In the relations v=u+at,findv,when u=6 a=10 t=2

The radius of convergence is 1/3. To find the radius of convergence for the power series using the ratio test, we need to analyze the general term of the series. The given series is:

Σ(an * x^n)

where an is the coefficient of the term with x raised to the power n. The coefficients in the given series are:

a1 = 3
a2 = 36
a3 = 243
a4 = 1296
a5 = 6075
...

Notice that each coefficient is a multiple of 3^n. Thus, we can write the general term as:

an = 3^n

Now, we apply the ratio test. The ratio test states that the series converges if the limit as n approaches infinity of the absolute value of the ratio of consecutive terms is less than 1:

lim (n → ∞) |(a(n+1) * x^(n+1)) / (an * x^n)|

= lim (n → ∞) |(3^(n+1) * x^(n+1)) / (3^n * x^n)|

To simplify, divide 3^(n+1) by 3^n:

= lim (n → ∞) |(3 * x)|

The series converges when |3 * x| < 1. To find the radius of convergence, solve for |x|:

|x| < 1/3

The radius of convergence is 1/3.

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Both Nori and her brother Sean made the same amount in interest, $100, assuming that their investments lasted 1 year.

The interest refers to the income or payment received or made for giving or taking credit from a lender.

The interest is usually depicted using a rate, which is expressed over 100.

Nori's Investment = $5,000

Interest rate = 2%

Interest amount = $100 ($5,000 x 2%)

Sean's investment = $10,000

Interest rate = 1%

Interest amount = $100 ($10,000 x 1%)

Thus, Nori and Sean equally made $100 in interest from their investments.

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The inverse relation is {(‐2,1), (3, 2),(‐3, 3),(2, 4)}, {(2, 4),(1, 5),(0, 6),(‐1, 7)}, the inverse equation is: y = (-x + 3)/8, y = (3/2)x - (15/2),  y = (1/2)x + 10,

x = sqrt(y) + 3 or x = -sqrt(y) + 3 and  f(g(x)) = g(f(x)) = x, f and g are inverse functions.

1.To find the inverse of the relation, we need to switch the x and y values of each point and solve for y:

{(‐2,1), (3, 2),(‐3, 3),(2, 4)}

2. Following the same process as above:

{(2, 4),(1, 5),(0, 6),(‐1, 7)}

So the inverse relation is {(2, 4),(1, 5),(0, 6),(‐1, 7)}.

3.To find the equation of the inverse, we can solve for x:

y = -8x + 3

x = (-y + 3)/8

So the inverse equation is: y = (-x + 3)/8.

4. Following the same process as above:

y = (2/3)x - 5

x = (3/2)y + 5

So the inverse equation is: y = (3/2)x - (15/2).

5. Following the same process as above:

y = (1/2)x + 10

x = 2(y - 10)

So the inverse equation is: y = (1/2)x + 10.

6.To find the inverse equation, we need to solve for x:

y = (x-3)^2

x = sqrt(y) + 3 or x = -sqrt(y) + 3

So the inverse equation is: x = sqrt(y) + 3 or x = -sqrt(y) + 3.

7,To verify that f and g are inverse functions, we need to show that f(g(x)) = x and g(f(x)) = x.

f(x) = 5x + 2

g(x) = (x-2)/5

f(g(x)) = 5((x-2)/5) + 2 = x - 2 + 2 = x

g(f(x)) = ((5x + 2)-2)/5 = x/5

Since f(g(x)) = g(f(x)) = x, f and g are inverse functions.

8.Following the same process as above:

f(x) = (1/2)x - 7

g(x) = 2x + 14

f(g(x)) = (1/2)(2x+14) - 7 = x

g(f(x)) = 2((1/2)x - 7) + 14 = x

Since f(g(x)) = g(f(x)) = x, f and g are inverse functions.

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Step-by-step explanation:

if this factorisation because I think you alr simplified, but here's the answer for factorisation anyways.

you can text me below in the comments section if that's not you want, I will try to answer if I can!!!

Answer:

3y(y - 2)(y - 1)

Step-by-step explanation:

Simplify by factoring

3y(y² - 3y + 2)

= 3y(y - 2)(y - 1)

Answer:

11.17, my answer needs to be 20+ characters soooooooo

A markup refers to the amount that is added on top of the cost price of a product to arrive at the selling price. In this case, the cost price of the roses was $4.50 per dozen. Therefore, a 90% markup would mean that the selling price is 90% more than the cost price.

To calculate the markup, we can use the following formula:
Markup = Cost Price x Markup Percentage

Markup Percentage = 90% = 0.9 (in decimal form)

Markup = $4.50 x 0.9 = $4.05

This means that the markup on the roses is $4.05 per dozen.

To calculate the final retail price, we simply need to add the markup to the cost price:
Retail Price = Cost Price + Markup

Retail Price = $4.50 + $4.05 = $8.55

Therefore, the final retail price for the roses that Larray bought at the flower shop is $8.55 per dozen.

In conclusion, Larray bought roses at the flower shop for $4.50 per dozen with a 90% markup, which resulted in a final retail price of $8.55 per dozen. The markup was calculated by multiplying the cost price by the markup percentage of 90%, and then adding it to the cost price to arrive at the selling price.

This is a common practice in the flower industry, where flower shops add a markup to the cost of their products to make a profit.

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The number of yellow marbles Stefan received is 4.

To find out how many yellow marbles Stefan received, we need to calculate 10% of the total number of marbles, which is 40.

Percentage calculations involve finding a part of a whole, and in this case, we are looking for the part that represents the yellow marbles. To find 10% of 40 marbles, you simply multiply the total number of marbles (40) by the percentage value (10%) as a decimal. To convert 10% to a decimal, you divide by 100, giving you 0.1.

Now, multiply the total marbles by the decimal value:

40 marbles * 0.1 = 4 marbles

So, Stefan received 4 yellow marbles in the bag he bought from the craft store.

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The critical points of the given function f(x) = ** + 5x/ (10x-60) are x = 6 and x = -6/5. The function is decreasing on (-∞, -6/5) and increasing on (-6/5, 6) and (6, ∞). The First Derivative Test shows that x = -6/5 is a local maximum and x = 6 is a local minimum.

To find the critical points, we need to first find the derivative of the function. Using the quotient rule, we get:

f'(x) = (10x - 60)(**)' - **(10x - 60)' / (10x - 60)²

Simplifying, we get:

f'(x) = 50 / (10x - 60)²

The critical points occur where the derivative is zero or undefined. Here, the derivative is never undefined, so we only need to find where it is zero:

50 / (10x - 60)² = 0

This occurs when x = 6 and x = -6/5.

Next, we need to determine the intervals on which the function is increasing or decreasing. To do this, we can use the first derivative test. We test a value in each interval of interest to see if the derivative is positive or negative:

For x < -6/5, we choose x = -2:

f'(-2) = 50 / (10(-2) - 60)² = -5/81 < 0

Therefore, the function is decreasing on (-∞, -6/5).

For -6/5 < x < 6, we choose x = 0:

f'(0) = 50 / (10(0) - 60)² = 5/9 > 0

Therefore, the function is increasing on (-6/5, 6).

For x > 6, we choose x = 10:

f'(10) = 50 / (10(10) - 60)² = 5/81 > 0

Therefore, the function is increasing on (6, ∞).

Finally, we can use the First Derivative Test to determine the nature of the critical points.

For x = -6/5:

f'(-6/5 - ε) < 0 and f'(-6/5 + ε) > 0, for small values of ε.

Therefore, x = -6/5 is a local maximum.

For x = 6:

f'(6 - ε) < 0 and f'(6 + ε) > 0, for small values of ε.

Therefore, x = 6 is a local minimum.

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The decomposition of  713 × 49 has been provided below

To multiply 713 and 49, we can use the distributive property and decompose the second number as follows:

49 = 40 + 9

Then, we can multiply each part of the sum by 713:

713 × 40 + 713 × 9

To calculate this, we can use the multiplication table and then add the results:

713

x 40

28520

713

x 9

6417

Then, we add the two results:

713 × 40 = 28520

713 × 9 = 6417

34997

Therefore, the multiplication 713 × 49, decomposed as 713 × 40 + 713 × 9, equals 34,997.

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When the value of pp=95 the value of qq will be equal to 6.

It is given that pp varies inversely with qq, so we can write that

pp=k/qq

where k is the proportionality constant.

here we can find the value of k by substituting the value of pp and qq with 19 and 30 in the relation that is given above, we get:

30=k/19

k=30*19

k=570

we the value of k to be 570 after putting the values in the relation.

Now if pp is changed to 95, and k is equal to 570 we can get the value of qq by putting the known values in the same relation.

pp=k/qq

qq=570/95

qq=6.

Therefore, when the value of pp is 95 the value for qq will be equal to 6.

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a. The down payment is $22,500.

b. The mortgage is $202,500.

c. The monthly mortgage payment is $1,027.

a. The down payment is 10% of the home price, which is $225,000 x 0.1 = $22,500.

b. The mortgage is the remaining amount that you need to pay, which is $225,000 - $22,500 = $202,500.

c. The monthly mortgage payment can be calculated using the formula for a fixed-rate mortgage:

Monthly Payment = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

where P is the principal amount (the mortgage), i is the monthly interest rate (4.5% / 12 = 0.375%), and n is the total number of monthly payments (30 years x 12 months/year = 360).

Plugging in the values, we get:

Monthly Payment = $202,500 [ 0.00375(1 + 0.00375)^360 ] / [ (1 + 0.00375)^360 – 1] = $1,027.

Therefore, your monthly mortgage payment will be $1,027.

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The quotient of 1.892×10^8 and 4.3×10^3 expressed in scientific notation is 4.4×10^4.

The quotient is determined by dividing any two numbers. In this case, the two numbers are 1.892×10^8 and 4.3×10^3. In order to calculate the quotient here, we will divide 1.892×10^8 by 4.3×10^3. Hence,

1. Divide the coefficients: 1.892 ÷ 4.3 = 0.44

2. Subtract the exponents: (10^8) ÷ (10^3) = 10^(8-3) = 10^5

3. Combine the results: 0.44 × 10^5

To express this answer in scientific notation, we need to move the decimal point one place to the left and adjust the exponent accordingly:

0.44 × 10^5 = 4.4×10^4

Therefore, the quotient expressed in scientific notation is 4.4×10^4.

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The interest that has to be paid for the car is $ 4534.2.

Compound interest is a type of interest calculation in which the interest earned is added to the principal amount.

The principal is the sum that is left to be paid after the down payment hence;

Principal = $24, 599 - $5, 000

= $19599

A = P(1 + r/n)^nt

A = amount

P =principal

r = rate

n = Number of times compounded

t = time

Then we have that;

A = 19599( 1 + 0.0425)^5

A = $24133.2

Then ;

Interest = Amount - Principal

Interest = $24133.2 -  $19599

=$ 4534.2

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The value of x that maximizes revenue is x 28.99 and maximum revenue is $1680 (thousand).

The revenue function for a company that sells x (thousand) items is R(x) = x² + 840. To find the value of x that maximizes revenue, we need to differentiate the revenue function, set it equal to zero and solve for x. The maximum revenue can then be calculated by substituting the value of x into the revenue function.

Revenue function: R(x) = x² + 840

To find the value of x that maximizes revenue, we differentiate the revenue function with respect to x:

dR/dx = 2x

Setting this equal to zero, we get:

2x = 0

x = 0

However, this value does not make sense in the context of the problem, as the company cannot sell 0 items. Therefore, we need to consider the critical points of the function, which occur when dR/dx = 0 or is undefined.

dR/dx = 0 when 2x = 0, so x = 0 is a critical point.

dR/dx is undefined when x = ±√840, so these are also critical points.

We can use the second derivative test to determine which critical point corresponds to a maximum. The second derivative of the revenue function is:

d²R/dx² = 2

At x = 0, d²R/dx² = 2 > 0, so this critical point corresponds to a minimum.

At x = ±√840, d²R/dx² = 2 > 0, so these critical points correspond to a minimum.

Therefore, the value of x that maximizes revenue is x = √840 ≈ 28.99 (thousand items).

To find the maximum revenue, we substitute x = √840 into the revenue function:

R(√840) = (√840)² + 840 = 1680

So the maximum revenue is $1680 (thousand).

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There is no fixed number of trials, so X is not a binomial variable. (Choice B) B is the right response.

Discrete random variables are within the category of binomial random variables. A binomial random variable keeps track of how frequently an event occurs over a predetermined number of trials. ALL of the following prerequisites have to be satisfied for a variable to qualify as a binomial random variable:

A predetermined sample size (number of trials) is used.

The relevant occurrence either takes place or doesn't in every trial.

On each trial, the likelihood of occurrence (or not) is the same.

Trials run separately from one another.

While Yoshi has a 30% chance of success for each shot and the trials are independent, the number of attempts is not fixed, as he continues until he makes the shot.

Thus, the correct answer is (Choice B) B. There is no fixed number of trials, so X is not a binomial variable.

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Answer:

The perimeter of rectangle ABCD can be calculated by adding up the lengths of its sides. Using the distance formula, we can find that AB has a length of 2 units, BC has a length of 2 units, CD has a length of 2 units, and AD has a length of 4 units. Therefore, the perimeter of rectangle ABCD is 10 units.

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The calculated number of police cadets in the group is 25

From the question, we have the following parameters that can be used in our computation:

Scouts = 8/13

Police cadets = the rest

This means that

Police cadets = 1 - 8/13

Evaluate

Police cadets = 5/13

Also, we have

Prefects = 3/8 or 15 of scouts

This means that

3/8 * Scouts = 15

Scouts = 40

So, we have

Total = 40/(8/13)

Total = 65

Recall that

Police cadets = 5/13

So, we have

Police cadets = 5/13 * 65

Evaluate

Police cadets = 25

Hence, the number of police cadets in the group is 25

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a) The height of the scale model is 105 m. b) The actual dimensions of the bed, couch, and desk are twice as large as their corresponding dimensions in the scale model.

a) To determine the height of the scale model, we multiply the height of the actual building by the scale factor of 0.5:

Height of scale model = 0.5 x 210 m = 105 m.

b) Since the scale factor is 0.5, the actual dimensions of the bed, couch, and desk are twice as large as their corresponding dimensions in the scale model.

For example, if the length of the couch in the scale model is 10 cm, then the actual length of the couch is 2 x 10 cm = 20 cm. Similarly, if the width of the desk in the scale model is 8 cm, then the actual width of the desk is 2 x 8 cm = 16 cm.

Therefore, to find the actual dimensions of the bed, couch, and desk, we simply multiply the corresponding dimensions in the scale model by 2.

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The probability that Anne could pass both mathematics and English courses is 0.19 or 19%.

To find the probability that Anne could pass both mathematics and English, we can use the formula for the probability of the union of two events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where A is the event of passing mathematics, B is the event of passing English, and A ∩ B is the event of passing both courses.
We are given:
P(A) = probability of passing mathematics = 0.42
P(B) = probability of passing English = 0.47
P(A ∪ B) = probability of passing at least one course = 0.7

Now we need to find the probability of passing both courses, P(A ∩ B).
Using the formula, we have:
0.7 = 0.42 + 0.47 - P(A ∩ B)
To find P(A ∩ B), we rearrange the equation:
P(A ∩ B) = 0.42 + 0.47 - 0.7
Now, calculate the probability:
P(A ∩ B) = 0.19
So, the probability that Anne is 0.19 or 19%.

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The probability of Shayla winning the $200 prize with 10 lottery tickets is approximately 0.2753%.

In a probability context, an event refers to an outcome or set of outcomes of an experiment or process. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The probability of winning the lottery can be calculated using the formula:

Probability of winning = 1 / odds

Here, the odds of winning are given as 1-in-3,598. So, the probability of winning is:

Probability of winning = 1 / 3,598

= 0.000278

= 0.0278%

Shayla has bought 10 lottery tickets. So, the probability of winning the $200 prize with at least one ticket can be calculated as the complement of the probability of not winning with any of the tickets. That is:

Probability of winning with at least one ticket = 1 - Probability of not winning with any ticket

The probability of not winning with a single ticket is 1 - 0.000278 = 0.999722. So, the probability of not winning with all 10 tickets is:

Probability of not winning with all 10 tickets = (0.999722)¹⁰

= 0.997247

Therefore, the probability of winning with at least one ticket is:

Probability of winning with at least one ticket = 1 - Probability of not winning with all tickets

= 1 - 0.997247

= 0.002753

= 0.2753% (approx)

So, the probability of Shayla winning the $200 prize with 10 lottery tickets is approximately 0.2753%.

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Shayla's probability of winning the $200 prize with 10 lottery tickets are at 0.2753%.

An event in the context of probability is a result, or series of results, of an experiment or procedure. By dividing the number of favourable outcomes by the total number of possible outcomes, the probability of an event is determined.

The following formula can be used to determine the likelihood of winning the lottery:

Probability of winning = 1 / odds

The odds of winning in this case are 1 in 3,598. Therefore, the likelihood of winning is:

Probability of winning = 1 / 3,598

= 0.000278

= 0.0278%

Shayla purchased ten lottery tickets. As a result, the likelihood that at least one ticket will win the $200 reward can be computed as the complement of the likelihood that none of the tickets will win. Which is:

winning chances with at least one ticket = 1 - likelihood of failing to win with any ticket

The likelihood that a single ticket won't be the winner is 1 - 0.000278 = 0.999722. Consequently, the likelihood of not winning with all ten

tickets is:

with all ten tickets, what is the likelihood of not winning = (0.999722)¹⁰

= 0.997247

Consequently, the following is the likelihood of winning with at least one ticket:

winning chances with at least one ticket = 1 - likelihood of failing to win with any ticket

= 1 - 0.997247

= 0.002753

= 0.2753% (approx)

Shayla's chances of winning the $200 prize with 10 lottery tickets are at 0.2753%.

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The ordered pairs of the linear expression y = 4x - 9 is (0, -9)

From the question, we have the following parameters that can be used in our computation:

The linear expression y = 4x - 9

To determine the ordered pairs of the linear expression, we set x to any value say x = 0 and then calculate the value of y

Using the above as a guide, we have the following:

y = 4(0) - 9

Evauate

y = -9

Divide both sides by 1

y = -9

This means that the value of y is equal to -9

So, we have (0, -9)

Hence, the ordered pairs of the linear expression is (0, -9)

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Answer:

15 cubic centimeters

Step-by-step explanation:

The figure is in the shape of a rectangular and the formula for volume of such a rectangular box is

V=lwh, where V is the volume, l is the length, and h is the height.

Since each cube is 1 cm, we see that the length is 5 cm (1 cm cube * 5 = 5 cm), the width is 3 cm (1 cm cube * 3 = 3 cm), and the height is 1 cm (1 cm cube * 1 = 1 cm).

Thus, we the product of our length, width, and height will give us the volume of the figure:

V = 5 * 3 * 1

V = 15 cubic centimeters

Answer:

I guess you need the value of (x) if that's so then

x= -4

Step-by-step explanation:

The value from the Student's t distribution that we would use to calculate a 95% confidence interval is 2.048

When the population standard deviation, σ, is unknown, we use the sample standard deviation, s, to estimate it. The t-distribution is used to calculate the confidence interval when we have a small sample size (less than 30) and the population standard deviation is unknown.

The value from the t-distribution that we would use to calculate a 95% confidence interval for the mean with a sample size of 28 is the t-value with 27 degrees of freedom, denoted by t(0.025,27) is 2.048.

This value can be obtained from a t-distribution table or calculator, and it represents the number of standard errors away from the mean that corresponds to a 95% confidence interval.

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Answer: x^2 + 3x - 70 = 0

Step-by-step explanation:

Answer:

x=180-90-54, y=180-x,z=90

Step-by-step explanation:

the sum of the degree of a triangle will equal 180. the sum of the degree of a line will equal 180.

The probability that both marbles drawn will be green is 16.4%.

The probability of drawing a green marble on the first draw is 8/19.

Since there are no replacements, the probability of drawing another green marble on the second draw is 7/18 (since there are now only 18 marbles left in the bag, including 7 green marbles).

Therefore, the probability of drawing two green marbles in a row is:

(8/19) × (7/18)

= 56/342

To convert this to a percentage, we can divide 56 by 342 and multiply by 100:

(56/342) × 100 = 16.37%

Therefore, the probability that both marbles drawn will be green is 16.4%.

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The volume of the smaller cone is approximately [tex]5.5 cm^3[/tex], rounded to the nearest tenth

If the cones are similar, then the ratio of the corresponding dimensions of the cones is the same.

Let's denote the height and radius of the smaller cone as h and r, respectively. Then, the height and radius of the larger cone are 3h and 2r, respectively.

Since the volumes of the cones are proportional to the cube of their radii and heights, we can write:

(volume of smaller cone) / (volume of larger cone) = [tex](r^2 * h) / ((2r)^2 * 3h)[/tex]

Simplifying this expression, we get:

(volume of smaller cone) / (volume of larger cone) = 1/12

Since we are given that the volume of the larger cone is [tex]66 cm^3[/tex], we can solve for the volume of the smaller cone as follows:

(volume of smaller cone) =[tex](1/12) * (66 cm^3) = 5.5 cm^3[/tex]

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a) To find the total surface area of the cuboid, we need to find the area of each face and then add them up.

Area of one face = length x width

Area of top and bottom faces = 1.1 m x 0.55 m = 0.605 m² (2 faces)

Area of front and back faces = 2.2 m x 0.55 m = 1.21 m² (2 faces)

Area of side faces = 2.2 m x 1.1 m = 2.42 m² (2 faces)

Total surface area = (2 x 0.605) + (2 x 1.21) + (2 x 2.42) = 7.7 m²

Each tin of varnish covers 20 m², so Emma needs:

Number of tins = (total surface area x number of coats) / coverage per tin

Number of tins = (7.7 x 3) / 0.02 = 1155

Emma needs to buy 1155 tins of wood varnish.

b) The cost of each tin of varnish is $3.99 for 100 ml. To find the cost of 1155 tins, we first need to convert the volume of varnish needed into liters.

Volume of varnish needed = (total surface area x number of coats) / coverage per litre

Volume of varnish needed = (7.7 x 3) / 20 = 1.155 liters

The number of tins required to make up 1.155 liters of varnish is:

Number of tins = (1.155 / 0.1) = 11.55

So Emma needs to buy 12 tins of varnish. The total cost is:

Total cost = cost per tin x number of tins

Total cost = $3.99 x 12 = $47.88

The total cost of the wood varnish is $47.88.

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Where the above is given, it is correct to state that "Yes; it is a reflection over line y = –1." (Option C)

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.

Note that in the above prompt, Since the horiztonal line y = -1 is equidistant between the bases of the trapezoids, ABCD and A'B'C'D and the corresponding coordinates are therefore equidistant from the line.

Hence Option C is correct.

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