The arrangement of the points in increasing order of the slopes are (27, 2) and (243, 18), (63, 9) and (84, 12), (45, 15) and (60, 20), (27, 12) and (72, 32), (15, 30) and (20, 40), (12, 32) and (18, 48), (18, 63) and (24, 84)
How to Arrange the points in increasing order of the slopes of the lines joining them?
Slope is defined as the change in y divided by the change in x. Mathematically:
Slope = (y2 - y1) / (x2 -x1)
To arrange the pair of points. You need to find the slope:
For (15, 30) and (20, 40):
x1 = 15, y1 =30 and x2 =20, y2=40
slope = (40-30)/(20-15) = 10/5 =2
For (12, 32) and (18, 48):
slope = (48-32)/(18-12) = 16/6 = 2.67
For (27, 12) and (72, 32):
slope = (32-12)/(72-27) = 20/45 = 0.44
For (45, 15) and (60, 20):
slope = (20-15)/(60-45) = 5/15 = 1/3 = 0.33
For (27, 2) and (243, 18):
slope = (18-2)/(243-27) = 16/216 = 0.07
For (18, 63) and (24, 84):
slope = (84-63)/(24-18) = 21/6 = 7/2 = 3.5
For (63, 9) and (84, 12):
slope = (12-9)/(84-63) = 3/21 = 1/7 = 0.14
Therefore, the pairs of points in increasing order of the slopes are (27, 2) and (243, 18), (63, 9) and (84, 12), (45, 15) and (60, 20), (27, 12) and (72, 32), (15, 30) and (20, 40), (12, 32) and (18, 48), (18, 63) and (24, 84)
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PLEASE HELP ME!!!!!!
Answer:
7/65
Step-by-step explanation:
At a baseball game, a vender sold a combined total of sodas and hot dogs. the number of sodas sold was three times the number of hot dogs sold. find the number of sodas and the number of hot dogs sold.
The number of sodas sold is 168
The number of hot dogs sold is 56
Total of sodas and hot dogs=224
Let the number of sodas sold be s, and the number of hot dogs sold be s
So we have the following:
s=3h.................i
s+h=224..........ii
we solve the two equation to find the value of s and h,
From equation ii, s=224-h, replacing this in equation i, we have:
224-h=3h
224=4h
h=56
Now, s=3*56
=168
s=168
Number of sodas=168
Number of hot dog sold=56
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The complete question is given below;
A vender sold a combined total of 224 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
a₁ = 7
an = an-1 - 3
Write explicitly.
Answer:
a(n) = 10 -3n
Step-by-step explanation:
You want the explicit formula for the sequence recursively defined by a(1)=7, a(n)=a(n-1) -3.
Common differenceThe recursion relation tells you that each term is 3 less than the one before. That is, the common difference between terms is -3.
Explicit formulaA sequence with a common difference is an arithmetic sequence. The formula for the n-th term is ...
a(n) = a(1) +d(n -1)
where a(1) is the first term and d is the common difference.
The first term is given by the recursive definition as 7. Then the explicit formula is ...
a(n) = 7 -3(n -1)
This can be simplified to ...
a(n) = 10 -3n
Help please. Isabelle's lemon cookie recipe calls for 5 cups of sugar.
How much sugar would Isabelle use to make 4 1/5 batches of cookies?
The quantity of sugar Isabelle would need to make 4 1/5 batches of cookies is 21 cups of sugar
Calculating the quantity of sugar neededFrom the question, we are to determine the quantity of sugar that Isabelle would need to make the given number of batches. The number of batches Isabelle wants to make is 4 1/5 batches.
From the given information, Isabelle's lemon cookie recipe calls for 5 cups of sugar. If 1 batch of the lemon cookie calls for 5 cups of sugar
Then, 4 1/5 batches of the lemon cookie will call for 5 × 4 1/5 cups of sugar 5 × 4 1/5
= 5 × 21/5= 21
Hence, Isabelle will need 21 cups of sugar
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how many different three-letter strings can be formed from the letters a, b, c, d, e (repeats allowed) if the string must contain either all vowels or all consonants?
8 strings can be formed with all vowels from a, b, c, d, e and 27 strings can be formed with all consonants from a, b, c, d and e.
What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]
Given, the letters that can be used to create the required three letter word in question: a, b, c, d, e.
Total number of letters that can be used = 5
Total number of vowels in the available letters to be used = 2 ('a' and 'e')
Total number of consonants in the available letters to be used = 3 ('b', 'c' and 'd')
Case 1: A three letter word having all vowels where letters can be repeated
Here, since two letters are to put in three empty positions, the total number of ways to form this word = 2³ = 2 × 2 × 2 = 8
Case 2: A three letter word having all consonants where letters can be repeated
Here, since three letters are to put in three empty positions, the total number of ways to form this word = 3³ = 3 × 3 × 3 = 27
Thus, 8 strings can be formed with all vowels from a, b, c, d, e and 27 strings can be formed with all consonants from a, b, c, d and e.
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when playing yahtzee, you roll five regular 6-sided dice. how many different outcomes are possible from a single roll? the order of the dice does not matter.
Answer:
6
Step-by-step explanation:
how many groups of participants would be needed to partially (e.g., using latin square arrangement) counterbalance a within-subjects experiment with three treatment conditions?
24 groups of participants would be needed to partially counterbalance a within-subjects experiment with three treatment conditions.
Given that;
How many groups of participants would be needed to partially counterbalance a within-subjects experiment with three treatment conditions.
Every participant in an experiment is exposed to every treatment or condition in a within-subject design, sometimes referred to as a repeated measures design.
The term "between-subjects design" is comparable to this within-subjects design. People are solely assigned to one treatment in a between-subjects design. As a result, one therapy would be given to one group of volunteers, while a different treatment would be given to another group. After that, the variations between the two groups would be contrasted.
24 groups would be required for a perfectly counterbalanced design for even four treatment conditions. This would obviously be impracticable because a large enough sample size would be required to conduct such an experiment.
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you play tennis regularly with a friend, and from past experience, you believe that the outcome of each match is independent. for any given match you have a probability of 0.6 of winning. what is the probability that you win the next two matches?
Answer:
0, 6 * 0,6 = 0.36
Step-by-step explanation:
Keyword is AND.First AND second matches both. It means you need to use *.
The probability of winning both matches is 0.36 or 36%.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
Since the outcome of each match is independent, we can use the multiplication rule of probability to find the probability of winning the next two matches:
P(win both matches) = P(win first match) x P(win second match)
The probability of winning a single match is given as 0.6.
Therefore, the probability of winning the first match is 0.6.
Now, assuming you won the first match, you still have a probability of 0.6 of winning the second match.
Therefore, the probability of winning both matches is:
P(win both matches) = P(win first match) * P(win second match)
= 0.6 x 0.6
= 0.36
Therefore,
The probability of winning both matches is 0.36 or 36%.
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what is the notation used for a vector pointing into the page? what about a vector pointing out of the page?
The notation used for a vector pointing into the point is X.
A quantity with a magnitude and direction is called a vector. A vector quantity will be identified in these annotations by a bold letter (such as the electric field vector E). Vectors appear graphically as straight arrows. The magnitude of the vector is commonly represented by the length of the arrow, and both the arrow and the vector point in the same general direction.
Arrows are drawn on the page to represent vectors in the page's plane. Typically, circles with an X engraved on them are used to represent vectors that enter the screen's plane. A vector that deviates from the screen's plane is often represented by circles with dots in the center.
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answer help this image needs andwer for domain range pls
Answer:
the domain is the x values: -5,-4,-2,0,1
The range is the y values: -1, 1, 3, 4
Step-by-step explanation:
Find an equation, in slope-intercept form, that passes through point (-2, 2) with slope -2.
[A] y = -2x-2 [B] y = 2x-2
[C] y = 2x-4 [D] y = -2x-4
The equation of a line on a point (-2,2) is y = -2x-2. That option A is correct.
Here we have to find the equation of a line.
The given data:
Point = ( -2, 2)
Slope(m) = -2
Equation of a line:
y = mx + c
Now putting the values as
y = 2
x = -2
m = -2
We will get the y-intercept.
So we have:
2 = -2 × -2 + c
c = 2 - 4
= -2
So, y = -2x -2
Therefore we get the equation of line as y = -2x -2.
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estimate a 15% tip on a dinner bill of $61.53 by first rounding the bill amount to the nearest $10
well, 61.53 is really 10 + 10 + 10 + 10 + 10 + 10 + 1.53.
well, 1.53 doesn't really come nowhere near close to round up to 10, so it boils down to 0, so 61.53 will just be 10 + 10 + 10 + 10 + 10 + 10 + 0 or just 60 once rounded up, now, what's 15% of 60?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 60}}{\left( \cfrac{15}{100} \right)60}\implies 9[/tex]
well, we can get the 15% of 61.53 by just (15/100) * 61.53
however, the exercise is asking on rounding it up to "tens" first
61.53 has "10" six times plus 1.53, the rounding happens with the "surplus"
in this case the surplus is 1.53.
now, for rounding anything the tipover point is at the half, for $10 the half is $5, so if the amount is $5 or more, rounds up to $10, if less than that goes to 0.
1.53 is nowhere near 5, which is the halfpoint or tipover point, because of that, it rounds up to 0, so 61.53 rounded up to "tens" only will be "six tens" only, or 60.
"I have drawn a polygon who's sum of interior angles is 800"
explain why this is impossie
We know that the sum of all the interior angles of the polygon with sides n is (n - 2)*180.
It is given in the question that,
Sum of all the interior angles of the polygon is 800.
Hence, according to the data given in the question, we can write,
(n - 2)*180 = 800
n - 2 = 800/180
n - 2 = 40/9
n = 40/9 + 2
n = 58/9 = 6.44
As number of sides should always be in integer form, it is not possible to have the sum of all the interior angles of the polygon to be 800 degrees.
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helppppppppppppp can you tell me where to put the answers
After applying the distributive property, Ezra's expression was 8y + 16.
After he used the commutative property, his expression was 16 + 8y.
How to use the distributive and commutative properties?When using the distributive property, we are able to expand an expression with a bracket by multiplying the things in the bracket with the things outside:
8( y + 2) becomes:
= (8 x y) + (8 x 2)
= 8y + 16
The commutative property on the other hand, means that when adding, the position of the number does not matter. For instance, a + b = b + a
When the commutative property is applied therefore, we get:
8y + 16 = 16 + 8y
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The cost of hiring a car is $40 plus a charge of $30 per day. How much will it cost to hire the car for 2 days?
Step-by-step explanation:
we have a basic fee of $40 just for renting the car.
and we rent it for 2 days for $30 per day.
so, this costs
40 × 2×30 = 40 + 60 = $100
a computer store compiled data about the accessories that 500 purchasers of new tablets bought at the same time they bought the tablet. here are the results: 411 bought cases 82 bought an extended warranty 100 bought a dock 57 bought both a dock and a warranty 65 both a case and a warranty 77 bought a case and a dock 48 bought all three accessories 58 bought none of the accessories find the probability that a randomly selected customer bought: a. exactly one of the accessories. b. exactly two of the accessories. c. at least one of the accessories. d. at least two of the accessories. e. at most one of the accessories. f. at most two of the accessories. g. a case or a warranty, but not both, and did not buy a dock. h. a case but neither of the other two accessories. i. a warranty and a dock but not a case.
The probability that exactly one of the accessories, be 0.678
The probability that exactly two of the accessories, be 0.11
The probability that at least one of the accessories, be 0.884
The probability that at least two accessories, be 0.206
The probability that at most one of the accessories, be 0.794
The probability that at most two of the accessories, be 0.904
The probability that a case or a warranty, but not both be, 0.726
The probability that a case but neither of the other two accessories be, 0.634
The probability that a warranty and a dock but not a case be, 0.018
Given, a computer store compiled data that 500 purchasers of new tablets bought at the same time they bought the tablet.
Let A be the set of purchasers we bought cases,
B be the set of purchasers we bought extended warranty,
C be the set of purchasers we bought dock,
Now, A = 411 , B = 82 , C = 100
also, A∩B = 65 , B∩C = 57 , A∩C = 77 and A∩B∩C = 48 , A'∩B'∩C' = 58
(a) the probability that exactly one of the accessories, be
P(A)-P(A∩B)-P(A∩C)+P(A∩B∩C) + P(B)-P(A∩B)-P(B∩C)+P(A∩B∩C) + P(C)-P(C∩B)-P(A∩C)+P(A∩B∩C) = 411-65-77+48+82-57-65+48+100-57-77+48
= 339/500
= 0.678
(b) the probability that exactly two of the accessories, be
P(A∩B)+P(B∩C)+P(A∩C)-3P(A∩B∩C) = 65+57+77-48-48-48
= 55/500
= 0.11
(c) the probability that at least one of the accessories, be
who bought 1 or 2 or all 3 accessories be,
= 0.678 + 0.11 + 0.096
= 0.884
(d) the probability that at least two accessories, be
who bought 2 or all 3 accessories be,
= 0.11 + 0.096
= 0.206
(e) the probability that at most one of the accessories, be
who bought nothing or one accessories be,
= 0.116 + 0.678
= 0.794
(f) the probability that at most two of the accessories, be
who bought nothing or 1 or 2 accessories be,
= 0.116 + 0.678 + 0.11
= 0.904
(g) the probability that a case or a warranty, but not both
= 0.822 + 0.164 - 0.26
= 0.726
(h) the probability that a case but neither of the other two accessories
= 0.634
(i) the probability that a warranty and a dock but not a case
= 0.018
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How would you solve (5x - 7) (4x + 1)?
Using distributive property, the simplified form of (5x - 7)(4x + 1) is 20x^2- 23x - 7.
In the given question we have to solve the given expression.
The given expression is (5x - 7)(4x + 1).
To simplify the given expression we use the distributive property.
According to property; a(b+c) = ab+bc
Now simplifying the expression;
(5x - 7)(4x + 1)=5x(4x + 1) - 7(4x + 1)
(5x - 7)(4x + 1)=(5x*4x + 5x*1) - (7*4x + 7*1)
(5x - 7)(4x + 1)=(20x^2 + 5x) - (28x + 7)
Simplifying
(5x - 7)(4x + 1)=20x^2+5x -28x - 7
(5x - 7)(4x + 1)=20x^2- 23x - 7
The simplified form of (5x - 7)(4x + 1) is 20x^2- 23x - 7.
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Use the given vertices to graph quadrilateral TUVW and its image after a dilation centered at the origin with scale factor
k=2/3
T(9,-3), U(6,0), V(3,9), w(0,0)
Answer:We know that the dilation transformation of a figure either shrink or expand the original figure depending on the scale factor of the dilation.
As here we have scale factor=3>1.
Hence, the dilation changes the original will expand the original figure.
Hence, each of the coordinate of a figure get multiplied by 3.
Hence, the co
ordinates of the image are given as:
i.e. A(0,0) → A'(0,0)
B(2,3) → B'(6,9)
C(1,-2) → C'(3,-6)
D(-3,-3) → D'(-9,-9)
Step-by-step explanation:
PLEASE HELP ASAP ILL GIVE BRAINLIEST
Find x and y
*image is linked*
The values of x and y in the similar triangles are 3 and 2 respectively.
What are similar triangle?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
In similar triangles, corresponding sides are always in the same ratio.
Therefore, using similar triangle ratio, let's find the value of x and y.
x / 6 = 1.5 / 3
cross multiply
3x = 1.5 × 6
3x = 9
divide both sides by 3
x = 9 / 3
x = 3
Let's find y.
y / 4 = 1.5 / 3
cross multiply
3y = 6
divide both sides by 3
y = 6 / 3
y = 2
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Solve each equation for y
A. (y- 10) = -3(x - 2)
B. (y-2) = 3(x+1)
C. (y-2 = 1/3(x-3)
Will do brainliest! 100%
Answer:
A. [tex]y=-3x+16[/tex]
B. [tex]y=3x+5[/tex]
C. [tex]y=\frac{1}{3}x+1[/tex]
Step-by-step explanation:
A.
[tex]y-10=-3(x-2)[/tex]
[tex]y-10=-3x+6[/tex]
[tex]y=-3x+16[/tex]
B.
[tex]y-2=3(x+1)[/tex]
[tex]y-2=3x+3[/tex]
[tex]y=3x+5[/tex]
C.
[tex]y-2=\frac{1}{3}(x-3)[/tex]
[tex]y-2=\frac{1}{3}x-1[/tex]
[tex]y=\frac{1}{3}x+1[/tex]
15/20+16/20 as a mixed number
Answer: 1 11/20
hope this helps :)
Here you go LOL didn't get all the files. I need help TWT
Answer:
First option
Step-by-step explanation:
→ Define domain
The set of x values a function can take
→ Identify
2 to negative infinity
Each tire on the toy car has a diameter of 5. 6cm, the tire spin completely around 15 times when the car was pushed in a straight line. About how far was the car pushed
The distance covered by the car is 264cm.
Here we have to find the distance covered by the car.
Information provided:
Diameter (d) = 5.6cm
radius(r) = 5.6/2
= 2.8cm
Rotation = 15 times
Formula to find the circumference of the tire:
Circumference = 2πr
= 2 × 22/7 × 2.8
= 17.6cm
This is the distance covered by the tire in one rotation.
Distance covered after 15 rotations = 15× 17.6
= 264 cm
Therefore distance covered is 264 cm.
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Drew painted his uncle's barn on saturday. it took him 7 hours to paint the whole barn, and his uncle paid him 133 dollars for his work. what was drew's pay rate, in dollars per hour?
The total amount paid in dollars per hour is $19.
Unitary Method:
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
It is given that the total amount given by the uncle is $133 for the work done by Barn for 7 hours.
We have to find the amount paid per hour.
Total amount given = $133
Number of hour Barn work = 7 hours
Amount paid per hour = 133/ 7
= $ 19
Therefore the amount paid per hour is $19.
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[tex]\frac{5\sqrt{7} }{\sqrt{35} }[/tex]
The simplified expression of the radical expression given as 5√7/√35 is 7
How to evaluate the expression?From the question, we have the following expression that can be used in our computation:
5√7/√35
The above expression is a fraction and at the same time it is a radical expression
The denominator of the fraction is √35
So, we start by rationalizing the expression by the fraction
This is represented as
5√7/√35 = 5√7/√35 * √35/√35
Evaluate the products of the numerator
So, we have the following representation
5√7/√35 = 5√245/√35 * 1/√35
Evaluate the products of the denominator
So, we have the following representation
5√7/√35 = 5√245/35
Simplify the fraction
This gives
5√7/√35 = √245/7
Simplify the fraction
5√7/√35 = 7√5/7
So, we have
5√7/√35 = 7
Hence, the simplified expression is 7
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multiply the maclaurin series for e z and 1 1 z to obtain the series expansion for e z 1 z up to z 5 . on what disk does it converge?
The series expansion for e z 1 z up to z 5 is obtained by multiplying the Maclaurin series for e z and 1 1 z. For |z| 1, this series converges.
The Maclaurin series for e^z is:
e^z = 1 + z + z^2/2! + z^3/3! + z^4/4! + ...
The Maclaurin series for 1/1-z is:
1/(1-z) = 1 + z + z^2 + z^3 + z^4 + ...
Multiplying these two series together gives:
e^z/(1-z) = (1 + z + z^2/2! + z^3/3! + z^4/4! + ...)(1 + z + z^2 + z^3 + z^4 + ...)
= 1 + (1+z) + (z + z^2/2! + z^2) + (z^2/2! + z^3 + z^3/3!) + (z^3/3! + z^4 + z^4/4!) + ...
= 1 + z + 2z^2 + 3z^3 + 5z^4 + ...
This series converges for |z| < 1
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How do you use distributive property to answer (15x6) + (85x6)
Answer:
600
Step-by-step explanation:
You want to use distributive property to answer (15x6) + (85x6).
Distributive propertyThe distributive property shows you what you can do with a common factor:
(15×6) + (85×6) = (15 +85)×6 . . . . . . apply the distributive property
= 100 × 6 . . . . . . evaluate the sum in parentheses
= 600 . . . . . . perform the multiplication
1. The slope of the line
y = x + 17 is ___.
2. The slope of the line
y = x - 7/9 is ___.
Explanation:
The slope of the line
y = x + 17 is ___. 1
2. The slope of the line
y = x - 7/9 is ___. 1
Jose has $580 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $284.52. He buys 4 bicycle reflectors for $15.65 each and a pair of bike gloves for $11.31. He plans to spend some or all of the money he has left to buy new biking outfits for $31.95 each. What is the greatest number of outfits Jose can buy with the money that's left over?
The greatest number of outfits Jose can buy is 6
How to determine the greatest number of outfits he can buy?The given parameters are:
Budget = $580New bicycle = $284.524 bicycle reflectors = $15.65 eachPair of a bike gloves = $11.31New biking outfits = $31.95 each.Let the number of new biking outfits be x
So, we have
New bicycle + 4 * price of bicycle reflectors + Pair of a bike gloves + New biking outfits ≤ Budget
This gives
284.52 + 4 * 15.65 + 11.31 + 31.95x ≤ 580
This gives
358.43 + 31.95x ≤ 580
Solve the inequality
31.95x ≤ 221.57
Divide
x ≤ 6.93
This gives
x ≤ 6
Hence, the greatest number of outfits is 6
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Find the distance between
(4, 8) and (-2, 2).
Answer:
[tex]6\sqrt{2}[/tex]
Step-by-step explanation:
Using the distance formula,
[tex]\sqrt{(4-(-2))^2+(8-2)^2} \\ \\ =\sqrt{6^2+6^2} \\ \\ =6\sqrt{2}[/tex]
Answer:
6(sqrt(2))
Step-by-step explanation:
Use the "distance formula" (sqrt((x2-x1)^2 - (y2-y1)^2)), plugging in (4,8) for x1 and y1, and (-2,2) for x2 and y 2
