Therefore, when you solve this expression (6 + 5) x 2^2 - 4 , the solution is 23.
Here's an example of a numerical expression using at least three operations, a parenthesis, and an exponent that when solved has a solution of 23:
(6 + 5) x 2^2 - 4 = 23
Explanation:
- Parenthesis: (6 + 5) = 11
- Exponent: 2^2 = 4
- Multiplication: 11 x 4 = 44
- Subtraction: 44 - 4 = 40
- Solution: 40 divided by 2 = 20, then 20 plus 3 = 23
Therefore, when you solve this expression, the solution is 23.
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Henry's candy jar has the following pleces of candy in it:
3 Snickers
1 Reese's
1 Twix
2 Milky Ways
2 Skittles Packs
Henry will randomly choose one piece of candy,
He will then put it back and randomly choose another piece
of candy. What is the probability that he will
choose a Milky Way and then a Snickers?
The probability of Henry choosing a Milky Way and then a Snickers is 2/27.
1. First, let's find the total number of candy pieces in Henry's candy jar:
3 Snickers + 1 Reese's + 1 Twix + 2 Milky Ways + 2 Skittles Packs = 9 pieces of candy.
2. Next, we'll calculate the probability of choosing a Milky Way on the first pick:
There are 2 Milky Ways and 9 total pieces of candy, so the probability is 2/9.
3. Since Henry puts the candy back, there are still 9 pieces of candy for the second pick. Now, we'll calculate the probability of choosing a Snickers on the second pick:
There are 3 Snickers and 9 total pieces of candy, so the probability is 3/9 (or 1/3).
4. Finally, we'll multiply the probabilities of each individual event to find the probability of both events occurring together (choosing a Milky Way and then a Snickers):
(2/9) * (1/3) = 2/27
So, the probability of Henry choosing a Milky Way and then a Snickers is 2/27.
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Find the coordinates of the points on the curve x(????)=3????^2 +1 ????????????y(????)=????^3 −1, for which the tangent linehas a slope of 1/2
The coordinates of the point on the curve where the tangent line has a slope of 1/2 are (4, 0).
To find the coordinates of the points on the curve x(t) = 3t^2 + 1 and y(t) = t^3 - 1, where the tangent line has a slope of 1/2, follow these steps:
1. Calculate the derivatives of x(t) and y(t) with respect to t:
dx/dt = 6t
dy/dt = 3t^2
2. The slope of the tangent line is given by dy/dx, so calculate dy/dx using the chain rule:
dy/dx = (dy/dt) / (dx/dt) = (3t^2) / (6t) = t/2
3. Set the slope equal to 1/2 and solve for t:
t/2 = 1/2
t = 1
4. Plug the value of t back into the original equations for x(t) and y(t) to find the coordinates of the point:
x(1) = 3(1)^2 + 1 = 4
y(1) = (1)^3 - 1 = 0
The coordinates of the point on the curve where the tangent line has a slope of 1/2 are (4, 0).
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Area of this shape irregular polygon the high is 4 and width 13
:)
The area of this irregular polygon is 344.5 square units.
To find the area of an irregular polygon, you can divide it into smaller, simpler shapes.
In this case, we can divide the polygon into a rectangle and a right triangle.
The rectangle has a height of 4 and a width of 13, so its area is 4 x 13 = 52 square units.
The right triangle has a base of 13 and a height of (110 - 4 x 13) / 2 = 45, since the total height of the polygon is 110.
Therefore, the area of the right triangle is (1/2) x base x height = (1/2) x 13 x 45 = 292.5 square units.
Adding the areas of the rectangle and the triangle, we get a total area of 52 + 292.5 = 344.5 square units.
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"When a contractor paints a square surface that has a side length of x feet, he needs to know the area of the surface in order to buy the correct amount of paint. Since the contractor always adds 25 square feet to the area, he buys extra paint. Which function can be used to find the totall area in square feet, Ax , that the contractor will use to determine how much paint he needs to buy?
The function that can be used to find the total area is: (x^2 + 25) sq. ft.
What is a square?A square is a type of quadrilateral which has an equal length of sides. So then its area can be calculated as;
area of a square = length x length
We have from the question that; a square surface that has a side length of x feet. So that;
area of the square surface = length * length
= x * x
= x^2 square feet
But since the contractor always adds 25 square feet to the area, he buys extra paint, then the function required is:
total area = (x^2 + 25) sq. ft.
The function is (x^2 + 25) sq. ft.
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Answer:
A(x) = x² + 25----------------------
In order to find the total area, we need to consider both the area of the square surface and the extra paint he always adds.
Find the area of the square surface:
A = x² (since the side length is x feet)Add the extra 25 square feet of paint:
A(x) = A + 25Combining these steps, the function is:
A(x) = x² + 25Which one is it please help thank you.
The students who attend Memorial High School have a wide variety of extra-curricular activities to choose from in the after-school program. Students are 38% likely to join the dance team; 18% likely to participate in the school play; 42% likely to join the yearbook club; and 64% likely to join the marching band. Many students choose to participate in multiple activities. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors. If Event A = sophomore or junior, what is Event A'?
Event A' has a probability of 50% (25% for freshmen + 25% for seniors).
To determine Event A', we need to first identify what Event A represents. Event A is the probability that a student is a sophomore or junior. Since students have equal probabilities of being freshmen, sophomores, juniors, or seniors, the probability of Event A is 50% (25% for sophomores + 25% for juniors).
Event A' is the complement of Event A, which means it includes the other two grade levels not included in Event A, in this case, freshmen and seniors. Therefore, Event A' is the probability that a student is a freshman or a senior. Since students have equal probabilities of being in each grade level, Event A' also has a probability of 50% (25% for freshmen + 25% for seniors).
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Patricia bought 4 apples and 9 bananas for $12. 70. Jose bought 8 apples and 11 bananas for $17. 70 at the same grocery store. What's the price of one apple?
the price of one apple after solving the simultaneous equations is $1.45.
Let's denote the price of one apple by "a" and the price of one banana by "b". We can then set up a system of two equations to represent the given information:
4a + 9b = 12.70 (equation 1)
8a + 11b = 17.70 (equation 2)
To solve for the price of one apple, we want to isolate "a" in one of the equations. One way to do this is to multiply equation 1 by 8 and equation 2 by -4, which will allow us to eliminate "b" when we add the two equations together:
(8)(4a + 9b) = (8)(12.70) --> 32a + 72b = 101.60 (equation 3)
(-4)(8a + 11b) = (-4)(17.70) --> -32a - 44b = -70.80 (equation 4)
Adding equations 3 and 4 gives:
28b = 30.80
Solving for "b" yields:
b = 1.10
Substituting this value of "b" into equation 1 gives:
4a + 9(1.10) = 12.70
Solving for "a" yields:
a = 1.45
Therefore, the price of one apple is $1.45.
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Question: P7.18. Convert the following numbers to decimal form: a. * FA 5.6 16; b. * 725.38; c. 3F 4.8 16; d. 73.25 8; e. FF.F 0 16. P7.18.
a. FA5.6<sub>16</sub> = 15x16<sup>2</sup> + 10x16 + 5 + 6/16 = 4005.375<sub>10</sub>
b. 725.38<sub>10</sub> remains the same in decimal form
c. 3F4.8<sub>16</sub> = 3x16<sup>2</sup> + 15x16 + 4 + 8/16 = 1012.5<sub>10</sub>
d. 73.25<sub>8</sub> = 7x8 + 3 + 2/8 = 59.3125<sub>10</sub>
e. FF.F0<sub>16</sub> = 15x16 + 15 + 15/16 + 0/256 = 255.9375<sub>10</sub>
Decimal form is a way of representing numbers using the base 10 number system. In this system, there are 10 digits from 0 to 9 that are used to represent all possible numbers. Each digit in a decimal number has a place value that is determined by its position. The rightmost digit represents units, the next digit to the left represents tens, and so on, with each successive digit representing higher powers of 10.
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Fries 420 grams = $2.77
How much if its 1kg?
The length of a rectangle is 4 m more than the width. if the area of the rectangle is 77 m2. how many meters long is the width of the rectangle?
answer choices d: -11 m: 7 z: 9
The width of the rectangle is approximately 5.39 meters.
Let's denote the width of the rectangle by x. According to the problem, the length of the rectangle is 4 meters more than the width, which means that the length can be represented as x+4.
The formula for the area of a rectangle is A = length x width. In this case, we know that the area of the rectangle is 77 square meters, so we can set up the following equation:
77 = (x+4)x
Expanding the brackets, we get:
77 = x² + 4x
Rearranging this equation into standard quadratic form, we get:
x² + 4x - 77 = 0
To solve for x, we can use the quadratic formula:
[tex]x = \frac{(-b ± sqrt(b^2 - 4ac))}{ 2a}[/tex]
Plugging in the values for a, b, and c, we get:
[tex]x = \frac{(-4 ± sqrt(4^2 - 4(1)(-77)))}{ 2(1)}[/tex]
Simplifying this expression, we get:
[tex]x = \frac{(-4 ± sqrt(336)} { 2}[/tex]
[tex]x = \frac{(-4 ± 4sqrt(21))}{ 2}[/tex]
x = -2 ± 2[tex]\sqrt{(21)}[/tex]
Since the width of a rectangle cannot be negative, we discard the negative solution and get:
x = -2 ± 2[tex]\sqrt{(21)}[/tex]
Therefore, the width of the rectangle is approximately 5.39 meters (rounded to two decimal places).
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What are two different ways you can solve 2(x – 3) = 8?
Answer:
There are three methods used to solve systems of equations: graphing, substitution, and elimination.
Step-by-step explanation:
A mover notes the weights of a table and 4 chairs and records t+4C >_100 on his invoice. What is he communicating?
The choices are,
A. The table and 4 chairs each weigh more than 100 pounds.
B. The table and 4 chairs weigh at most 100 pounds.
C. The table and 4 chairs weigh around 100 pounds, give or take a little.
D. The table and 4 chairs at
least 100 pounds
The mover is communicating that the weight of the table and 4 chairs combined, represented as t+4C, is greater than or equal to 100 pounds.
The expression t+4C represents the total weight of the table and 4 chairs. The mover's invoice states that this total weight is greater than or equal to 100 pounds, which means that the combined weight of the table and chairs is at least 100 pounds. Therefore, the correct answer is D, "The table and 4 chairs weigh at least 100 pounds."
To solve this mathematically, we can use algebraic inequalities. The inequality t+4C >_ 100 can be rearranged as t >_ 100-4C. This means that the weight of the table t must be greater than or equal to 100 minus four times the weight of a single chair C.
If each chair weighs less than 25 pounds, then the total weight of the table and 4 chairs combined will be at least 100 pounds. So D is correct answer.
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A point in the figure is chosen at random. Find the probability that the point lies in the shaded region of the circle.
To find the probability that the point lies in the shaded region of the circle, we need to compare the area of the shaded region to the total area of the circle. Let's say the radius of the circle is r.
The area of the shaded region can be found by subtracting the area of the unshaded region from the total area of the circle. The unshaded region is a square with side length equal to the radius of the circle. Therefore, its area is r^2. The total area of the circle is πr^2. So the area of the shaded region is:
πr^2 - r^2 = r^2(π - 1)
Now, if we choose a point at random from the circle, any point has an equal chance of being chosen. So the probability of choosing a point in the shaded region is equal to the area of the shaded region divided by the total area of the circle:
P(shaded) = (r^2(π - 1))/πr^2 = π - 1
Therefore, the probability of choosing a point in the shaded region of the circle is π - 1.
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i need to factor 1/2y-5 1/2 and i can't seem to get it
The factored form of the equation is 1/2(y - √5)
To factor this expression, we need to look for any common factors that can be pulled out of both terms. We can see that both terms contain a factor of 1/2, so we can factor that out:
1/2(y - 5 1/2)
Now we need to see if there are any further factors that we can find. The term inside the parentheses, y - 5 1/2, cannot be factored any further using real numbers. However, we can write the expression as y - √5, which shows that it involves the square root of 5.
So the final factored form of the expression is:
1/2(y - √5)
This means that if we multiply 1/2 by (y - √5), we get back the original expression 1/2y - 5 1/2.
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Solve for x. Round to the nearest hundredth if necessary.
X
24°
14
Step-by-step explanation:
there is no explanation about x so wierd
The temperature on skylar’s thermometer last night was −3°f. this morning it was colder. what could be the temperature on her thermometer this morning?−5°f−1°f0°f2°f
The only option left is −5°F, which is colder than −3°F and thus could be the temperature on her thermometer this morning.
The temperature on Skylar's thermometer is measured using a scale that indicates the degree of hotness or coldness of the atmosphere. In this case, we know that the temperature on her thermometer last night was −3°F. The negative sign indicates that the temperature was below the freezing point of water.
We are asked to determine what the temperature could be on her thermometer this morning. Since we are told that the temperature is colder than −3°F, we can eliminate 0°F and 2°F as possible options, as they are warmer than −3°F.
Similarly, −1°F is only slightly colder than −3°F, so it is unlikely to be the temperature on Skylar's thermometer this morning. Therefore, the only option left is −5°F, which is colder than −3°F and thus could be the temperature on her thermometer this morning.
It is important to note that temperature can have a significant impact on our daily lives. Extreme cold temperatures can cause frostbite, hypothermia, and other health hazards, while hot temperatures can lead to dehydration, heat exhaustion, and heat stroke. It is important to dress appropriately and take necessary precautions when the temperature is too low or too high.
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The volume of a pyramid is 51 cubic centimeters. The area of the base is 17 square centimeters What is its height?
f (x) = ¹4 - 6. Find the inverse of f(x) and its domain.
O A. f¹(x) =
6 + 4, where x #-6
O B. f¹(x) =
6 +4, where x #4
O c. f¹(x) =
¹6-4, where x 4
OD. f¹(x) = 2¹6-4, where x#-6
The correct option is the first one, and the domain is the set of real numbers except for x = -6.
How to find the inverse?The inverse will be a function such that when we take the composition we get the identity, then we can write:
[tex]f(g(x)) = \frac{1}{g(x) - 4} - 6 = x[/tex]
We need to solve that for g(x), we will get:
[tex]\frac{1}{g(x) - 4} - 6 = x\\\\\frac{1}{g(x) - 4} = x +6\\\\g(x) - 4 = \frac{1}{x + 6} \\g(x) = \frac{1}{x + 6} + 4[/tex]
That is the inverse function, and notice that if x = -6 the denominator becomes zero, so that value is not in the domain.
Then the correct option is the first one.
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You must build a ramp with a rise of 15 inches to roll some gym equipment into your school. If you follow the ADA specifications:
To build a ramp with a 15-inch rise for rolling gym equipment into your school, following ADA specifications, we should create a ramp with a run of 180 inches to maintain a 1:12 slope.
For building a ramp with a rise of 15 inches for rolling gym equipment into your school, following ADA specifications. Let's use these terms in our step-by-step explanation:
1. ADA specifications: The Americans with Disabilities Act (ADA) specifies that the slope of a ramp should be no more than 1:12, which means that for every 1 inch of rise, there should be 12 inches of run.
2. Ramp rise: In this case, the rise is 15 inches.
3. Calculate ramp run: To find the ramp run, we can use the ADA specification of 1:12. Multiply the rise (15 inches) by 12.
15 inches x 12 = 180 inches
4. Ramp run: Based on the calculation, the run for the ramp should be 180 inches.
5. Ramp length: To ensure a safe and accessible ramp, follow the ADA specifications and use a ramp length of 180 inches to achieve the 15-inch rise.
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A pathway made of slate tiles measures 5 1/3 yards long. A tile measuring 2 feet is added to the end of the pathway.
What is the total length of the pathway now?
1. 5 1/3 ft
2. 10 2/3 ft
3. 18 ft
4. 22 ft
Answer:
18 feet
Step-by-step explanation:
multiply 5 1/3 yards by 3 to find the measurement in feet.
16/3 x 3 = 16
16 + 2 = 18
Helping in the name of Jesus.
I NEED HELP ON THIS ASAP!!! IT'S DUE TONIGHT
Answer:
First Problem:
Transformation: Reflection across the x-axis, shift 2 units rightward
Equation: g(x)=-5^(x-2)
Second Problem:
Transformation: Reflection across the y-axis, shift 4 units upward
Equation: 10^-x+4
Step-by-step explanation:
Imagine folding a piece of paper and using the x or y axis as the crease marks. By folding them and comparing them, we can find out whether it is either the x-axis, y-axis, or both-axis. Then, we move the graph, to match the position in the second picture.
As for equations, exponential functions have the parent function of y=b^(x+c)+h. By plugging in any points given, let's say (1,5), we can see that 5=b^1 and simplifying shows 5=b. Therefore, the function is y=5^x. Using that first equation, we transform it. If over the x-axis, convert y=b^x to y=-b^x. If over the y-axis, convert y=b^x to y=b^-x. For horizontal shift, if going rightward, it is x-c. If going leftward, it is x+c. For vertical shift, if going up, b^x+h. If going down, b^x-h.
If unsure, plug-in points to see if your answer checks out with the equation :)
+
ent will
A circle with center (7,3) and radius of 5 is graphed below with a square inscribed in
the circle.
+
Dillon says to write the equation of the tangent line you need the opposite-reciprocal
slope of the slope of the radius and Chelsey says you need to use the same slope as
the radius. Who is correct and why? Write the equation of the tangent line.
Part B: Find the perimeter of BCDE.
Chelsey is correct.
The equation of the tangent line is y = 8
Perimeter of BCDE is 28.28
How to determine tangent line and perimeter?Chelsey is correct. The tangent line at a point on a circle is perpendicular to the radius at that point.
Therefore, it has the same slope as the radius at the point of tangency.
To find the equation of the tangent line at point B(7,8), find the slope of the radius at B.
The radius at B passes through the center of the circle (7,3) and B(7,8), so its slope is:
m = (8 - 3) / (7 - 7) = undefined
This is because the radius is a vertical line. The slope of the tangent line at B is the negative reciprocal of the slope of the radius at B, which is 0.
The equation of the tangent line is:
y - 8 = 0(x - 7)
y = 8
Part B: To find the perimeter of BCDE, we need to find the length of one of its sides and then multiply by 4. Since the square is inscribed in the circle, its diagonal is equal to the diameter of the circle, which is 10 (twice the radius).
Therefore, the length of one side of the square is:
s = 10/√(2) ≈ 7.07
The perimeter of BCDE is:
4s = 4(7.07) ≈ 28.28
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Area The measurement of the side of a square floor tile is 10 inches, with a possible error of 1/32 inch.
(a) Use differentials to approximate the possible propagated error in computing the area of the square. (b) Approximate the percent error in computing the area of the square.
The possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.
How to calculate the error propagation?
(a) Let A be the area of the square tile. The differential of A with respect to the side length x is dA/dx = 2x.
dA ≈ (dA/dx)dx
At the lower end of the possible range for x, we have:
x = 9 31/32 inches
dx = 1/32 inch
dA = (2x)(dx) = (2(9 31/32))(1/32) = 19/32 square inches
At the upper end of the possible range for x, we have:
x = 10 1/32 inches
dx = 1/32 inch
dA = (2x)(dx) = (2(10 1/32))(1/32) = 21/32 square inches
Therefore, the possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.
(b) The percent error in computing the area of the square is given by:
(percent error) = (error / actual value) x 100
(percent error) = [(21/32 - 100) / 100] x 100% = -79/1600 x 100% ≈ -4.94%.
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A, B, and C are points of tangency in the given Circle, a m equals 6, BK equals 4 in the perimeter of mkn is 34
The perimeter of triangle MKN is 34 units.
How to find the length of segment KN?Based on the information provided, we have a circle with three points of tangency: A, B, and C. Let's consider the triangle formed by these points: MKN.
We are given that the length of AM is 6 and the length of BK is 4. We need to find the perimeter of triangle MKN.
To find the perimeter, we need to know the lengths of all three sides. However, the length of side AC is not provided.
Without additional information, we cannot determine the lengths of sides MN and KN or calculate the perimeter of triangle MKN.
Therefore, with the given information, we cannot find the perimeter of triangle MKN or provide a numerical answer
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A bag has 6 red marbles, 3 blue marbles, and 1 orange marble. In a game to raise money for a class trip, parents pay $5 and pull a marble randomly from the bag. The payout is $10 for pulling an orange marble, $4 for a blue marble, and $1 for a red marble. How much can the class expect to earn per game?
Solve for x (2-3) 67
1. What is the volume of the sphere?
4
The volume of the given sphere having radius of 4 units is 267.94 units³.
Given the radius of the sphere (r) = 4 units
To find the volume of the given sphere, we have to substitute the radius in the below volume formula of the sphere,
the volume of the sphere = 4/3 * π * r³
the volume of the given sphere = 4/3 * 3.14 * (4)³
[π is approximately equal to 3.14]
the volume of the given sphere = 267.94 units³
So from the above analysis, we can conclude that the volume of the sphere having 4 units radius is 267.94 units³.
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Given question is not having complete information, the complete question is written below:
What is the volume of the sphere having 4 units radius?
Evaluate the following limits analytically. Show your work for full credit.
Iim (sin(9x))/x
x->0
The limit of (sin(9x))/x as x approaches 0 is equal to 9.
To evaluate this limit analytically, we can use L'Hopital's Rule.
Taking the derivative of the numerator and denominator with respect to x, we get:lim (sin(9x))/x = lim (9cos(9x))/1as x approaches 0.
Substituting x = 0, we get:lim (sin(9x))/x = 9cos(0)/1 = 9Therefore, the limit of (sin(9x))/x as x approaches 0 is equal to 9.
We know already how to apply or make the procedures mathematically talking so this short program will eventually help you how to find logic.
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at a local farmers market a farmer pays $10 to rent a stall and $7 for every hour he stays there. if he pays $45 on saturday how many hours did he stay at the market
Answer: 5
Step-by-step explanation:
10 + 7h = 45
-10 -10
7h = 35
divide by 7 to both sides
h = 5
Find the slope of the points (-10, -52)
and (-70, -32)
Answer:
Slope= -1/3
Step-by-step explanation:
The slope is found using (y₂ - y₁) / (x₂ - x₁)
(y₂ - y₁)
So let's do the numerator first with the y. -52-(-32). The two negative signs make 32 positive so -52 + 32= -20
(x₂ - x₁)
Now the denominator, x. -10-(-70). Same thing here, the two negative signs make 70 positive so -10 + 70 = 60
(y₂ - y₁) / (x₂ - x₁)
Now put them together so -20/60 which equals -1/3 which the slope
Graph the image of △WXY after the following sequence of transformations: Reflection across the y-axis Rotation 180° counterclockwise around the origin
The old coordinates are;
W (3, 14)
Y (12, 14)
X (6, 11)
While the new coordinates for the reflected triangle are:
W'' (3, -14)
X'' (6, -11)
Y'' (12, -14).
See the attached image.
What is reflection?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line.
A figure is said to mirror another figure when every point in one figure is equidistant from every point in another figure.
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