The largest δ value of the given limit [tex]\lim_{x \to 1^+} \frac{1}{x^2-1}=\infty[/tex] and M=1000 is calculated. The required δ value is [tex]\delta=\sqrt{1+10^{-3}}-1[/tex].
When no values are defined, a limit is used to assign values to certain functions. It is possible to assess the limits using algebraic techniques. A collection of guidelines for manipulating limits when using other operators is known as the algebra of limits. Given the expression [tex]\lim_{x \to 1^+} \frac{1}{x^2-1}=\infty[/tex] and M=1000. When x>1, we write this expression as,
[tex]\begin{aligned} \frac{1}{x^2-1}& > 1000\\x^2-1& < 1000^{-1}=10^{-3}\\x^2& < 10^{-3}+1\\x& < \sqrt{1+10^{-3}}\end{aligned}[/tex]
Now, choosing, [tex]\delta=\sqrt{1+10^{-3}}-1[/tex] when we have δ > 0. Therefore, [tex]\sqrt{1+10^{-3}} > 1[/tex]. Then, [tex]x\in(1, 1+\delta)[/tex]. This is given by,
[tex]\begin{array}{ccc}1& < x& < 1+\delta\\1& < x& < \sqrt{1+10^{-3}}\end{array}[/tex]
This implies, [tex]\frac{1}{x^2-1} > 1000=M[/tex].
Therefore, the largest δ value will be [tex]\sqrt{1+10^{-3}}-1[/tex].
The complete question is -
For each limit, use graphs and algebra to approximate the largest δ or the smallest magnitude N that corresponds to the given value of ∈ or M, according to the appropriate formal limit definition.
[tex]\lim_{x\to 1^+} \frac{1}{x^2-1}=\infty[/tex], M=1000, find largest δ > 0.
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Mario wants to mail three books with the following
weights:5/8 pound,7/16 pound, and 3/4
pound. Can Mario
mail the books in a box that can hold up to 2 1/2 pounds?
Use benchmarks to justify your answer.
Mario can mail the books in the box, as the weight of the books is less than the weight of the box.
How to obtain the total weight?The total weight is obtained applying proportions, converting the fractions to decimal, dividing the numerator by the denominator.
The weights of each book are given as follows:
5/8 pounds = 0.625 pounds.7/16 pounds = 0.4375 pounds.3/4 pounds = 0.75 pounds.Hence the total weight for the books is given as follows:
0.625 + 0.4375 + 0.75 = 1.8125 pounds.
The weight of the box is given as follows:
2 + 0.5 = 2.5 pounds.
Hence Mario can mail the books in the box, as the weight of the books is less than the weight of the box.
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Write an explicit formula for the sequence generated by a1 = 10, an = an − 1 + 7 where n = 2, 3, 4, ….
Group of answer choices
an = n + 7 where n = 1, 2, 3, …
an = 3n + 4 where n = 1, 2, 3, …
an = 7n − 10 where n = 1, 2, 3, …
an = 7n + 3 where n = 1, 2, 3, …
Answer:
= 7n − 3 emde n = 1, 2, 3, ...
The function f(x) is shown on the graph.
The graph shows a downward opening parabola with a vertex at 3 comma 25, a point at negative 2 comma 0, a point at 8 comma 0, a point at 0 comma 16, and a point at 6 comma 16.What is the standard form of the equation of f(x)?
a) f(x) = x2 − 6x + 16
b) f(x) = x2 + 6x + 16
c) f(x) = −x2 − 6x + 16
d) f(x) = −x2 + 6x + 16
The correct answer is d. The standard form of the equation of f(x) is −x2 + 6x + 16.
What is downward opening parabola?A downward opening parabola is a curve in the shape of a parabola that opens downward and is symmetrical about the x-axis. The equation of a downward opening parabola is y = ax^2 + bx + c, where a is a negative number, and b and c are constants.
The focus of a downward opening parabola is the point on the parabola where the curvature is greatest and is located at the vertex of the parabola.
The directrix of a downward opening parabola is a line parallel to the x-axis and the distance from the focus to the directrix is equal to the length of the latus rectum of the parabola. The equation of the directrix is y = -a(x - h)^2 + k, where h and k are constants.
Downward opening parabolas can be used to graphically represent any type of data that follows a parabolic shape. This includes physical phenomena such as the path of a projectile or the vibration of a string.
Downward opening parabolas can also be used to model economic or financial data, such as the demand for a product or the price of a commodity. They may also be used to describe relationships between two variables in a mathematical equation.
The standard form of a parabola equation is f(x) = ax2 + bx + c, where a, b, and c are real numbers. In this case, the vertex of the parabola is at (3, 25), so the equation is in the form f(x) = a(x - 3)2 + 25. Putting in the other points on the graph to solve for a, b, and c yields the equation f(x) = -x2 + 6x + 16.
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reduce to simplest form
-3/2 - 3/8
Answer:
To add or subtract fractions, they must have a common denominator. In this case, the denominators of the fractions are 2 and 8, which are not the same. To find the least common multiple of 2 and 8, we can list the multiples of each number and find the smallest one that is common to both:
2: 2, 4, 6, 8, 10, 12, 14, ...
8: 8, 16, 24, 32, ...
The least common multiple of 2 and 8 is 8. Therefore, to add or subtract the fractions, we must convert them to have a denominator of 8.
-3/2 = -12/8 and 3/8 = 3/8
So, -3/2 - 3/8 = -12/8 - 3/8
Now we can subtract the fractions directly:
-12/8 - 3/8 = -12 - 3 / 8
= -15/8
Therefore, the simplified form of -3/2 - 3/8 is -15/8
really confused please help
The given relationship is such that 1 / z⁴ = z ⁻⁴.
What is the relationship ?When given 1 / z⁴, this can be rewritten in such a way that it becomes z ⁻⁴.
This is because when a denominator is raised to a exponent , it can be transformed to a numerator if the sign on the power is changed to the negative.
This means that when the fraction was 1 / z⁴, it can become the value of z ⁻⁴ because the negative in front of the 4 shows that it is a fraction.
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PLEASE HELP ITS DUE TODAY WOULD GIVE ALOT OF POINTS IF SOMEONE SHOWS THE ANSWER ANY SPAM ANSWERS WILL BE REPORTED!
THANK YOU!
Answer:
y ≥ -x -7
Step-by-step explanation:
The inequality is greater than or equal to because it is above the line and it is a solid line.
The slope is -1. If you select a point on the line, you go down one unit and one unit to the right to get back on the line. The slope is the rise over the run. -1/1 = -1
The y intercept is where the graph crosses the y axis (0,-7) So the y intercept is -7
The roof shingles are arranged so that each row has 7 fewer shingles than the row below it. If the first row has 75 shingles, how many shingles are in the 6th row?
The shingles are in the 6th row is 110 using arithmetic process.
What is arithmetic process?A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The study of numbers and the operations on those numbers, which are relevant to all other branches of mathematics, is the focus of a branch of mathematics known as arithmetic operations. It includes addition, subtraction, multiplication, and division as its fundamental operations.
Given that A = 75 and d = 7, n = 6
A₆ = A + (n-1)d
A₆ = 75 + (6-1)7
A₆ = 75 + 5 * 7
A₆ = 75 + 35
A₆ = 110
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Answer:
33
Step-by-step explanation:
it starts with 75 and decreases by 7 for each row. on the 6th row youll be at 33!
STARTS AT 75
row one: 68
row two: 61
row three:54
row four: 47
row five: 40
row six: 33
If 28% of 581 people replied newton ate the apple what’s the margin of error %
The margin of error, given the percentage who replied that Newton ate the apple, is 3.5%.
How to find margin of error ?The margin of error is a measure of how much the sample results are likely to vary from the true population value.
To calculate the margin of error, you need to know the sample size, the proportion of the sample that gave a particular response, and the level of confidence.
The formula for the margin of error is:
Margin of Error = z x √(p x ( 1 - p) / n)
where:
z = the critical value from the standard normal distribution table
p = the proportion of the sample that gave a particular response
n = the sample size
The margin of error for Newton eating the apple is therefore:
Margin of Error = 1.96 x √(0.28 x (1 - 0.28) / 581)
Margin of Error = 1.96 * √(0.00035)
Margin of Error = 1.96 * 0.018
Margin of Error = 0.035
The margin of error is therefore 3.5%.
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Simplify each expression by combining like terms
-9y-10y -2z
By Simplify expression -9y-10y -2z this we get - 19y - 2z.
What is the Simplify expression ?Expression simplification is a crucial skill to master if you want to comprehend algebra. We can convert a complicated expression into one that is more condensed and straightforward by simplifying it.When constants and variables are merged with the help of the operation symbols (+, -, x, and ), the result is an algebraic expression.The process of solving a math problem is simply known as simplifying an expression. An expression is simplified when it is written in the most straightforward way feasible. There should be no more multiplying, dividing, adding, or subtracting to be done once everything is done.Examples :
-9y-10y -2z
Simplify
-9y - 10y - 2z : -19y - 2z
-9y - 10y - 2z
= - 19y - 2z.
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What is the answer to this?
Step-by-step explanation:
what is missing is the definition that QS is the height and therefore standing at a right angle (90°) at PR.
then this can be solved.
we use Pythagoras
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
let's start with the triangle PQS.
21² = 15² + QS²
441 = 225 + QS²
QS² = 216
QS = sqrt(216) = sqrt(36×6) = 6×sqrt(6) = 14.69693846...
now for triangle QSR
(5x - 16)² = (3x - 4)² + QS²
25x² - 160x + 256 = 9x² - 24x + 16 + 216
16x² - 136x + 24 = 0
2x² - 17x + 3 = 0
the solution to a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (17 ± sqrt(17² - 4×2×3))/(2×2) =
= (17 ± sqrt(289 - 24))/4 = (17 ± sqrt(265))/4
x1 = (17 + 16.2788206...)/4 = 8.319705149...
x2 = (17 - 16.2788206...)/4 = 0.180294851...
but using x2 in side lengths 3x - 4 or 5x - 16 gives us negative side lengths. that does not make any sense for actual side lengths.
so, x1 is our solution :
x = 8.319705149...
What represents the expression below simplified?
[tex](4x-1) + (-6x+3)[/tex]
Solve this system of linear equations. Separate
the x- and y-values with a comma.
2x + 2y = -8
-13x + 7y = -48
Enter the correct answer.
Answer:
x = 1, y = - 5
Step-by-step explanation:
2x + 2y = - 8 → (1)
- 13x + 7y = - 48 → (2)
multiplying (1) by 7 and (2) by - 2 and adding will eliminate y
14x + 14y = - 56 → (3)
26x - 14y = 96 → (4)
add (3) and (4) term by term to eliminate y
40x + 0 = 40
40x = 40 ( divide both sides by 40 )
x = 1
substitute x = 1 into either of the 2 equations and solve for y
substituting into (1)
2(1) + 2y = - 8
2 + 2y = - 8 ( subtract 2 from both sides )
2y = - 10 ( divide both sides by 2 )
y = - 5
then solution is x = 1, y = - 5
suppose that 40% of all adults regularly consume coffee, 60% regularly consume carbonated soda, and 35% regularly consumes both coffee and soda. draw a venn diagram, then answer the following:(a) What is the chance a randomly selected adult regularly drinks coffee but doesn't drink soda?(b) What is the probability that a randomly selected adult consumes coffee, soda or both?(c) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?
The probabilities of adults who drinks only coffee , both/ coffee ,soda and doesn't drink any are 5% , 65% and 35%.
Let A be the event that an adult consumes coffee.
Let B be the event that an adult consumes carbonated soda.
Given probabilities of the events.
P (A) = 0.4
P (B) = 0.6
P(A∩B) = 0.35
(a). P(A) - P(A∩B) = 0.4 - 0.35
= 0.05 OR 5 %
(b). P(AUB) = P (A) + P (B) - P(A∩B)
= 0.4 + 0.6 - 0.35
= 0.65 OR 65%
(c). The given case represents compliment of the event when the adult consumes at least one of the drink. According to probability axiom, the probability is given by:
P ((AUB)') = 1 - P (AUB) = 1-0.65 = 0.35
Therefore,
P ((AUB)') = 0.35 or 35 %.
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The U.S. population in 2018 was estimated to be 327,200,000 within that population, there were 30,357,000 people who were 18-29 years old and 52,431,000 people who were 65 years and older
According to the graphic, 85% of the 30,357,000 people who were 18-29 years old tried vaping or electronic cigarettes Approximately how many people ages 18-29 said that they have tried vaping or e-cigarettes? Show your work
We can see here that the people of ages 18-29 that have tried vaping or e-cigarettes is: 25,803,450.
What is population?Population refers to the number of individuals of a particular species living in a particular area or region. In the context of human populations, it refers to the number of people living in a particular geographic area or country.
To find out the number of people ages 18-29 who said they have tried vaping or e-cigarettes, you can use the following calculation:
30,357,000 (the number of people ages 18-29) x 0.85 (the percentage of people who have tried vaping or e-cigarettes) = 25,803,450.
So, approximately 25,743,950 people ages 18-29 said that they have tried vaping or e-cigarettes.
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whats the solution to the equations
Answer:
A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value. To solve an equation is to find the solution(s) for that equation.
Step-by-step explanation:
Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-4,8)
(-6,-2)
(4,5)
The coordinates of the fourth vertex is (1,-8).
Find the coordinates of the fourth vertex?As three of a parallelogram's vertices, we were given:
(3,-2), (-1,-4), (5,-6). (5,-6).
We see that (3,-2) and (-1,-4) form a diagonal after charting the points as in the attachment.
The midpoint formula determines what point on this diagonal is in the middle.
Keep in mind that both diagonals' midpoints are identical.
Specify the coordinates of the fourth point (x,y).
As a result of once more applying the midpoint formula to (3, -2), we get:
x=1 and y=-8
The fourth point's locational details are as follows:
(1,-8).
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The complete question is,
A good can be produced for a total cost of 600 or 850 when making 100 units and 150 units, respectively. Discover an equation for TC in terms of Q, the number of generated units, presuming that the total cost function is linear.
Find the smallest value of m such that the product of 189m is a perfect square
Answer: 7
Step-by-step explanation:
First, we need to prime factorize the number 189,
189 = 3 × 3 × 3 × 7 × m
From the factors we can see that there is no pair of same numbers for 7, so if we replace m with 7, we can get a perfect square.
Hence the answer is 7
Question 4 of 10
The lines shown below are perpendicular. If the green line has a slope of
what is the slope of the red line?
ch
10
KO
1
-10
+0
6
10
16
OA
OB./
OC
OD
Answer:
B
Step-by-step explanation:
Trust
Slope of the line y=29/8x - 2/3
Answer:
The slope of a line is represented by the coefficient of the x-term in the equation, which is also known as the "rise over run" or change in y over change in x.
In this equation y = 29/8x - 2/3
The coefficient of the x-term is 29/8, so the slope of the line is 29/8.
A 2D depiction of what a 3D shape would look like if it was opened out and laid flat is called a
Answer: Net (of a shape)
Step-by-step explanation:
Answer:
Step-by-step explanation:
no need for step by step its called a net
given values of median, mean, mode, first and third quartiles for the observations of a numeric feature, what insights can we gain into the statistical distribution of its observations? you may use an example to further illustrate your points. (word limit: 100-150). you must post first before being able to read the responses of others. it is recommended that you respond to your classmates' responses, but not required.
The terms mean median, mode, and range describe properties of statistical distributions.
The statistical distributions' characteristics are described by the terms mean, median, mode, and range. The set of all potential values for terms that indicate predetermined events is known as a distribution in statistics. A term's value stated as a variable is referred to as a random variable.
The two main categories of statistical distributions are as follows. There are discrete random variables in the first category. This indicates that each phrase has a distinct, precise numerical value. A continuous random variable is present in the distribution of the second major kind. An unlimited number of possible values can be represented by a continuous random variable. A term is said to have a probability density function when any value can be assigned to it within an uninterrupted interval or span.
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The probability of picking two black marbles from a box at random without replacement is 10/91 . The probability of drawing a black marble first is 5/14 . What is the probability of picking a second black marble, given that the first marble picked was black?
The probability of picking a second black marble is 4/13
What is probability?Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability helps us know the chance an event has to occur. The closer it gets to zero(0) the less chance it has to occur. The closer it gets to one(1) the more chance it has to occur.
Therefore, The probability of picking a second black marble is 4/13
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The option are :
4/13
85/182
25/637
45/182
Please help with their question
If f(x) = x⁴ + 2, g(x) = x-6 and h(x) = √x , then the simplified form of f(g(h(x))) is f(g(h(x))) = (√x - 6)⁴ + 2.
What is the polynomial expression?
Any expression which consists of variables, constants, and exponents, and is combined using mathematical operators like addition, subtraction, multiplication, and division is a polynomial expression.
We can simplify f(g(h(x))) by first evaluating h(x), then substituting the result into g(x), and finally substituting the result into f(x).
Starting with h(x) = √x, we can substitute this into g(x) to get:
g(h(x)) = g(√x) = √x - 6
Next, we can substitute g(h(x)) = √x - 6 into f(x) to get:
f(g(h(x))) = f(√x - 6) = (√x - 6)⁴ + 2
Simplifying this expression requires some algebraic manipulation, but we can expand (√x - 6)⁴ using the binomial theorem or by using the method of FOIL (first, outer, inner, last) repeatedly. Either way, we will end up with a polynomial expression in x with terms of various degrees.
Therefore, the simplified form of f(g(h(x))) is f(g(h(x))) = (√x - 6)⁴ + 2.
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24 of the students in a Biology class passed a Biology test. If these students are 80% of
all the students in the class, how many students are in this Biology class? Round your
answer to the nearest whole number if necessary.
Trapezoid PQRS has vertices P(0, 0), Q(0, 4), R(6, 4), and S(12, 0).
What is the length of the midsegment?
please help me its the last question on this test and i only have 20 mins left of this class
Trapezoid PQRS having vertices P(0, 0), Q(0, 4), R(6, 4), and S(12, 0),
has the length of the midsegment as 11.07 units.
What is a trapezoid?
A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.
The length of the mid segment of trapezoid is half the sum of the lengths of the two parallel sides, PQ and RS.
The points for vertices are given as - P(0, 0), Q(0, 4), R(6, 4), and S(12, 0).
Length of sides PQ and RS is given as -
The line segment PQ = √(x2 - x1)² + (y2 - y1)²
PQ = √(0 - 0)² + (4 - 0)²
PQ = √0² + (4)²
PQ = √0 + 16
PQ = √16
PQ = 4 units
The line segment RS = √(x2 - x1)² + (y2 - y1)²
RS = √(12 - 6)² + (0 - 4)²
RS = √(6)² + (-4)²
RS = √36 + 16
RS = √50
RS = 5√2 units
To find the mid segment add the length of PQ and RS.
So, the equation will be -
Midsegment = PQ + RS
Midsegment = 4 + 5√2
Midsegment = 11.07 units
Therefore, the length of midsegment is 11.07 units.
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Answer: 9
Step-by-step explanation: (6+12) / 2 = 9
Question
This graph shows a proportional relationship.
What is the constant of proportionality?
Enter your answer in the box.
Graph titled Math Test Raw Scores. The vertical axis is labeled Points. The horizontal axis is labeled Correct answers. The horizontal axis ranges from 0 to 24 in increments of 2. The vertical axis ranges from 0 to 120 in increments of 10. A line passes through the origin and the points begin ordered pair 5 comma 30 end ordered pair and begin ordered pair 12 comma 72 end ordered pair and begin ordered pair 18 comma 108 end ordered pair and begin ordered pair 20 comma 120 end ordered pair.
The constant of proportionality is equal to 6.
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x represents the correct answers.y represents the points.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) for the relationship between correct answers and points on this graph as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 30/5 = 72/12 = 108/18 = 120/20
Constant of proportionality, k = 6
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Answer:
6
Step-by-step explanation:
120/20 = 6
108/18 = 6
72/12 = 6
30/5 = 6
See the pattern? :)
(50 points and brainlyest)
Because the diameter of the circle is now known 19.8, the base area of the cylinder can be calculated. Ignore the square base of the prism.
Answer:
307,8
Step-by-step explanation:
The area of a circle is 3.14 times the radius squared, and the radius is the diameter divided by 2. Hence the area is 307.8
shawna reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country. the plot shows a strong positive correlation. shawna recalls that correlation does not imply causation. in this example, shawna sees that increasing the number of cars per household would not cause members of her community to purchase health insurance. identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance.
The average income per household that is causing an increase in both the number of cars owned and the average number of citizens with health insurance.
The correlation of variables is the statistical relationship between two variables.
A correlation is positive if both variables move in the same direction and negative if the variables move in different directions - as one variable increases, the other decreases.
Correlation does not imply causation: This means that one can not legitimately associate a cause-and-effect relationship between the two variables.
In this example, it cannot be legitimately shown that increasing the number of cars per household would cause members of the community members to purchase health insurance, but when we bring in the lurking variable.
which is the increase in average income per household, we can see that this possibility might cause more people to buy more health insurance even after they have purchased cars, because they have more money to spend.
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what is the value of 8 divided by 3
Answer:
there's ur answer ...........
: AXYZ is located on the coordinate
plane below.
X
4
If the triangle is transformed following
the rule (x, y) → (x, -y), will congruence
be maintained? Why or why not?
If KL
show
When two pairs of corresponding angles and the included pair of sides are likewise congruent, a triangle is said to be congruent.
What is the congruent triangle?When two triangles can be superimposed, have identical side lengths, and equal angles, they are said to be congruent.
Triangles with the same angle measurements and side lengths are said to be congruent. SSS (Side-Side-Side) SAS are the triangle congruence criteria (Side-Angle-Side). When they have, triangles are congruent. There are precisely the same three sides and three angles.
Triangles are said to be congruent if two pairs of corresponding angles and the included pair of sides are also congruent. The triangles are congruent if a pair of sides that are not included and two pairs of comparable angles are congruent.
When the coordinates of XYZ are converted to produce its congruent image, X'Y'Z.
The triangle XYZ's translated picture is X'Y'Z'.
The triangle XYZ's reflected image becomes X'Y'Z'.
The triangle XYZ does not turn into its rotated counterpart, X'Y'Z'.
Therefore, Option I and II are true statements. so D is the correct answer.
The complete question is:
XYZ is transformed on a coordinate plane to obtain its congruent image X'Y'Z. Which of the following statements could be true?
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