Therefore, the equation for that value x = 6, and m(A) = 90.
What is a formula or equation?A mathematical equation expresses two things as being equal to one another, or as having the same value and worth. A specific equation that expresses a significant link between variables and numbers is called a formula.
The fact that the sum of a triangle's angles is 180 degrees must be used to determine the value of x. Angles J, A, and K in the triangle AJK allow us to write:
m(J) + m(A) + m(K) = 180
We can substitute the given angle measures into this equation:
(8x - 7) + m(A) + (x + 7) = 180
Simplifying this equation, we get:
9x + m(A) = 180 - 7 - 7
9x + m(A) = 166
We can use the same reasoning for triangle AJL:
m(J) + m(A) + m(L) = 180
Substituting the given angle measures, we get:
(8x - 7) + m(A) + (2x + 15) = 180
Simplifying this equation, we get:
10x + m(A) = 172
The two unknowns in our current set of equations are x and m(A). By removing the first equation from the second, we can find m(A):
10x + m(A) = 172
(9x + m(A) = 166)
x = 6
Now that we know x, we can substitute it into either equation to find m(A):
8x - 7 + m(A) + x + 7 = 180
15x + m(A) = 180
m(A) = 180 - 15x
Substituting x = 6, we get:
m(A) = 180 - 15(6) = 90
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HELP FASTTTTT PLAZSSSS
Please help !!!!!!!!!!
The total amount of interior angles featured on a polygon with 'n' sides can be determined through the equation (n-2)*180 degrees. This formula applies to all types of polygons, such as triangles.
How to explain the triangleIn order to calculate the sum of each individual angle in the polygon, we must consider the total degree measure formed within each triangle. Every triangle consists of three different sized interior angles that together form an count of 180 degrees.
For instance, when a polygon containing 'n' sides is divided into separate triangles by interconnecting certain vertices, the overall number of triangles produced can be worked out using the equation (n-1). A square, for example, can be broken down into two distinctive triangles, whereas a pentagon structures five triangles, and finally, a hexagon results in four.
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Vanessa purchased a used car on a payment plan. Four months after purchasing the car, the balance was $1,200. Seven months after purchasing the car, the balance was $975.
Write an equation that models the balance y after t months.
y =
t +
The equation that models the balance y after t months is y = -75t + 1,500
To write an equation that models the balance y after t months, we need to use the given information to determine the rate at which the balance is decreasing. We can use the formula for a straight line, y = mx + b, where m is the slope and b is the y-intercept.
We can start by finding the change in the balance over the three-month period from four to seven months after the purchase:
Change in balance = $1,200 - $975 = $225
The rate of change can be calculated by dividing the change in the balance by the number of months:
Rate of change = $225 / 3 months = $75 per month
We can use this rate of change as the slope of the equation:
y = -75t + b
To find the y-intercept b, we can use the fact that the balance was $1,200 four months after the purchase:
1,200 = -75(4) + b
b = 1,500
Therefore, the equation that models the balance y after t months is:
y = -75t + 1,500
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I need the best answer to this question complete sentences (I will give 20 points for the full question answered how it says to do it.)
The three types of rock are igneous, sedimentary, and metamorphic.
What are the three types of rock?There are three types of rocks as explained below.
Igneous rocks are formed from the cooling and solidification of molten rock, either on the Earth's surface (extrusive) or beneath the surface (intrusive). Examples of igneous rocks include basalt, granite, and pumice.
Sedimentary rocks are formed from the accumulation and cementation of sediment particles (such as sand, silt, and clay) or the precipitation of minerals from a solution. Examples of sedimentary rocks include sandstone, limestone, and shale.
Metamorphic rocks are formed from the alteration of pre-existing rocks by heat, pressure, and chemical reactions. Examples of metamorphic rocks include marble, slate, and gneiss.
The rock cycle is the process by which one type of rock can be changed into another type of rock.
The rock cycle involves three main processes:
Weathering and erosionDeposition and lithificationMelting and solidificationTherefore, one type of rock can be changed into another type of rock through the rock cycle by undergoing weathering, erosion, deposition, lithification, metamorphism, melting, and solidification, depending on the specific conditions and processes involved.
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Solve for p.
p − 4
2
= 3
The value of p in the expression is 45
What is additive inverse?Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.
For example a+5 = 2 , by solving this we add the additive inverse of 5 to both sides. The additive inverse of 5 is -5
this means,
a+5-5 = 2-5
a = 2-5
a = -3
Similarly, p-42 = 3 is solved in the same way. we add the additive inverse of -42 which is +42 to both sides,
p-42+42 = 3+42
p = 3+42
p = 45
therefore the value of p is 45
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On a recent survey from Starbucks, 4200 people were asked their age. The mean age was found to be 28 years with a standard deviation of 18 months. Assume that the data is normally distributed and use the 68-95-99.7 Rule to answer the following questions. a) Of those surveyed, about how many people are at least 26.5 years old? people b) of those surveyed, about how many people are less than 26.5 years old? people
a) Approximately 84% of the people are at least 26.5 years old. So, about 3528 people (0.84 * 4200).
b) Approximately 16% of the people are less than 26.5 years old. So, about 672 people (0.16 * 4200).
How to solvea) 26.5 years is 1.5 years (18 months) less than the mean (28 years). This is 1 standard deviation (18 months) below the mean.
The 68-95-99.7 Rule states that 68% of the data falls within 1 standard deviation of the mean. So, 100% - 68% = 32% is outside 1 standard deviation.
Since it's symmetrical, one-half of that 32% (16%) is less than 26.5 years, and the other half (16%) is older than 29.5 years.
Consequently, 100% - 16% = 84% is over 26.5 years old. If you multiply 0.84 by 4200, you get 3528 people.
b) As calculated earlier, 16% of the people are less than 26.5 years old. 0.16 * 4200 = 672 people.
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In circle S with
m
∠
R
S
T
=
102
m∠RST=102 and
R
S
=
6
RS=6 units, find the length of arc RT. Round to the nearest hundredth.
In a circle, the measure of a central angle is equal to the measure of its intercepted arc. Since ∠RST is a central angle of circle S and its measure is 102 degrees, the measure of its intercepted arc ⌢RT is also 102 degrees.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Since RS is a radius of circle S and its length is 6 units, the circumference of circle S is C = 2π * 6 = 12π units.
The length of an arc is proportional to its measure in degrees. Since the measure of ⌢RT is 102 degrees and the total measure of a circle is 360 degrees, the length of ⌢RT is (102/360) * 12π = 3.4π units.
Rounded to the nearest hundredth, this is approximately 10.68 units.
I may be able to figure out part (b) of this one, but I do need help with parts (a) and (c). Any help would be greatly appreciated.
(a) The shape of sampling distribution is not too close to 0 or 1 (b) The mean of standard deviation = 0.033
(c) [tex]P(Z > (P-P + 0.03) / 0.033) = P(Z > 0.91)[/tex]
According to given information:(a) The sampling distribution of p-p is approximately normal by the Central Limit Theorem because both sample sizes are large enough (n₁ = n₂ = 240) and the sample proportions of orange candies are not too close to 0 or 1.
(b) The mean of the sampling distribution of p-p is equal to the difference between the population proportions, which is 0.20 - 0.23 = -0.03. The standard deviation of the sampling distribution of p-p is given by:
sqrt[(p₁q₁/n₁) + (p₂q₂/n₂)]
= sqrt[(0.200.80/240) + (0.230.77/240)]
= 0.033
The standard deviation represents the amount of variation we expect to see in the differences between sample proportions of orange candies from multiple random samples of the same size.
(c) To find P(P-P>0), we need to standardize the difference between the sample proportions and the population difference and then find the probability that the standardized difference is greater than 0. That is:
(P-P - (p₁ - p₂)) / sqrt[(p₁q₁/n₁) + (p₂q₂/n₂)]
= (P-P - (-0.03)) / 0.033
= (P-P + 0.03) / 0.033
Using a standard normal distribution table or calculator, we can find the probability that a standard normal variable is greater than this value. For example, if we use a calculator, we get:
P(Z > (P-P + 0.03) / 0.033) = P(Z > 0.91)
where Z is a standard normal variable. The probability is approximately 0.18. This means that if we take many random samples of 240 M&M's milk chocolate candies and 240 peanut M&M's and calculate the difference between the sample proportions of orange candies, about 18% of the time we would expect to see a difference of 0.03 or greater (favoring M&M's milk chocolate candies).
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Suppose that the production of plastic creates a social cost which is depicted in the graph above. Without any government regulation, how much plastic will be produced?
Suppose that the production of plastic creates a social cost which is depicted in the graph above. Without any government regulation, about 650 units of plastic will be produced. (Option C)
Why is this so?This is because, when the market forces are left to play out, competition drives efficiency upwards, which enable suppliers to produce at lower price thus offering consumers more quantity demanded for lower prices.
Hence, without government intervention, the unit produced will be 650 at the price of 7.
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Answer this question soon
Answer:
CA - 144
AD - 98
ABD - 49
BC - 134
C - unsure
Step-by-step explanation:
how large a sample should be taken if the population mean is to be estimated with 98 percent confidence to within $100? The population has a standard deviation of $800.
A sample of at least 433 individuals would need to be taken to estimate the population mean with 98% confidence to within $100.
Understanding Population EstimateTo estimate the sample size needed to estimate the population mean with 98% confidence to within $100, we can use the formula:
n = (z * σ / E)²
where:
n = sample size
z = z-score for the desired level of confidence (98% in this case), which can be found using a standard normal distribution table or calculator. For 98% confidence, the z-score is approximately 2.33.
σ = population standard deviation ($800 in this case)
E = margin of error ($100 in this case)
Plugging in the values, we get:
n = (2.33 * 800 / 100)²
n ≈ 432.64
Rounding up to the nearest whole number, we get a sample size of 433. Therefore, a sample of at least 433 individuals would need to be taken to estimate the population mean with 98% confidence to within $100.
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You start at (2, -1). You move left 4 units. Where do you end?
Answer:
(-2, -1)
Step-by-step explanation:
You want the point that is 4 units left of (2, -1).
X-coordinateThe x-coordinate of an (x, y) coordinate pair tells you the number of units to the right of the x=0 point. It increases for points farther right, and decreases for points farther left.
Moving left 4 units decreases the x-coordinate by 4 units. The x-coordinate of 2 becomes ...
2 -4 = -2
The coordinates of the moved point are (-2, -1).
<95141404393>
Help please!!!!
Whoever answers right gets brainliest!
When w = 10 and z = 2, the value of expression 2w⁻²z⁰ is equal to 1/50. So, correct option is A.
The expression 2w⁻²z⁰ can be simplified as follows:
2w⁻²z⁰ = 2/w² * z⁰
Since z⁰ = 1 for any non-zero value of z, we can simplify further:
2w⁻²z⁰ = 2/w² * 1
Now we can substitute w = 10 into the expression:
2(10)⁻² * 1 = 2/100 = 1/50
In general, when we have a negative exponent in an expression, we can rewrite it as a positive exponent in the denominator. In this case, w⁻² can be rewritten as 1/w². Additionally, any number raised to the power of 0 is always 1, so z⁰ = 1. By simplifying the expression, we can easily substitute the given values of w and z to evaluate the expression.
So, correct option is A.
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The hypotenuse of a certain right triangle is twice the length of the
shorter leg. The shorter leg is 4 cm.
Answer:
Step-by-step explanation:
If the hypotenuse of a right triangle is twice the length of the shorter leg and the shorter leg is 4 cm, then the hypotenuse is 2 * 4 cm = 8 cm.
Using the Pythagorean theorem, we can find the length of the longer leg. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Letting c represent the length of the hypotenuse and a and b represent the lengths of the other two sides, we can write this as c^2 = a^2 + b^2.
Substituting in the known values for c and one of the other sides (let’s say a), we have:
8^2 = 4^2 + b^2 64 = 16 + b^2 b^2 = 48 b = sqrt(48)
So, the length of the longer leg is sqrt(48) cm, or approximately 6.93 cm.
Four data sets are shown below. Set 1: {10, 19, 38, 50, 51} Set 2: {5, 21, 26, 39, 51} Set 3: {9, 38, 50, 50, 51} Set 4: {5, 28, 28, 28, 51} Which data set has the largest standard deviation? * Set 1 Set 2 Set 3 Set 4
Answer:
Set 1: {10, 19, 38, 50, 51}
Step-by-step explanation:
To calculate the standard deviation of a data set, we first find the mean of the data set. The mean is simply the sum of all the values in the data set divided by the number of values. For example, the mean of Set 1 is:
(10+19+38+50+51)/5=33.6
Next, we find the variance of the data set. The variance is the average of the squared differences between each value in the data set and the mean. For example, the variance of Set 1 is:
((10−33.6)^2+(19−33.6)^2+(38−33.6)^2+(50−33.6)^2+(51−33.6)^2)/5=323.84
Finally, we take the square root of the variance to get the standard deviation. For example, the standard deviation of Set 1 is:
[tex]\sqrt{323.84}[/tex]=17.99
We can repeat this process for each of the four data sets and find that Set 1 has the largest standard deviation.
What are the roots of the quadratic equation below?
2x² + 8x+7= 0
O A. x = = 2√2
1
O B. x =
-8+√120
8
O
O D. x =
C. x = = 4+√/²
-2+√120
Answer:
Step-by-step explanation:
c
A wheelchair ramp is in the shape of a triangular prism. It has a base area (B) of 37.4 and a height of 5 yards. Find the volume of the ramp.
The volume of the ramp ishow many yd3
Answer:
Step-by-step explanation:
The formula for the volume of a triangular prism is:
V = Bh, where B is the base area and h is the height of the prism.
Substituting the given values, we get:
V = 37.4 x 5
V = 187 yd^3
Therefore, the volume of the ramp is 187 cubic yards.
What is the standard form of the equation for the circle
A. (X-3)^2+(y-2)^2=32
The standard form of the equation for the circle is (x - 3)² + (y - 2)² = 8.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.
Based on the information provided above, we have the following parameters:
Radius, r = √[(3 - 5)² + (2 - 4)²] = √8
Center, (h, k) = (3, 2).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 3)² + (y - 2)² = (√8)²
(x - 3)² + (y - 2)² = 8.
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Complete Question:
A circle is shown on the coordinate plane. The graph shows a circle with the origin point A at (3, 2), and a point B on its circumference at (5, 4) and intersects the x-axis at 1 and 5 units. What is the standard form of the equation for the circle?
Solve the quadratic equation 2x2 – x = 15 using the quadratic formula.
Answer:
x = 3, -5/2
Step-by-step explanation:
First, you move the 15 onto the left of the equation by subtracting it from both sides.
Second, you plug your info into the quadratic equation. (1 +- sqrt(1+4*15*2))/4
write the equation of a circle with center (-4,3) and radius 9 ?
Step-by-step explanation:
Standard form of circle with center (h.k) and radius r :
( x-h)^2 + (y-k)^2 = r^2
FOr the data given:
(x + 4)^2 + ( y-3)^2 = 81 (81 is the radius, 9, squared)
Answer this pleaseeee
The solution of the trigonometric equation on the interval (, 360) is
x = 90° or x = 126.87° or x = 216.87 What is a trigonometric equation?A trigonometric equation is an equation that contains trigonometric ratios.
Given the trigonometric equation
2sinx = 1 - cosx, we proceed to solve for x as follows.
Since 2sinx = 1 - cosx
Using sin²x = 1 - cos²x
⇒ sinx = √(1 - cos²x )
Substituting this into the equation, we have that
2sinx = 1 - cosx
2√(1 - cos²x ) = 1 - cosx
Squaring both sides, we have that
[2√(1 - cos²x )]² = (1 - cosx)²
4(1 - cos²x ) = (1 - cosx)²
4 - 4cos²x = 1 - 2cosx + cos²x
Collecting similar terms, we have that
1 - 4 - 2cosx + 4cos²x + cos²x = 0
- 3 - 2cosx + 5cos²x = 0
Re-arranging the equation, we have that
5cos²x - 2cosx - 3 = 0
Let cosx = y
So, we have that
5y² - 2y - 3 = 0
Factorizing, we have that
5y² - 2y - 3 = 0
5y² - 5y + 3y - 3 = 0
5y(y - 1) + 3(y - 1) = 0
(5y + 3)(y - 1) = 0
⇒ 5y + 3 = 0 or y - 1 = 0
⇒ 5y = -3 or y = 1
⇒ y = -3/5 or y = 1
Since y = cosx, we have that
cosx = -3/5 or cosx = 1
cos(180° - x) = 3/5 or cos(270° - x) = 3/5 or cosx = 1
Taking inverse cosine, we have that
180° - x = cos⁻¹(3/5) or 270° - x = cos⁻¹(3/5) or x = cos⁻¹(1)
180° - x = 53.13° or 270° - x = 53.13° or x = 90°
x = 180° - 53.13° or x = 270° - 53.13° or x = 90°
x = 126.87° or x = 216.87 or x = 90°
So, the solution is
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1. A biologist hypothesizes that the mean life expectancy of a cockroach is 17 days. Researchers believe the true mean is less than 17 days and they plan a hypothesis test at the 10% significance level on a random sample of 80 of these cockroaches. If the alternative hypothesis is correct, for which of the following values of μ is the power of the test greatest?
A. μ = 9
B. μ = 10
C. μ = 17
D. μ = 20
E. μ = 21
2.Automobile tires can have a symmetric tread or an asymmetric tread. An experiment is to be conducted to determine whether the stopping distance is the same for both types of tire treads. In previous studies, it was determined that automobile size (small, medium, large) is associated with stopping distance, but automobile type (van, truck, SUV, and so on) is not associated with stopping distance. How could the experiment BEST be conducted?
A. By blocking on stopping distance
B. By blocking on tire tread type
C. By blocking on automobile type
D. By blocking on automobile size
E. Without blocking
3. A popular podcast wants to know the proportion of listeners that think assault weapons should be banned for civilians. Listeners are asked to text "Y" for yes or "N" for no to a provided number. Sixty-five percent of the 1,500 people that responded texted "Y." Which condition for inference has NOT been met?
A. All conditions appear to be met.
B. The sample is an SRS of the population.
C. N > 10n
D. np ≥ 10 and n(1 - p) ≥ 10
E. Inference about a proportion is the objective.
4.Fifteen pairs of measurements were taken at random to estimate the relation between variables X and Y. A least-squares line was fitted to the collected data. The resulting residual plot is shown.
Which of the following conclusions is appropriate?
A. A line is an appropriate model to describe the relation between X and Y.
B. A line is not an appropriate model to describe the relation between X and Y.
C. The assumption of the Law of Averages has been violated.
D. The variables X and Y are not related at all.
E. There is not enough information about the variables X and Y to form a conclusion.
help please
The half-life of Radium-226 is 1590 years. If a sample contains 500 mg, how many mg will remain after 1000 years? -----------
after 1000 years, there will be approximately 218.7 mg of Radium-226 remaining in the sample. use formula for radioactive decay to solve
what is radioactive decay ?
Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation, such as alpha particles, beta particles, and gamma rays. The decay occurs in order to achieve a more stable configuration of the nucleus.
In the given question,
The formula for radioactive decay is:
N(t) = N0 * (1/2)ᵃ⁾ᵇ
where:
N(t) is the amount of radioactive material at time t
N0 is the initial amount of radioactive material
t is the time elapsed since the initial measurement
T is the half-life of the radioactive material
We can use this formula to solve the problem as follows:
N0 = 500 mg (the initial amount)
T = 1590 years (the half-life)
t = 1000 years (the time elapsed)
N(t) = 500 * (1/2)¹⁰⁰⁰⁾ ¹⁵⁹⁰
N(t) = 500 * 0.4374
N(t) = 218.7 mg
Therefore, after 1000 years, there will be approximately 218.7 mg of Radium-226 remaining in the sample.
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PLEASE HELP ITS DUE TOMORROW!!!
Answer:
Step-by-step explanation:
House
B) Down Payment: $151,800
C) $607,200
D) $819,720
E) $1,426,920
F) $47,564
Car:
B) $2,902.50
C) $16,447.50
D) $3,700.6875 = $3,700.69
E) $20,148.1875 = $20,148.19
F) $335.803125 = $335.80
DONE !!! :)
I NEED HELP ASAP I have to tern this packet in tomorrow and i do not know how to solve scales in geometry
Answer:
The anser is letter C)
Step-by-step explanation:
because it multiplies x3
0,5×3=1,5
1,5×10=15
10×3=30
Answer:
1cm=30m
Jamal is planning a conference. A local hotel rents a ballroom for $620 and charges $35 per guest for food.
Step 2 of 5: Determine the total charge if 138 guests attend the conference.
The total charge if 138 guests attend the conference is $5450
Determining the total charge if 138 guests attend the conference.From the question, we have the following parameters that can be used in our computation:
A local hotel rents a ballroom for $620 And charges $35 per guest for food.Using the above as a guide, we have the following:
Total = ballroom + food * number of guests
Substitute the known values in the above equation, so, we have the following representation
Total = 620 + 35 * 138
Evaluate
Total = 5450
Hence, the total charges is $5450
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I would be rally thankful if you help
The matrix after the row operation is given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
The row operation is given as follows:
Division by 7 = multiplication by 1/7, as the element at the desired position is of 7.
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
We want to have element 1 into row 1 and column 1, that is, the element of 7 at row 1 and column 1 of the matrix must assume a value of -1.
An example of a valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:
7/k = 1
k = 7.
Dividing every element of the first row by 7, the resulting matrix is then given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
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The angle of depression from the window of a building to a parked car is 38°. If the car is parked 320 feet away from the base of the building, what is the distance between the window and the car to the nearest tenth?
Answer:
Set your calculator to degree mode.
Please sketch the figure to confirm my answer.
cos(38°) = 320/d
d•cos(38°) = 320
d = 320/cos(38°) = 406.1 feet
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Answer:
23098376=890754730.0%
please help for this question
The single transformation that maps shape A to shape B is: Reflection about the line x = -2
What is the transformation rule?There are different ways of carrying out transformation of objects and they are:
Reflection whereby all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection
Rotation whereby all points are rotated about a point.
Dilation where the object is reduced or increased by a scale factor.
Translation where the object is moved from one point to another.
Looking at the given image, we can tell that this denotes a reflection because it is the exact same shape and looks like a mirror image which was reflected over the line x = -2
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