The triangle should have 4.35 metres of wire, which means the square should have 6.978 meters
Let "x" is the cutting distance from one end of the wire.
Then, area of square would be ,
Area = (x/4)²
The side of equilateral triangle would be,
L=(10-x)/3
height would be (10-x)/3*√(3)/2
=> (10-x)√(3)/6
So, the area of triangle is
Area of triangle= ((10-x)/3)² ×√(3)/4
=> (10-x)² ×√(3)/36
So, the total area is ,
A = (x/4) + (10 - x)²/36√3
Differentiating Area w.r.t x
dA/dx=x/8-2 ×√(3)/36(10-x)
=> x/8+20× √(3)/36-2 × √(3)/36x
Putting the expression equal to 0,
x/8+20× √(3)/36-2 × √(3)/36x = 0
=> x(1/8+ √(3)/18
=> 10√(3)/18
x*0.22122 = 0.96225
x=4.35
Substituting the value of x
This corresponds to minimum area which is:
A(4.35)=(4.35/4)^2+(10-4.35)^2 × √(3)/36=1.183+1.536
=> 2.719m²
Thus , the minimum area is 2.71 square meters when x=4.35 m. As a result, the wire should be cut such that the dimension of the square is formed by the piece having a length of 4.35 m, and the equilateral triangle is formed by the piece having a length 5.65 m.
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I need this answer i dont think this is the right anwser please help
Answer: 11 ft.
Step-by-step explanation:
Start by listing the variables that you have.
-Total Area=1,848; lot a 33ft wide, 42ft long; lot b xft wide, 42ft long.
- so, our equation looks like 1,848=(33x42)+(42x)
-multiply 33x42=1,386
-subtract 1,386 from both sides to get 462.
-equation should look like 462=42x
-divide by 42 to 11
Question 6 If z is a standard normal variable, find the probability. The probability that z is less than 1.13 a. 0.8708 b. 0.8907 c.0.1292 d.0.8485
If z is a standard normal variable, the probability that z is less than 1.13 is given by: A. 0.8708.
What is the standard normal distribution table?In Statistics, the standard normal distribution table is designed and developed to provide only the area to the left of a specified z-score.
Additionally, since z-score (z₁) and z-score (z₂) are generally symmetric about z = 0 and are negatives of one another, then, by symmetry, the area to the right of z-score (z₂) is always equal to the area to the left of z-score (z₁).
This ultimately implies that, the total areas under a standard normal distribution curve in two tails can be determined by calculating the area to the left of z-score (z₁) and multiplying the value by two (2).
From the z-score table, the area to the left of z-score (z₁ = 1.13) is the same as the probability that z is less than 1.13 and this is given by:
Area to the left of z-score (z₁ = 1.13) = 0.8708.
Probability, P(z ≤ 1.13) = 0.8708.
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Priya invests a sum of money at an interest rate of 8% per year.
At the end of one year, the interest she receives is 1800 rupees.
Work out the value of Priya’s investment at the end of one year.
The value of Priya's investment at end of the year is Rs. 24300.
Simple Interest:The formula for simple interest is given by
Simple interest, I = PTR/100Where, P = Principal amount, T = Time period, and R = Rate of interest
And the formula for the Amount at end of the time period is given by
Amount, A = P + IHere we have
Priya invests a sum of money at an interest rate of 8% per annum
The interest that she gained after 1 year = 1800 Rs.
Let P be the principal amount i.e Priya's investment
Then calculate Simple interest on P at 8% for 1 year
As we know Simple interest = PTR/100
Interest on P = P(1)(8)/100 = 0.08P
From the given data, interest at end of the year = Rs. 1800
=> 0.08P = 1800
=> P = 1800/0.08
=> P = 22500
The amount that Priya invested = Rs. 22500
As we know Amount = Principal amount + interest
= Rs. 22500 + Rs. 1800
= Rs. 24300
Therefore,
The value of Priya's investment at end of the year is Rs. 24300.
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50 POINTS DUE TODAY, Giselle wants to buy the newest book in her favorite series. She has some money saved but does not want to use all her savings on the book. Giselle’s grandma offers to pay some of the cost of the book for every weed she pulls in her grandma’s garden. The graph shows the cost to Giselle for the purchase of the book after pulling x weeds in her grandma’s garden.
Select True or False to describe each statement.
Answer:
Step-by-step explanation:
Based on the graph, it appears that Giselle's grandma is offering to pay for a certain percentage of the cost of the book for every weed that Giselle pulls in her garden. The more weeds Giselle pulls, the more money her grandma will contribute, which will reduce the amount that Giselle has to pay for the book. This can be a good way for Giselle to save money on the book without using all of her savings.
1. True, the graph's beginning represents cost before she picks any weeds.
2. False, the graph shows that the cost for he goes into the negatives, showing that she is still able to earn more money from picking weeds.
3.True, from 0 weeds to 5 weeks picked you can see the price change from $18 to $17.
4. True, once she picks 90 weeds she earns the exact amount of money needed to buy the book.
5. False, she would need to pull 90 weeds in order to not spend her own money.
What is the answer?
Please help
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Answer: 105 frames
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Given: [tex]\textsf{25 frames per second, starts at 0 seconds already played 190 frames}[/tex]
Find: [tex]\textsf{Frame count already played when time = -3.4}[/tex]
Solution: In order to find the number of frames that have already played when the time was equal to -3.4 seconds, we must first figure out long the delay is. We can do this by dividing 25 frames per second from 190 frames which gives us that 7.6 seconds passed before we started counting at 0.
Therefore, if we want to look at -3.4 seconds out of -7.6 seconds that means that 4.2 seconds passes after the initial playing to get to -3.4 seconds. Now we can just multiply 4.2 seconds by 25 frames per second which gives us that about 105 frames have played when the time was equal to -3.4
When archeologists excavate a site, they mark it off with a coordinate grid so that they can easily
identify where artefacts are found and keep a record of the site forever. At the West Kennet Long
Barrow in England, a grave site back to 3600 BCE was found. There are three chambers at the
coordinates (7,9), (17, 33) and (-36,41). It has been said that they form an isosceles triangle with
height twice the length of its base.
Determine whether the statement is true. Justify your answer. Hint: An isosceles triangle has at
least two sides of equal side lengths.
Expectation of Product of Random Variables Proof From the definition of the expected value, the expected value of the product of two random variables is E(X . Y) = EErr-r2 . P(X=Y =r2) where the sum is over all possible values of r1 and r2 that the variable X and Y can take on_ Using the definition above formally prove that if the events X = r1 and Y =r2 are independent (for any r1 and r2) , we have E(X . Y) = E(X) . E(Y). Now; if you have two random variables X and Y and Y=aI+c, show that if E[X2] # E[XJ? , then E(X . Y) # E(X) . E(Y). If you roll a die 6 times in a rOW what is the expected value of the product of the 6 outcomes?
Look to the photo and you will find the answers there ✔️
start from left to right
Select all the coefficients in the simplified form of (4y + 5y2-6) - (5y + 27-2²).
A -1
B. 4
C. 5
D. 6
E. 33
The coefficient of x² in simplified form is 5
What is coefficient ?
A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.
a symbol or number that multiplies another symbol or number (used as a mathematical variable). The coefficient of x in the phrase 3x is 3, and it is a number that represents a quality (such as the metal's coefficient of expansion) of a substance or device.
(4y + 5y² - 6) - (5y + 27 - 2²)
4y + 5y² - 6 - 5y - 27 + 4
5y² - 1y - 29
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The perimeter is less than
or equal to 51 meters.
10 m
8m
8 m
10 m
Solve the inequality
(16-24)-(57-77) divided by (-2)
The answer will be -6 when (16-24)-(57-77) divided by (-2).
What is division?
One of the basic mathematical operations is division, which splits a bigger number into smaller groups with the same number of components. For example, if 20 students need to be divided into groups of five for a sporting event, how many total groups will be created? Dealing with such challenges is made easier by the division operation. In this instance, divide 20 by 5. The result will be 20 x 5 = 4. There will be 4 groups total, each with 5 students. You can verify this number by multiplying 4 by 5 and getting the answer 20, which equals 20.
Here (16-24)-(57-77)/-2
= (-8)-(20)/-2
=12/-2
=-6
Hence the answer will be -6.
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Find the Amount (A) (Principal Rs 50000 Time = 7 years interest = 3%.
Answer: Rs 60500
Step-by-step explanation:
Principal = Rs 50000 = p
Time = 7 years = t
Simple interest rate = 3% = r
Interest = p*t*r/100
using above formula,
50000*7*3/100=10500
So, final amount = principal + interest = 50000+10500 = Rs 60500
An oil company fills 1 over 12 of a tank in 1 over 4 hour with gasoline. At this rate, which expression can be used to determine how long it will take for the tank to fill completely? (1 point)
Group of answer choices
1 over 4⋅ 1 over 12
1 over 12⋅ 4
1 over 4⋅ 12
12 ⋅ 4
The expression that can be used to determine how long it will take for the tank to fill completely is C. 1 over 4 . 12.
How to illustrate the rate?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10.
In this case, the oil company fills 1 over 12 of a tank in 1 over 4 hour with gasoline.
The rate will be:
= 1/4 ÷ 1/12
= 1/4 × 12
= 3
The correct option is C
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If f(x) + x^2[f(x)]^5 = 34 and f(1) = 2, find f '(1). F '(1) = Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y sin 12x = x cos 2y, (pi/2, pi/4)
To find the derivative of f(x) at x = 1, we can use the formula for implicit differentiation:
d/dx[f(x) + x^2[f(x)]^5] = 0
Substituting the given values, we get:d/dx[f(1) + 1^2[f(1)]^5] = 0
d/dx[2 + 1[2]^5] = 0
Solving for the derivative, we get:d/dx[2 + 1[2]^5] = 0
d/dx[2 + 32] = 0
0 + 32 = 0
Therefore, the derivative of f(x) at x = 1 is 32.
To find the equation of the tangent line to the curve at the given point (pi/2, pi/4), we can use the formula for the slope of a tangent line:
m = f'(x) = d/dx[y sin 12x] / d/dx[x cos 2y]
Substituting the given values, we get:m = d/dx[pi/4 sin 12(pi/2)] / d/dx[pi/2 cos 2(pi/4)]
m = d/dx[pi/4 sin 6pi] / d/dx[pi/2 cos pi/2]
m = 0 / 0
Since the derivative of the numerator is 0 and the derivative of the denominator is 0, the slope of the tangent line is undefined. This means that the tangent line is vertical and parallel to the y-axis.
The equation of the tangent line at the given point is therefore of the form:
x = c
where c is the x-coordinate of the given point, which is pi/2. Therefore, the equation of the tangent line is:
x = pi/2
Note that this is just the equation of a vertical line with an x-intercept at pi/2.
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The coordinates of the endpoints A B are given. A (7,6) and B (-9,-6). Point K is located on AB so that AK= 3/1. What is the x-coordinate of point K?
The x-coordinate of the point K that divides AB in 3:1 will be -5.
What is the section of the line?Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
The directions of the endpoints A and B are given. A (7,6) and B (- 9,- 6). Point K is situated on the Stomach muscle with the goal that AK: KB = 3/1.
Then the x-coordinate of the point K is given as,
x = (mx₂ + nx₁) / (m + n)
x = [3(-9) + 1(7)] / (3 + 1)
x = (- 27 + 7) / 4
x = - 20 / 4
x = - 5
The x-coordinate of the point K that divides AB in 3:1 will be -5.
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in the simek and o'brien study, a novice golfer had to sink four consecutive putts before going to the next step. this exemplifies:
In the Simek and O'Brien study, progressive overload was used by requiring the novice golfer to sink four consecutive putts before moving on to the next step. Progressive Overload.
Progressive overload is the gradual increase of stress placed on the body during physical activity. By requiring the novice golfer to sink four consecutive putts before moving on to the next step, the study is increasing the difficulty of the task and placing additional stress on the body.
Progressive overload is an effective and essential technique for improving physical performance. It involves gradually increasing the intensity of the activity or exercise, which places additional stress on the body and forces it to adapt and become stronger. In the Simek and O'Brien study, progressive overload was used by requiring the novice golfer to sink four consecutive putts before moving on to the next step. This increased the difficulty of the task and allowed the golfer to gradually improve their performance. By gradually increasing the difficulty of the task, the study was able to effectively use progressive overload to improve the golfer's performance.
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x and y are declared as integer variables.
You are given the following expression:
x >= y
Which of these expressions is the opposite of the above expression and has valid syntax?
-x <= y
- x =< y
- There's not enough information to determine this.
- x == y
- x < y
- x =< y is the expression and acceptable syntax.
Explain about the expression?
A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases.
A term may be a number, a variable, a product of two or more variables, or a combination of both. A single phrase or a set of terms can make up an algebraic expression. The two terms in the formula 4x + y, for instance, are 4x and y.
Algebra's associative, commutative, and distributive characteristics are the ones that are most frequently utilized to make algebraic expressions simpler.
The converse of the expression and having proper syntax is
= x >= y.
= -x <= y
=- x =< y
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50 POINTS Giselle wants to buy the newest book in her favorite series. She has some money saved but does not want to
use all her savings on the book. Giselle’s grandma offers to pay some of the cost of the book for every weed she
pulls in her grandma’s garden.
The graph shows the cost to Giselle for the purchase of the book after pulling x weeds in her grandma’s garden.
Select True or False to describe each statement.
(2 points for each correct answer = 10 points)
SELECT True or False
Answer:
true false false true true
Which of the following is not a criterion for congruence of ∆ s a SAS B ASA C SSA D SSS?
(C) SSA is not a requirement for triangle congruence.
What is the congruence of triangles?
Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.
We can move, flip, twist, and turn these triangles to produce the same effect.
When relocated, they are parallel to one another.
Two triangles are congruent if they satisfy all five conditions for congruence.
Right angle-hypotenuse-side (RHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) are the four terms (RHS).
We know that SSA is not the criteria for the congruence of the triangles.
Therefore, (C) SSA is not a requirement for triangle congruence.
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14% of americans like to only cook and 48% of americans like to only shop, while 85% enjoy either cooking or shopping. what is the probability that a randomly selected american enjoys both activities?
The probability that a randomly selected american enjoys both activities is 23 % .
Given :
14 % of americans like to only cook and 48 % of americans like to only shop, while 85 % enjoy either cooking or shopping .
14 % = 0.14
48 % = 0.48
overlapping is 85 % = 0.85
P ( A ) = 0.14
P ( B ) = 0.48
P ( A and B ) = 0.85
we know that,
P ( A or B ) = P ( A ) + P ( B ) - P ( A and B )
= 0.14 + 0.48 - 0.85
= 0.62 - 0.85
= -0.23
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How do you use the Binomial Theorem to expand (1+x)^−1?
The Binomial expansion of given expression, (1+x)⁻¹ is 1 − x + x² - x³+ x⁴ + ...
What is binomial theorem?Binomial theorem primarily helps to find the expanded value of the algebraic expression of the form (x + y)ⁿ
Using the Binomial theorem we can expand the series of ( x + y )ⁿ as
( x + y)ⁿ = ∑ ⁿCₖ xⁿ⁻ᵏ yᵏ
k= 0 to n
= xⁿ + (n(n-1)/2!)x⁽ⁿ⁻¹⁾y + (n(n-1)(n-2)/3!)x⁽ⁿ⁻²⁾y² + .......
where n ≥ 0 and (ⁿCₖ ) is known as a binomial coefficient and they should be positive integers.
We have given that (1+x)⁻¹ comparing it with ( x + y )ⁿ we get, y = 1 ; n = -1
Binomial expansion for this is followed the same way as expanding larger power expansion,
So (1+x)⁻¹ = 1 + (-1)x + (-1)(-1–1)/2! x² + (-1)(-1–1)(-1–2)/3! x³+…….
= 1 -x + x²- x³ +….
but this will result in an infinite series and will converge for values belonging to
|x|<1. So, the required binomial series is
1 -x + x² - x³ +….
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Spin a spinner numbered 1-8 and you land on 8 twice in a row what is the probability?
The probability that you land on 8 twice is 1/64
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
We spin a spinner numbered 1-8 twice
The total sample space can be given by considering all the possible values
Hence the total number of spins are 8*8= 64 spins
The possibility that getting 8 twice is only once possible. As it will be only one pair in all the possible values.
Hence, The total probability is 1/64
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Which equation choice could represent the graph shown below?
By analizying the zeros on the graph, we conclude that the equation that could represent the graph is:
y = (x + 5)²*(x - 3)²
Which equation choice could represent the graph?On the graph, we have a polynomial.
Remember that the degree of the polynomial is related to the zeros of the polynomial. Here we can see that we have two double zeros, one at x = -5 and other at x = 3
We know that are double zeros because the curvature of the polynomial changes there.
Then the equation will be something like:
y = (x + 5)²*(x - 3)²
So that is the correct option, top right.
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opponent has 2 dollars, you have 1 dollar. you play a game where you each wager 1 dollar. opponent has 1/3 chance of winning each game, you have 2/3 chance of winning each game. you play until someone is bankrupt, and then they lose. what is the probability you win the game?
The probability to win the game is 4/7.
Clearly, you can not win with zero dollars:
Pr(W|S0)=0
and you cannot lose with three dollars:
Pr(W|S3)=1
If you start with two dollars, then the probability of winning is:
Pr(W|S2)=Pr(S1|S2)Pr(W|S1)+Pr(S3|S2)Pr(W|S3)=1/3×Pr(W|S1)+2/3
If you start with one dollar, then the probability of winning is:
Pr(W|S1)=Pr(S2|S1)Pr(W|S2)+Pr(S0|S2)Pr(W|S0)=2/3×Pr(W|S2)
So, we have two equations in two unknowns:
Pr(W|S1)=2/3×Pr(W|S2)
Pr(W|S2)=1/3×Pr(W|S1)+2/3
Solving them we get:
Pr(W|S1)=4/7
Pr(W|S2)=6/7
So, your chance of winning when you start with one dollar is 4/7.
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Sara calculated the product 33 × 34 × 35 × 36 × 37 × 38 and got a number. Which of these digits will be in the ONES place of the number?
Answer:
It's the digit 3.
Step-by-step explanation:
Since all digits from 33 to 38 are digits not less than 3, it follows that in the result there will be at least one digit bigger than 3. Since 33 to 38 represent a set with six numbers, we can conclude that the product of those numbers must have at least six digits to the left of the decimal, which is the ones place. Therefore, the digital 3 gets into the ones place.
HELPPPPPPPP PLEASE HELP ME EEEEEE
Answer: The correct answer is b
Step-by-step explanation:
25% off $30 is 22.50 and then when you add 7%ax it turns out to be 24.08
Which of the following quadratic equations has roots 3, 5? a)`x^2-15x+3=0` b)`x^2-8x+15=0` c)`x^2+3x+5=0` d)`x^2+8x-15=0`
The quadratic equation (B) x²-8x+15=0 has the required roots 3 and 5.
What is a quadratic equation?ax2 + bx + c = 0 is a quadratic equation or a second-order polynomial equation with a single variable.
The algebraic's theorem guarantees that it is a second-order polynomial equation, hence it must have at least one solution.
The answer might be straightforward or challenging.
x2 - 5x - 3x + 15 = 0 are the roots of the quadratic equation x2 - 8x + 15 = 0.
x(x-5)-3(x-5)
(x-3)(x-5)=0
x = 3, 5
So, the correct answer is x² - 8x + 15 = 0.
Therefore, the quadratic equation (B) x²-8x+15=0 has the required roots 3 and 5.
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Any help would be appreciated
The values for a and b in the expression for the area of the rhombus, a·√b, where the area of the regular hexagon that forms the rhombus that has an area of 24·√3, are; a = 8, b = 3
a + b = 8 + 3 = 11
What is a rhombus?A rhombus is a quadrilateral in which the length of the each of the four sides are the same.
Coprime integers integers are two integers that have 1 as their only common divisor
The area of the hexagons = 24·√3
The formula for the area of regular hexagon, A = 3·√3×s²/2
Where;
s = The sider length of the regular hexagon
Therefore; 24·√3 = 3·√3×s²/2
The division property indicates that dividing booth sides of the above equation by √3, we get;
24 = 3×s²/2
2 × 24/3 = s²
16 = s²
s² = 16 (symmetric property)
s = ±√(16) = ±4
The possible value for the side length of the regular hexagon is +4
The formula for the area of a rhombus = s²·sin(θ)
Where;
θ = The interior angle of a regular hexagon = 120°
Therefore; A = 4² × sin(120°) = (16 × √3)/2 = 8·√3
Therefore; a·√b = 8·√3
a = 8, b = 3
a + b = 8 + 3 = 11
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A water tank is built in the form of a right rectangular prism, with dimensions that measure 13.1 ft by 7.5 ft by 7.2 ft. How many cubic feet of water would it hold when it is full? Round your answer to the nearest tenth if necessary.
The rectangular prism has a capacity of 707.4 ft3 when it is fully filled with water.
What is the Volume of Rectangular Prism?Thus, volume of a rectangular prism (V) = l w h is the formula for a rectangular prism's volume. We multiply the length, width, and height, or the area of the base is multiplied by the height, to find the volume of the rectangular prism.Volume is equal to the sum of the dimensions of length, width, and height.Given:Dimensions: 13.1 ft long, 7.5 ft wide, and 7.2 ft tall.
Thus:
Water volume equals 13.1 × 7.5 × 7.2
Water capacity is 707.4 feet3
Consequently, 707.4 ft3 of water will fit inside the rectangular prism when it is full.
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WILL MARK AS BRAINLEST!!!!!!!!!!!!!!!!
figure abcdef was reflected across the line y = –x to create figure a'b'c'd'e'f'. what are the coordinates of the pre-image of f'?
(C) F = (2, -4) are the coordinates of the pre-image of F'.
What are coordinates?A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
So, the result of reflecting Figure ABCDEF across y = -x is A'B'C'D'E'F'.
The transformational rule is:
(x, y) ⇒ (-y, -x)
Which means:
(x, y) ⇒ (-y, -x) ⇒ (4, -2)
In contrast:
-y = 4
-x = -2
Solving for x and y as follows:
y = -4
x = 2
Therefore, (C) F = (2, -4) are the coordinates of the pre-image of F'.
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Complete question:
Figure ABCDEF was reflected across the line y = –x to create figure A'B'C'D'E'F'.
On a coordinate plane, a 6-sided figure has points A prime (negative 2, negative 2), B prime (negative 4, 2), C prime (negative 2, 6), D prime (4, 6), E prime (6, 2), and F prime (4, negative 2).
What are the coordinates of the pre-image of F'?
a. (–2, 4)
b. (4, 2)
c. (2, –4)
d. (–4, –2)
