The fourth integer is 16.
Key skills needed: Casework, Mean, Median, and Mode
1) We start with 4 numbers _ _ _ _
2) We can determine two of the numbers by using the fact that the median is 14 and the mode is 14.
3) The numbers would have to be:
_ 14 14 _
_ 14 14 14
The 2nd one does not work because the last number would have to be a 6 to have a mean of 14, but the range would not be 14.
4) So, our numbers are _ 14 14 _
5) The two numbers add up to 20 (in order to have a mean of 14. If you subtract the bigger one by the smaller one, it will be 14.
6) We can make a system: saying x is the bigger number and y is the smaller number.
x + y = 20
x - y = 14
Add both and you will get 2x = 32 (since the y values cancel out).
7) divide by on both sides, and x = 16.
8) To find y, we can plug x back in to one equation:
16 + y = 20
y = 4
Our smaller number is 4 and our bigger number is 16.
9) Therefore the numbers are: 4, 14, 14, 16
Hence the answers is, the fourth integer is 16.
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Find the length of the hypotenuse in this right triangle.
Answer:
13
Step-by-step explanation:
This is a special right triangle with side lengths 5-12-13 respectively.
If we can't remember the lengths we can use the following formula to calculate the lentgh of hypotenuse:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
the sum of square measure of both legs is equal to the square measure of hypotenuse
[tex] {5}^{2} + {12}^{2} = {c}^{2} [/tex]
25 + 144 = c^2
169 = c^2 find the root of both sides
13 = c, hypotenuse.
a rectangular container with a square base, an open top, and a volume of 4,000 cm3 is to be made. what is the minimum surface area for the container? enter only the minimum surface area, and do not include units in your answer.
A rectangular container with a square base, an open top, and a volume of 4,000 cm³. The minimum surface for the container is 1,200 cm².
The result is obtained by using the derivative.
Determine the minimum surface areaThese are the specified parameters:
Volume container is 4,000 cm³.
Let side of square base = a, and height of the container = h, so:
Volume = a × a × h
4,000 = a² h
h = [tex]\displaystyle \frac{4000}{a^2}[/tex] ... (1)
Surface area with a square base, an open top is area of a square + 4 times the vertical side.
Surface area (A) = a² + 4ah
Substitute the value of h = [tex]\displaystyle \frac{4000}{a^2}[/tex] into surface area.
A = a² + 4ah
A = a² + 4a ([tex]\displaystyle \frac{4000}{a^2}[/tex])
A = a² + [tex]\displaystyle \frac{16000}{a}[/tex]
So that the surface area is minimal, when the derivative and equate to 0.
A = a² + 16000 a⁻¹
A' = 0
2 a²⁻¹ + (-1) 16000 a⁻¹⁻¹
2a - 16000 a⁻² = 0
2a - [tex]\displaystyle \frac{16000}{a^2}[/tex] = 0
2a = [tex]\displaystyle \frac{16000}{a^2}[/tex]
2a³ = 16000
a³ = [tex]\displaystyle \frac{16000}{2}[/tex]
a³ = 8000
a = ∛8000
a = 20
Surface area with a square base, an open top.
Substitute the value of a = 20
A = a² + [tex]\displaystyle \frac{16000}{a}[/tex]
A = 20² + [tex]\displaystyle \frac{16000}{20}[/tex]
A = 400 + 800
A = 1200
The minimum surface for the container is 1,200 cm².
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∠1 and ∠2 are supplementary. m∠1=124°m∠2=(2x+4)° What is the value of x? Select from the drop-down menu to correctly answer the question. x = Choose... 13 26 40 36 41
Answer:
26
Step-by-step explanation:
Supplemental means that the two angles together equal 180
124 + 2x + 4 = 180 Combine like terms
128 + 2x = 180 Subtract 128 from both sides of the equation
2x = 52 Divide both sides by 2
x = 26
An employee opens a credit union account and deposits
$90 at the end of each month. After two years, the account
contains $2,177.48. What annual nominal rate compounded
monthly has the account earned?
Annual nominal rate compounded monthly has the account earned is 0.84% .
In the question ,
it is given that ,
An employee opened a credit union account ,
amount deposited each month (PMT) = $90
number of period (n) = 2 years = 24 months
Future value after 2 years (FV) = $2177.48
let the rate of interest compounded monthly has the account earned be "r"
we know that the future value formula is
Future Value = PMT× [tex](\frac{(1+\frac{r}{12})^{n} -1 }{\frac{r}{12} } )[/tex]
Substituting the value of n = 24 , PMT = 90 and FV = 2177.48 in the Future Value Formula ,
we get ,
2177.48 = 90 × [tex](\frac{(1+\frac{r}{12})^{24} -1 }{\frac{r}{12} } )[/tex]
[tex](\frac{(1+\frac{r}{12})^{24} -1 }{\frac{r}{12} } )[/tex] = 2177.48/90
( 1 + r/12 )²⁴ -1 = (r/12) × 24.194
Solving further , we get
r = 0.0084
that means rate is = 0.84%
Therefore , Annual nominal rate compounded monthly has the account earned is 0.84% .
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please help Me I dint get this question
Part a: The side of the square is found as 6 cm.
Part b: The side length of the square is found as 10 cm.
What is the definition of the term perimeter of square?The sum of the lengths of all the sides of a square is its perimeter. Thus, by summing the lengths of a square's four sides, we to get its perimeter.For the given dimensions for the question,
Length = 18 cm.Breadth = 2 cmPart a: Area of square is same as area of rectangle.
Rectangle area = Length x breath
Rectangle area = 18 x 2
Rectangle area = 32 sq. cm
Now,
Area of square = Rectangle area
Area of square = side²
36 = side²
side = √36
side = 6 cm.
Thus, the side of the square is found as 6 cm.
Part b: Side length of square.
Rectangle perimeter = square perimeter
Rectangle perimeter = 2(length + width)
Rectangle perimeter = 2(18 + 2)
Rectangle perimeter = 40
square perimeter = 4 side
40 = 4 side
side = 40/4 = 10 cm.
Thus, the side length of the square is found as 10 cm.
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The ordered pairs below represent a function.
What is the range of the function?
O {-2,0,1,2,4,6}
O {-2,1,4}
O {-2,1,2,4,6}
O {0,1,2,4,6}
{(-2,4), (4,-2), (1, 1), (0, 1), (2,-2), (6,4)}
Answer:yesno
Step-by-step explanation:
yes
in two or more complete sentences, describe choices that a consumer can make that could lead to financial irresponsibility.
Choices made by consumer leads to financial irresponsibility are as follow:
Spend money on emotional feelingDon't save money for emergency purposeSpending money without knowing your limitsSpending money doing comparisonAs given in the question,
Choices made by consumer leads to financial irresponsibility are as follow:
Spend money on emotional feelingWhen a person is spending money just on emotional feeling and buying large gifts for children which is beyond the budget. Due to this habits a person may have to take debt.
Don't save money for emergency purposeWhen a person is not saving enough money for the time of emergency, it can be a medical emergency then it is financial irresponsible behavior.
Spending money without knowing your limitsWhen you are not making any budget and spending money ,it might possible at the end of the month or some time you have to face financial crises.
Spending money doing comparisonDon't compare yourself with anyone, this might lead you to take loan or debts which lead your life in facing financial trouble.
Therefore, choices made by consumer leads to financial irresponsibility are as follow:
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construct a 95% confidence interval for the mean number of defects per screen for all screens produced by this manufacturer. a) what is the lower limit on the interval? give your answer to three decimal places. 1.691 incorrect: your answer is incorrect. seenkey 1.703 b) what is the upper limit on the interval? give your answer to three decimal places. 2.589 incorrect: your answer is incorrect. seenkey 2.577 c) based on the interval above, would you believe that the mean number of defects per screen for all screens from this manufacturer is 1.78? yes because 1.78 is not inside the interval. no because 1.78 is inside the interval. correct yes because 1.78 is inside the interval. no because 1.78 is not inside the interval. correct: your answer is correct. d) if we are very certain that the true standard deviation of the number of defects per screen is below 2, what sample size would be required so that the width of the 95% confidence interval for the mean number of defects per screen is at most 0.34? make sure you enter a whole number below. 532 correct: your answer is correct. seenkey 532
The 95% Confidence Interval for the mean number of defects per screen for all screens produced by this manufacturer is (1.447646, 2.352354)
Given Data:
3, 5, 0, 3, 5, 2, 5, 1, 0, 0, 0, 4, 2, 1, 0, 5, 1, 0, 1, 1, 0, 2, 0, 2, 1, 0, 2, 4, 4, 3, 2,
2, 3, 2, 1, 2, 1, 1, 4, 1, 1, 6, 0, 3, 1, 0, 2, 2, 1, 3
We calculate sample mean and standard deviation from given data.
Sample Mean, a = 2 (2) _ 95
-50
= 1.9
Sample Variance, $2 _ _(2 -x)2 _130.5
= 2.663265
n - 1
49
Sample std dev, s = V82 = v2.663265 ~ 1.631951
95% CI for u using Normal dist
Sample Mean = T = 1.9
Since sample size is large, sample standard deviation can be taken as an approx-
Limation of population standard deviation.
Population Standard deviation = o ~ 1.631951
Sample Size = n = 50
Significance level = 0 = 1- Confidence = 1 - 0.95 = 0.05
The Critical Value = za/2 = 20.025 = 1.96 (From z table)
Critical Values , 1za/2 = 41.96
Margin of Error = E = za/2 X -= 1.96 x 1.631951
0.452354
V50
Margin of Error, E = 0.
Limits of 95% confidence interval are given by:
Lower limit = I - E = 1.9 -0.452354 ~ 1.447646 ~ 1.448
Upper limit = I + E = 1.9 + 0.452354 ~ 2.352354 ~ 2.352
95% confidence interval is: T + E = 1.9 4 0.452354
= (1.447646, 2.352354)
95% CI using normal dist: (1.448 ) < < (2.352)
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a baker is deciding how many batches of muffins to make to sell in his bakery. he wants to make enough to sell to everyone and no fewer. through observation, the baker has established a probability distribution. what is the probability the baker will sell exactly one batch? (find p(x
Form the given probability distribution, the probability of selling exactly one batch by baker is equal to 0.10.
As given in the question,
Probability distribution established by baker :
x : 1 2 3 4
P(x) : 0.10 0.30 0.40 0.20
As it is give that number of batches made by baker to sell muffins .
For selling 1 batch x = 1.
For selling 2 batch x = 2.
For selling 3batch x = 3.
For selling 4 batch x = 4
Probability of selling exactly one batch by baker is given by when x =1
Probability of x = 1 is given by :
P( x = 1 ) = 0.10
Therefore, form the given probability distribution, the probability of selling exactly one batch by baker is equal to 0.10.
The complete question is :
A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. x P(x) 1 0.10 2 0.30 3 0.40 4 0.20 What is the probability the baker will sell exactly one batch.
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modeling real life an animal shelter director is planning to build a rectangular playpen. the playpen must have a perimeter of 150 feet and an area of at least 1000 square feet. describe the possible lengths of the playpen. the length must be at least feet and at most feet.
For the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.
As given in the question,
For the given rectangular playpen,
Perimeter of rectangular playpen is equal to 150 feet .
Area of the rectangular playpen is equal to at least 1,000 squared feet .
Area = length × width
Let x be the length of the rectangular playpen .
Then its width is equal to 1000 / x.
Substitute the value of length and width in perimeter we get,
Perimeter of rectangular playpen = 2 ( length + width )
⇒ 150 = 2 [ x + (1,000/x)]
⇒ 150 / 2 = ( x² + 1,000 ) / x
⇒ x² + 1000 = 75x
⇒ x² -75x + 1,000 =0
Simplify quadratic equation using discriminant we get,
x = [ -( -75) ± √(-75)² - 4(1) (1,000) ] / 2(1)
⇒ x = ( 75 ± √5625 - 4000) /2
⇒ x = (75 ± 40.31) / 2
⇒ x = 57.66 or 17.35
Therefore, for the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.
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Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the fu
decrease quickly at first, then decrease more slowly as time passes. Which best describes this function?
O It is linear because the graph decreases over time.
O It is linear because there is both an independent and a dependent variable.
O It is nonlinear because linear functions are increasing functions.
O It is nonlinear because linear functions increase or decrease at the same rate.
It is nonlinear because linear functions, which correspond to option D on the provided graph, grow or shrink at the same rate.
What is linear function?On the coordinate plane, a straight line can be represented by a linear function. In the coordinate plane, for instance, the linear function denoted by the equation y = 3x - 2 is a straight line. The graph of a linear function is a straight line. The form of a linear function is depicted below. a + bx = y = f (x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.
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Solve for y
3+3(2y-3)=-3(3y-4)+y
Answer: y=9/7
Step-by-step explanation:
There are 72 mg of choleterol in a 3. 6 ounce erving of lobter how much choleterol i in 11 ounce of lobter round to the nearet tenth place
Answer:
The amount of cholesterol in 11 ounces of lobster is 220 mg
Step-by-step explanation:
The amount of cholesterol in 11 ounces of lobster can be calculated as follows
The first step is to convert all units of measure from ounce to mg
1 gram = 0.0352 ounce
Divide both sides by 0.0352 to get the value of 1 ounce
[tex]\frac{1}{0.0352}[/tex] gram = [tex]\frac{0.0352}{0.0352}[/tex] ounce
28.35 gram = 1 ounce
Since 1 gram equals 1000 milligrams, then multiply the left side by 1000 and change the unit of measure to milligram
28.35 [tex]\times[/tex] 1000 mg = 1 ounce
28350 mg = 1 ounce
Convert 3.6 ounces to milligrams
3.6 ounces = 3.6 [tex]\times[/tex] 28350 mg
3.6 ounces = 102060 mg
Convert 11 ounces to milligrams
11 ounces = 11 [tex]\times[/tex] 28350 mg
11 ounces = 311850 mg
Since there are 72 mg of cholesterol in a 3.6 ounces serving of lobster, then the ratio equation to follow is
[tex]\frac{72}{102060}=\frac{x}{311850}[/tex]
Where x is the amount of cholesterol in 11 ounces of lobster
Multiply both sides by 311850 to isolate x
[tex]\frac{72}{102060}\times 311850=\frac{x}{311850}\times 311850[/tex]
[tex]\frac{22453200}{102060} =x[/tex]
Simplify the left side of the equation
220 = x
Since the value of x is 220, then the amount of cholesterol in 11 ounces of lobster is 220 mg
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Samantha is a salesperson who sells computers at an electronics store. She makes a base pay amount each day and then is paid a commission for every computer sale she makes. The equation P=6.25x+75 represents Samantha's total pay on a day on which she sells x computers. What is the slope of the equation and what is its interpretation in the context of the problem?
The slope is 6.25, it means that her day pay increases by $6.25 for each computer sold
What is the slope of the equation?
A general linear equation in the point-slope form is written as:
y = a*x + b
Where y and x are the two variables, a is the slope, and b is the y-intercept.
In this case, the linear equation is:
P(x) = 6.25*x + 75
We know that P(x) represents her pay, and x represents the amount of computers she sold.
Here we can see that the slope is 6.25, it means says how much her pay increases per computer sold.
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Which of the functions is represented by the graph
O f(x)=2x²+3
O f(x) = -x² + 3
O f(x) =1/2x² + 3
O f(x) = -1/2x +3
Number 1
Step-by-step explanation:
Number 1 it is a good answer
Please help 25 points and brainlest
Please pick the TWO properties of a incenter
*
Equidistant from the vertices
Equidistant from the sides
Where the angle bisectors cross
Where the perpendicular bisectors cross
Answer:
Where the angle bisectors cross
Where the perpendicular bisectors cross
−1/2(7z+4)+1/5(5z−15) =
Answer:
- 5/2 (z + 2)
Step-by-step explanation:
Distribute
- 7/2 z - 2 + z - 3
Subtract the numbers
- 7/2 z - 5 + z
Combine like terms
- 5/2 z - 5
Common factor
- 5/2 (z + 2)
2 1/2x + 1/4 + 3/4x = 1/8
[tex]\frac{5}{2}x+\frac{1}{4} +\frac{3}{4} x=\frac{1}{8} \\\\\frac{5}{2}(8)x+\frac{1}{4} (8)+\frac{3}{4}(8) x=\frac{1}{8}(8)\\20x+2+6x=1\\20x+6x=1-2\\26x=-1\\\frac{26x}{26} =\frac{-1}{26} \\x=-\frac{1}{26}[/tex]
I WILL GIVE YOU 25 POINTS JUST PLEASE HELP ASAP! Wilma works at a bird sanctuary and stores birdseed in plastic containers. She has 3 small containers that hold 8 pounds of birdseed each and 8 large containers that hold 12 pounds of birdseed each. Each container was full until she used 6 pounds of birdseed. She wants to put some of the remaining birdseed into 23 bird feeders that can hold 2 pounds each. How much birdseed does she have left over?
Answer:
the amount of birdseed leftover is 32
Step-by-step explanation:
Find one terminating decimal and one repeating decimal between -1/2and -1/3.
one example of terminating decimal and one repeating decimal between -1/2and -1/3
terminating decimal = -2/5
repeating decimal = -3/11
What is terminating decimal?A decimal with an end digit is referred to as a terminating decimal. It is a decimal with a limited number of digits.
examples of terminating decimal are
0.5 = 1/20.25 = 1/40.4 = 2/5 and many moreWhat is repeating decimal?When a number's digits are periodic and its indefinitely repeated portion is not zero, the representation of that number as a decimal is said to be repeating or recurring.
Examples of a repeating decimal are
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There are four consecutive odd integers such that five times the second number minus twice the fourth number is the third number subtracted by 252
If there are four consecutive odd integers such that five times the second number minus twice the fourth number is the third number subtracted by 252 then the four consecutive integers are -2, -3, -4, -5 (or) -2, -1, 0, 1.
What are consecutive integers?
Whole numbers that follow each other without gaps are known as consecutive integers.
For example, the numbers 15, 16, and 17 are all consecutive integers.
If 'n' is an integer, then the following consecutive integers begin at n, n+1, n+2, n+3, and so on.
Let x be the 1st of the four consecutive integers.
the other three consecutive integers could be
(x + 1) , (x + 2), and (x + 3).
By using the given conditions, we get
From the question,
(x + 1) = (5 * (x + 2)) - (x + 3)
Expand, and subtract like terms:
x + 1 = 5x + 10 - x - 3.
Simplifying the above expression, we get
x + 1 = 4x + 7.
3x = -6.
x = -2.
Hence, the four consecutive integers are -2, -3, -4, -5 (or) -2, -1, 0, 1.
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What’s 2\3 - 5/9 ?
NEED HELP ASAP!
Answer:1/9 or decimal form it’s ≅ 0.111111
QUESTION 3/10 HELP ASAPP
Situations a and c can represent a proportional relationship. Options a and c are correct.
What is directly proportional?It is defined as the relationship between two quantities as one quantity increases the other quantity also increases and vice versa.
The following situations are found to represent proportionality using the concept of proportionality:
A) The total amount a babysitter makes who earns $10 an hour for babysitting r hours.
C) The total amount Andrew saves when he saves $24 a week for w weeks.
Thus, situations a and c can represent a proportional relationship. Options a and c are correct.
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Exercise equipment advertised at $2200 is sold on sale for $1950. What percentage discount is this?
Percentage discount is 11.36%
Given in question,
Marked price = MP = $2200
Selling price = SP = $1950
Discount = D
= MP - SP
= 2200 - 1950
= 250
Discount % = (D/MP)*100
= (250/2200)*100
= 250/22
= 11.36
Hence, discount percent is 11.36%.
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what is the value of 36(3) - 8(-6)
Answer:
156
Step-by-step explanation:
36*3=108
8*-6=-48
108-(-48)=156
The solution of the expression 36(3) - 8(-6) will be 156.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 36(3) - 8(-6). the expression will be solved as below,
E = 36(3) - 8(-6)
E = 108 - ( -48 )
E = 108 + 48
E = 156
Hence, the solution will be 156.
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Help fast, please!
Reduce -56/-70 to the lowest terms
Answer:
-4/-5
Step-by-step explanation:
Gotchu bro
Answer:
4/5 or 0.8
Step-by-step explanation:
may i have the brainiest crown pls
solve the equations
Answer:
n = 8
Step-by-step explanation:
to solve this equation you must first isolate the variable
that is n
so first
add 2n to both sides to get rid of n on one of the sides
-4n + 2n + 14 = -2 - 2n + 2n
-2n + 14 = -2
now subtract 14 to both sides to isolate n
-2n + 14 - 14 = -2 - 14
-2n = -16
now divide everything by -2 to isolate n completely
(-2n)/(-2) = (-16)/(-2)
n = 8
that is your answer
Answer:
[tex]\boxed{\sf n=8}[/tex]
Step-by-step explanation:
[tex]\sf -4n+14=-2-2n[/tex]
Subtract 14 from both sides:-
[tex]\sf -4n+14-14=-2-2n-14[/tex]
Simplify:-
[tex]\sf -4n=-2n-16[/tex]
Add 2n to both sides:-
[tex]\sf -4n+2n=-2n-16+2n[/tex]
Simplify:-
[tex]\sf -2n=-16[/tex]
Divide both sides by -2:-
[tex]\sf \cfrac{-2n}{-2}=\cfrac{-16}{-2}[/tex]
Simplify:-
[tex]\sf n=8[/tex]
____________________
Hope this helps!
Have a great day!
A dressmaker sells a shirt for $75 she makes a 25% profit how much did it cost her to make the shirt?
Answer:
Explanation:
Selling price:$75
Profit made:25%
Cost price:100/100-25
100/75
1.3333
Write the EXPLICT equation for the arithmetic sequence below: 12, 10, 8, 6
aₙ = 14- 2n is the EXPLICT equation for the arithmetic sequence below: 12, 10, 8, 6
What is Sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters
this is an arithmetic sequence whose n th term ( explicit formula) is
aₙ = a + (n - 1 )d
where d is the common difference and a the first term
The given sequence is 12,10,8,6
twelve comma ten comma eight comma six
d=10-12=-2
a=12
Apply in explicit formula
aₙ = 12+ (n - 1 )(-2)
aₙ = 12-2n +2
aₙ = 14- 2n
Hence aₙ = 14- 2n is the EXPLICT equation for the arithmetic sequence below: 12, 10, 8, 6
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I need Help ASAP!!!! PLease help!!!
The new coordinate after the given composite translation (x,y) → (x-5,y+5) will be (x+3,y+12).
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
Reflection is a mirror image of a graph about any axis.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
As per the given translation rule,
(x,y) → (x+8,y+7)
The next translation is (x,y) → (x-5,y+5)
The resultant translation will be,
(x,y) → (x+8,y+7) to (x+8-5,y+7+5)
⇒ (x+3,y+12)
Hence "The new coordinate after the given composite translation (x,y) → (x-5,y+5) will be (x+3,y+12)".
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