CD = 3. No congruent
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Evaluate the expression for the given value of the variable 4|3x-1| - |9x+6| ; x=-5
Answer: 5
Step-by-step explanation:
4|3x-1| - |9x+6| ; x=-5
Insert 5 into the x's
4|3(5)-1| - |9(5)+6|
Multiply the 5's
4|(15)-1| - |(45)+6|
Now add/subtract within the absolute values
4|14| - |51|
Get rid of the absolute vaules
4(14) - 51
Multiply 4(14) = 56
56 - 51 = 5
Kendra and her horse completed the barrel racing in 15.839 seconds. What is this number rounded to the nearest tenth?
Answer:
15.8
Step-by-step explanation:
To round to nearest tenth we only go so far as the first decimal place. If the second decimal digit is less than 5 we leave that number as it is otherwise we increase it by 1
In 15.839, the second decimal digit is 3 so we get 15.8
(If it had been 15.864 then it would be 15.9)
Which shows 0.00234 written in scientific notation?
A 2.34 ×10⁵
B 2.34× 10³
C 2.34 × 10⁻²
D 2.34 × 10⁻³
is 8.141141114 a ratinial number
Based on the number given of 8.141141114, it is NOT a rational number.
What is a rational number?A rational number refers to one that does not extend to infinity after the decimal. Some rational numbers will extend to infinity but they will have repeating numbers such as 0.3333333333.
The number 8.141141114, is not a rational number because it extends into infinity and the numbers after the decimal point are nonrepeating.
In conclusion, 8.141141114 is not a rational number.
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32^10-33x^5+1 find the real roots
By algebra properties, the roots of the quintic equation are approximately 541.159 with a multiplicity 5.
How to find the roots of polynomial by algebraic proceduresIn this problem we find a quintic equation, whose roots have to be found by using algebra rules:
33¹⁰ - 33 · x⁵ + 1 = 0
33 · x⁵ = 33¹⁰ + 1
x⁵ = (33¹⁰ + 1) / 33
x⁵ = 33⁹ + 33⁻¹
x = [tex]\sqrt[5]{33^{9}+33^{- 1}}[/tex]
x ≈ 541.159
By using algebra properties, the roots of the quintic equation are approximately 541.159 with a multiplicity 5.
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Evaluate each
a. -4+|-5|-4
b. -3•-8
c. 32 divided by -2
Answer:
A is -3 B is 24 and c is -16
Step-by-step explanation:
Identify a pattern and find the next three numbers in the pattern. 5,3,1,-1, . . .
The next three numbers of the sequence are -3, -5, -7,........
What is an arithmetic progression?An arithmetic progression, or AP, is a series in which the next term is derived from the previous one. by modifying the previous word with a constant d known as the common difference. The arithmetic progression is if the first term of the series is a, a + d, a + 2d, a + 3d, ...
The given pattern forms an Arithmetic progression (A.P.)
The sequence is - 5 , 3, 1, -1, -3, -5, -7,........
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Smiling is a facial expression of happiness or contentment. In math, what is the expression that represents the quotient of 3 and 3 less than a number?
A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.
The expression that represents the quotient of 3 and 3 less than a number is 3/(x - 3).
What is an expression?A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms. In order to help establish the order of operations and other elements of logical syntax, mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.Depending on the semantics associated with the expression's symbols, this value is determined.Let, x be a number
So the expression is, 3/(x - 3)
A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.
The expression that represents the quotient of 3 and 3 less than a number is 3/(x - 3).
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O Rachel was checking the weight of a gold nugget and a piece of fool's gold. Together
they weighed 120.5 grams. If the fool's gold was 23.90 grams, how much did the gold
nugget weigh?
Answer:
96.6
Step-by-step explanation:
120.5 subtracted by 23.90 give you how much the gold nugget weight.
Identify a pattern and find the next three numbers in the pattern.
1,4,3,6,5, . . .
The pattern exists described as a sequence of repeating objects, shapes, or numbers.
The pattern follows the rule(+3) and (-1).
The next three numbers is 8, 7, 10.
The numbers in the pattern be 1, 4, 3, 6, 5, 8, 7, 10.
What is meant by pattern?A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
Let the numbers in the pattern be 1, 4, 3, 6, 5, . . .
1(+3) = 4
4(-1) = 3
3(+3) = 6
6(-1) = 5
5(+3) = 8
8(-1) = 7
7(+3) = 10
The pattern follows the rule (+3) and (-1).
The next three numbers is 8, 7, 10.
Therefore, the numbers in the pattern be 1, 4, 3, 6, 5, 8, 7, 10.
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A construction worker makes $30.62 an hour. If they worked 45 hours a week and 50 hours the second week, how much will they get paid? (remember overtime is anthing over 40 hours and is one and a half times their pay.) Round to the nearest cent.
Using unitary method, it is found that the total money construction worker get paid will be 2908.5 dollars.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We have been given that construction worker makes $30.62 an hour. If they worked 45 hours a week and 50 hours the second week, then we need to find how much will they get paid.
For an hour he get paid = $30.62
For 45 hours a week = 30.62 x 45
= 1377.9 dollars
For 50 hours the second week = = 30.62 x 50
= 1531 dollars
The total money he get paid will be; 1377.9 + 1531 = 2908.5 dollars.
Hence, the total money construction worker get paid will be 2908.5 dollars.
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Elizabeth wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a 17 ∘ ∘ angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch if necessary.
If Elizabeth wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a 17 ∘ ∘ angle of elevation from the ground. How high will the ramp rise from the ground at its highest end is: 7.895 inches.
HeightGiven:
Sheet of fiberboard=27 inches
Angle of elevation=17°
Height (h)=?
Hence,
Sin 17°=h/27
h=27 Sin 17°
h=27×0.2924
h=7.8948 inches
h=7.895 inches (Approximately)
Therefore If Elizabeth wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a 17 ∘ ∘ angle of elevation from the ground. How high will the ramp rise from the ground at its highest end is: 7.895 inches.
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ALGEBRA The Ross Family drove 300 miles to visit their grandparents. Mrs. Ross drove 70 miles per hour for 65% of the trip and 35 miles per hour or less for 20% of the trip that was left. Assuming that Mrs. Ross never went over 70 miles per hour, how many miles did she travel at a speed between 35 and 70 miles per hour?
A 195
B 84
C 21
D 18
She has driven 84 miles at speeds ranging from 35 to 70 miles per hour.
The correct option is B.
What exactly is algebra in mathematics?Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions. In algebra, we utilize integers with definite or fixed values such as 2, 7, 0.068, and so on. In algebra, we use variables such as x, y, and z in addition to numbers. In algebra, signs are employed.
According to the given information:She drove 70 miles per hour for 65% of the journey hour.
So she covered = ((65)*100)*300
= 195 miles.
The remaining distance is 300 – 195 = 105 miles.
She drove just under 35 miles per hour for the remaining 20% of the route.
So she covered. = ((20)/100)*105
or 21 miles
So, totally she covered 195 +
21 or 216 miles at 70 miles per hour maybe less than 30 miles per hour However, since the trip is 300 miles long, this same remaining distance becomes 300 - 216 or 84 miles.
She has driven 84 miles at speeds ranging from 35 to 70 miles per hour.
The correct option is B.
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please help me with this
Answer: Angle R is 15.8 and angle S is 15.4.
Step-by-step explanation: Equal 3x + 5 to 9x - 17, to each other and get 3.6 and 3.6 equals x. Q and R are congruent. for 3x +5, multiply 3.6 by three and add 5. Multiply 3.6 by 9 and subtract 17. I hope this helps :)
Millie and kim both entered a pumpkins in the county fair. Millie's pumpkin weighs 52 1/4 lbs. Kim's pumpkin is 90% as big as Millie's pumpkin. How much does Kim's pumpkin weigh? Give your answer as a decimal
I dont know if its adding, subtracting, dividing, or multiplication. Please include the answer and how you got it!!
Step-by-step explanation:
Millies pumpkin: 52.25 lbs. (25 is one quarter of 100)
Kims is 90% as heavy.
We know in percentage, it only goes up to 100%.
Concept #1Dividing
We can divide 100% into 10 chunks of 10%. In this instance, 52.25 lbs is 100%. So we divide 52.25 lbs into 10 chunks of 5.225 lbs.
Concept #2
Multiplying
90% is 9 times those little chunks of 10%. In this instance, 1 chunk is 5.225 lbs. So we simply multiply that by 9 because it's 90%.
Concept #3
Actually multiplying it
5.225 x 9 = 47.025 lbs
So 47.025 lbs is 90% of 52.25 lbs which is Millie's pumpkin.
Therefore your answer for "how much does kims pumpkin weigh" is
47.025 lbs
hoped this helped
create two different infinite geometric series that each have a sum of 8
Two different infinite geometric series that each have a sum of 8 are 32 + 32(3) +32(3)² + 32(3)³ + ................. and 24 + 24(2) + 24(2)²+ 24(3)³+ .............
What is an infinite geometric series?An Infinite geometric series is the sum of the infinite terms and these terms have constant ratio between successive terms.
Let us take first term of the infinite series be a and r be the constant ratio between successive terms. Then formula for such geometric series be a+ar+ar²+ar³+.............
And sum of such series is ,S =a/(1+r)
We have to find two infinite geometric series with sum S = 8
Let us take a=24 and r=2
Then sum, S = [tex]\frac{24}{2+1} =\frac{24}{3}=8[/tex]
Therefore such series will be:
24 + 24(2) + 24(2)²+ 24(3)³+ .............
Another possibility for sum 8 will be with a =32 and r=3
Then the sum, S = [tex]\frac{32}{3+1} =\frac{32}{4}=8[/tex]
Therefore another such infinite geometric series will be
32 + 32(3) +32(3)² + 32(3)³ + .................
Thus, two different infinite geometric series that each have a sum of 8 are 24 + 24(2) + 24(2)²+ 24(3)³+ ............. and
32 + 32(3) +32(3)² + 32(3)³ + .................
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90 points! Can someone please explain what ie substitution in the work? I dont get it. My teacher is asking me to not substitute but I dont know what that is. I would really appreciate an answer!
Answer:
x=5/11 | x=6, A
Step-by-step explanation:
For the first question- 3(4-2x)=-x+1
Use algebra to solve
1. 3(4-2x)=-x+1 Distribute
2. 12-6x=-x+1 Seperate like terms
3. 12-1=6x-x Combine
4. 11=5x
5. x=5/11
For the second babysitting question, since we want to multiply the combined hours worked by 9 (the amount of money per hour, the equation should be A. Use algebra to find the hours.
1. 9(5+x)=99 Distribute
2. 45+9x=99
3. 9x=54
4. x=54/9
5. x=6
Point U has Coordinates (-5,1) and point V has coordinates (7,9) find the coordinates of the midpoint of UV
The mid point of the given Coordinates U= (-5,1) and point V = (7,9):
= ( -6 , 5).
Midpoint of a Line Segment:
A line segment's midpoint is a point that divides the line segment across two equal sections. The midpoint of a line segment with coordinates at both ends X₁ , Y₁ and X₂, Y₂ is calculated using:
According to the given data:Point U has Coordinates (-5,1).
point V has coordinates (7,9).
Find coordinates of the midpoint of UV = ?
We know that to find Midpoint of a Line Segment:
= [tex]\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)[/tex]
Where U
X₁ = -5
Y₁ = 1
Whare V
X₂ = 7
Y₂ = 9
Putting the value in the formula:
UV = [tex]\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)[/tex]
= (-5 + 7)/2 , (1 + 9)/2
= -6 , 5
The mid point of the given Coordinates U= (-5,1) and point V = (7,9):
= ( -6 , 5).
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Alma is making bionicos at a food stand. She has 15 strawberries and 30 grapes. She plans to use all the strawberries and grapes, as well as some other fruits. Alma wants to know the greatest number of identical bionicos she can make.
The greatest number of identical arrangements is 1 arrangements of 15 strawberries and 2 grapes.
It is required to find the solution.
What is greatest common factor (GCF)?The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
Given:
In total, there are 15 strawberries and 30 grapes.
To find the greatest number of identical arrangements, first we need to find the greatest common factor of 15 and 30.
According to given question we have
GCF of (15,30) = 15
Therefore, the greatest number of identical arrangements is 1 arrangements of 15 strawberries and 2 grapes.
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