Vertex E corresponds to vertex S, and Vertex V corresponds to vertex W in the congruent polygons GEPVR and SKLWQ.
Based on the given information, we know that the polygons GEPVR and SKLWQ are congruent. This means that their corresponding sides and angles are equal. Using this information, we can determine which vertices correspond to each other.
First, let's look at the vertices E and S. These vertices are opposite each other and must correspond to each other because the sides and angles of the polygons are congruent. Similarly, we can see that vertices P and K correspond to each other because they are opposite each other.
Now we need to determine which vertices correspond to V and W. We know that the polygons are congruent, so the side EP must be congruent to the side SK. Therefore, the vertices that correspond to E and V must be the same distance from the center of the polygon as the vertices that correspond to S and W, respectively.
Looking at the diagram, we can see that the center of the polygon is at the point where the diagonals intersect. Let's label this point as O. Since EO and SO are diagonals of the polygon, they bisect each other at point O. Therefore, the distance from O to E is equal to the distance from O to S.
Using the same logic, we can see that the distance from O to V is equal to the distance from O to W. Therefore, we can conclude that vertex V corresponds to vertex W in the congruent polygons GEPVR and SKLWQ.
Vertex E corresponds to vertex S, and vertex V corresponds to vertex W in the congruent polygons GEPVR and SKLWQ.
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If Jonny was 21 years old . He is 3 times as old as Becky determined Becky’s age
Answer:
Becky is 7 years old.
Step-by-step explanation: Let b - Becky's age ; Equation - 3b = 21. Divide both size by 3 to isolate the variable.
Answer:
Becky's 7 seven years old
Step-by-step explanation:
If 21 = 3x
x = 21/3
x = 7
Hope this helps :)
Pls brainliest...
A quadratic function f(x) reaches a minimum value of -16 when x = 2 and the graph of f(x) passes through the x-axis at 6 and -2. Which of these are equivalent forms of the function f(x) ? Choose all that are correct.
A . f(x) = x ^ 2 - 4x - 12
B. f(x) = (x - 2) ^ 2 - 16
C. f(x) = (x - 2)(x + 16)
D. f(x) = (x - 6)(x - 2)
E. f(x) = (x - 6) ^ 2 + 2
F. f(x) = x ^ 2 - 8x + 12
f(x) = (x - 2)² - 16 is the equivalent forms of the function f(x).
Given that quadratic function f(x) reaches a minimum value of -16 when x = 2 and the graph of f(x) passes through the x-axis at 6 and -2.
We have to find the equivalent forms of the function f(x).
The equivalent form of the quadratic function f(x) that satisfies the given conditions is: f(x) = (x - 2)² - 16
This form represents a quadratic function with a vertex at (2, -16) and passes through the x-axis at x = 6 and x = -2.
The other options do not match all of the given conditions.
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For each circle equation, find the center and radius.
(x-9)²+(-6)²-100
(x-4)²+(y+2)²-32
drag and drop answer here
ITEM BANK: Move to Top
center (-3,-8)
radius - 10
drag and drop answer here
center (-6, 5)
-2√√2
radius -
This section is worth 8 points of 39 total.
(x+3)²+(y+8)²-81
drag and drop answer here
center (4, -2)
radius - 4√√2
(x+6)²+(-5)²-8
drag and drop answer here
center (9,6)
radius -9
Center and radius of circle are,
1) Center = (9, 6)
Radius = 10
2) Center = (9, - 2)
Radius = √32
3) Center = (- 3, - 8)
Radius = 9
4) Center = (- 6, 5)
Radius = √8 = 2√2
We have to given that;
Equation of circles are,
(x - 9)² + (y - 6)² = 100
(x - 4)² + (y + 2)² = 32
(x + 3)² + (y + 8)² = 81
(x + 6)²+ (y - 5)² = 8
Since, The equation of circle is,
⇒ (x - h)² + (y - k)² = r²
Where, (h. k) = center
Radius = r
Hence, We get;
For Equation of circles are,
(x - 9)² + (y - 6)² = 100 = 10²
Center = (9, 6)
Radius = 10
(x - 4)² + (y + 2)² = 32
Center = (9, - 2)
Radius = √32
(x + 3)² + (y + 8)² = 81
Center = (- 3, - 8)
Radius = 9
(x + 6)²+ (y - 5)² = 8
Center = (- 6, 5)
Radius = √8 = 2√2
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What is the meaning of "The set of all sets does not exist"?
The statement "The set of all sets does not exist" is one that connote the idea of a set that has every possible set as its elements.
What is the meaning of "The set of all sets does not exist"?The phrase of a set that is made up of all sets, commonly called the "universal set," has been discovered to result in contradictions, as demonstrated by Russell's Paradox.
The occurrence of Russell's Paradox is manifested when we contemplate the assortment of all groupings that lack themselves as constituents. It conveys the idea that it is impossible to formulate a set comprising of all conceivable sets as its constituents without encountering logical inconsistencies and conundrums such as Russell's Paradox.
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See text below
The safe way to eliminate paradoxes of this type is to abandon the Schema of Comprehension and keep its weak version, the Schema of Separation:
If P is a property, then for any X there exists a set Y = {x X: P(x)}.
Once we give up the full Comprehension Schema, Russell's Paradox is no longer a threat; moreover, it provides this useful information: The set of all sets does not exist. (Otherwise, apply the Separation Schema to the property xx.)
In other words, it is the concept of the set of all sets that is paradoxical, not the idea of comprehension itselfWhat is the meaning of "The set of all sets does not exist"?
find overtime and gross pay per week. pay rate: $10.18/hour total hours worked last week: 48
The overtime hours worked last week are 8 hours, and the gross pay per week is $529.36.
To calculate the overtime and gross pay per week, we need to determine the regular hours and overtime hours worked.
Regular hours refer to the standard hours worked within a week before reaching the threshold for overtime. In most cases, the threshold for overtime is typically 40 hours per week.
Overtime hours refer to any hours worked beyond the regular hours and are usually compensated at a higher rate than regular hours.
In this scenario, since the total hours worked last week are 48 and the threshold for overtime is 40 hours, we can calculate the regular hours and overtime hours as follows:
Regular hours = 40 hours
Overtime hours = Total hours worked - Regular hours
= 48 hours - 40 hours
= 8 hours
Now, let's calculate the gross pay per week:
Regular pay = Regular hours * Pay rate
= 40 hours * $10.18/hour
= $407.20
Overtime pay = Overtime hours * Overtime rate
= 8 hours * (1.5 * Pay rate)
= 8 hours * (1.5 * $10.18/hour)
= 8 hours * $15.27/hour
= $122.16
Gross pay per week = Regular pay + Overtime pay
= $407.20 + $122.16
= $529.36
Therefore, the overtime hours worked last week are 8 hours, and the gross pay per week is $529.36.
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A group consists of 12 persons, of whom 3 are extremely patient, other 6 extremely honest and the rest are extremely kind. A person from the group is selected at random.
Assuming that each person is equally likely to be selected, find the probability that a person selected is: (a) extremely patient (b) extremely kind or honest
The probability of selecting an extremely patient person is 25% and the probability of selecting an extremely kind or honest person is 75%.
To find the probability of selecting an extremely patient person, we need to divide the number of extremely patient persons by the total number of persons in the group.
So, the probability of selecting an extremely patient person is 3/12, which simplifies to 1/4 or 25%.
Similarly, to find the probability of selecting an extremely kind or honest person, we need to add the number of extremely kind persons and the number of extremely honest persons, and then divide by the total number of persons in the group.
So, the probability of selecting an extremely kind or honest person is (6+3)/12, which simplifies to 9/12 or 3/4 or 75%.
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Please answer 5-10 and lmk if I got 1-4 wrong (also giving brainliest if correct) ty :)
Answer:
Step-by-step explanation:
hehe 5 points is so less for this question but oh well
1: 10
2: -3
3: 13/2
4: -7
5: 2
6: 73
7: 14
8: 5/3
9: -4
10: 7/3
My skill be a bit rusty, so they might be wrong.
Calcular la altura de un arbol, sabiendo que; si nos situamos 8 metros de la base del trono vemos que la parte superior de su copa en un ángulo de 36.87°
Por lo tanto, la altura del árbol es aproximadamente 6 metros.Para calcular la altura de un árbol, podemos utilizar trigonometría y el concepto de tangente. Si nos situamos a una distancia de 8 metros de la base del árbol y vemos la parte superior de su copa en un ángulo de 36.87°, podemos utilizar la tangente de dicho ángulo para determinar la altura.
La tangente de un ángulo se define como la razón entre el cateto opuesto y el cateto adyacente. En este caso, el cateto opuesto es la altura del árbol y el cateto adyacente es la distancia desde la base hasta nuestro punto de observación.
La fórmula para calcular la altura es:
altura = distancia * tangente(ángulo)
Sustituyendo los valores conocidos, tenemos:
altura = 8 * tangente(36.87°)
Utilizando una calculadora, encontramos que la tangente de 36.87° es aproximadamente 0.75. Por lo tanto:
altura ≈ 8 * 0.75
≈ 6.
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Which is the correct solution for the integral
The correct solution for the integral would be D. 1.
How to find the solution ?We can solve using integration by parts based on the product rule for differentiation.
[tex]\int\limits^a_b ^{ \pi / 2 } \theta sin \theta d\theta[/tex]
Applying integration by parts gives:
[tex]\int\limits^a_0 ^ {\pi / 2} sin \theta d\theta = - \theta cos \theta |_{0} ^ {\pi / 2} + \int\limits^a_0 ^ {\pi / 2} cos \theta d \theta- \theta cos \theta |_{0} ^ {\pi / 2} + 1 = - [ ( \pi / 2 ) * cos ( \pi / 2 ) - 0 * cos ( 0 ) ] + 1\\\\= - [ 0 - 0 ] + 1 \\\\= 1[/tex]
In conclusion, the correct option for the integral is D. 1.
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state the remainder 72x5+60x4-18x3+16x2+x-7 is divided by x-6
Answer: 634313
Step-by-step explanation:
[tex]\frac{72x^{5} +60x^{4} -18x^{3}+ 16x^{2} +x-7}{x-6}[/tex]
I will use synthetic division to find remainder. The last number is your remainder
6 | 72 60 -18 16 1 -7
| 432 2952 17604 105720 634320
72 492 2934 17620 105721 634313
100 Points! Algebra question. For the graph, (a) describe the end behavior, (b) determine whether it represents an odd-degree or an even-degree function, and (c) state the number of real zeros. Please show as much work as possible. Photo attached. Thank you!
The end behavior of a function refers to how the function behaves as the input variable approaches positive or negative infinity.
Both to the left and to the right of the graph, the function decays, hence the end behavior of the function is given as follows:
As x -> ∞, f(x) -> -∞.
The zeros of the function are given as follows:
x = -3 -> odd multiplicity as the graph crosses the x-axis.x = -1 -> odd multiplicity as the graph crosses the x-axis.x = 1.5 -> odd multiplicity as the graph crosses the x-axis.x = 4 -> odd multiplicity as the graph crosses the x-axis.Four real zeros with odd multiplicity, meaning that the least degree is of 4 x 1 = 4, which is an even degree.
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The denominator of the circle measures 30 m. what is the circumference of the circle? Use 3.14 for pie,and do not round your answer.Be sure to include the correct unit in your answer
Answer:
The circumference of the circle is 94.2m.
Step-by-step explanation:
The circumference of a circle is:
C = pi•d
Fill in the diameter which was given, 30m.
C = pi•30
use 3.14 for pi
C = 3.14 • 30
C = 94.2
The circumference is 94.2m
Assume that a simple random sample has been selected from a normally distributed population and test the given claim.
Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s), or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim.
A light bulb manufacturer advertises that the average life for its lightbulbs is 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours:
995 590 510 539 739 917 571 555 916 728 664 693 708 887 849
At the 10% significance level, test the claim that the sample is from a population with a mean life of 900 hours. Use the P-value method of testing hypotheses.
In the above problem, there was enough evidence to support the claim that the average life of the lightbulbs is not 900 hours. Since the P-value (0.0189) is < 0.10 , we reject the null hypothesis.
Why is this so ?Null Hypothesis (H₀) - The average life of the lightbulbs is 900 hours.
Alternative Hypothesis (Hₐ) - The average life of the lightbulbs is not 900 hours.
Using the P-value method, the test statistic is calculated using
t = (x - μ) / (s / √n)
where
x is the sample mean μ is the population mean (assumed to be 900)s is the sample standard deviationn is the sample sizeNext we plug in the values
x = 726.1333
s = 175.4898
n = 15
t = (726.1333 - 900) / (175.4898 / √15) = -3.83716223712
Using a t-distribution table with 14 degrees of freedom and a significance level of 10%
⇒ the critical values to be -1.761 and 1.761.
To find the P- value, we look up the probability of getting a t-value of -2.2732 or less with 14 degrees of freedom. The P -value is found to be 0.001.
Since the P- value (0.001 ) is less than the significance level ( 0.10), we reject the null hypothesis.
So we ccan emphatically state that there is sufficient evidence to support the claim that the average life of the lightbulbs is not 900 hours.
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Faye got out of the movie theater at 6:15. If the movie was 1 hour and 50 minutes long, what time did it start?
Step-by-step explanation:
If Faye got out at 6:15
_1:50
4 : 25. Therefore the movie started with in 4 hours and 25 minutes.
PLEASE ASAP !!!
Complete the assignment with labelled diagrams showing all steps.
Find each missing side length to the nearest tenth of a unit.
a)
The side length x = 9.00m
Given,
Right angled triangle with base , perpendicular , hypotenuse.
Base = 9m
Perpendicular = xm
Hypotenuse = 12.73m
Apply Pythogoras theorem,
H² = P² + B²
Substitute the values,
12.73² = x² + 9²
x = 9.00m
Thus perpendicular of triangle is 9.00m .
b)
The side length x = 7.99m
Given,
Right angled triangle with base , perpendicular , hypotenuse.
Base = xm
Perpendicular = 7m
Hypotenuse = 10.63m
Apply Pythogoras theorem,
H² = P² + B²
Substitute the values,
10.63² = x² + 7²
x = 9.00m
Thus base of triangle is 7.99m .
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The purple shaded area, to the right in the graph, is the solution to which system of linear inequalities?
Answer:
2x + y ≥ 4, y < x + 1
Step-by-step explanation:
the thick (means we use ≤ or ≥) blue line that goes from top left to bottom right has a negative gradient, and it passes through (0,4).
taking the axes ((0,4) and (2,0)) intercepts into account, the gradient =
(4-0)/(0-2) = 4/-2 = -2.
the equation of the line is y - 0 = -2 (x - 2) = -2x + 4
that is y = -2x + 4. purple is shaded to the right of it. so we need y ≥ -2x +4,
y + 2x ≥ 4.
the dotted (meaning we use < or >) red line has a positive gradient. this line goes from bottom left corner of one square to top right of same square. it does this for all squares it passes through. we can see that the gradient is 1.
it passes through point (0 , 1).
equation of line = y - 1 = 1(x - 0) = x
y = x + 1.
purple is shaded below it. so we have y < x + 1.
There are 5 germs on your phone that double in number every minute. How many germs are on your phone in 20 minutes?
The number of germs that double every minute after 20 minutes will be 9.5×10¹³
Number of germs present = 5
Time taken to double in number = 1 minute
Time passed = 20 minutes
Number of times they have doubled in 20 minutes = [tex]\frac{20}{1}[/tex] =20 times
The total number of germs after 20 minutes = 5x5x5......(20 times) =95367431640625
This can be written in scientific notation as 9.5x10¹³
Thus, after 20 minutes there will be 9.5x10¹³ number of germs.
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Graph the line represented by each equation.
Y=-3x +4
Answer:
Step-by-step explanation:
The American Red Cross says that about 11% of the US population has type B blood. A blood drive is being held at your school. What is the probability that at least 2 of the first 10 blood donors has type b blood.
Answer: There is a 2.2 percent chance
How many pounds of candy that sells for $1.75 per lb must be mixed with candy that sells for $1.25 per lb to obtain
20 lb of a mixture that should sell for $1.60 per lb?
The required, we need 14 pounds of candy that sells for $1.75 per lb and 6 pounds of candy that sells for $1.25 per lb to obtain 20 lbs of a mixture that sells for $1.60 per lb.
Let x be the number of pounds of candy that sells for $1.75 per lb.
Then, the number of pounds of candy that sells for $1.25 per lb is 20 - x (since the total amount of candy in the mixture is 20 lbs).
The total cost of the candy that sells for $1.75 per lb is 1.75x, and the total cost of the candy that sells for $1.25 per lb is 1.25(20 - x) = 25 - 1.25x.
The total cost of the mixture is the sum of the cost of each type of candy, which must be equal to the cost of 20 lb of the mixture at $1.60 per lb:
1.75x + (25 - 1.25x) = 1.60(20)
Simplifying and solving for x, we get:
1.75x + 25 - 1.25x = 32
0.5x + 25 = 32
0.5x = 7
x = 14
Therefore, we need 14 pounds of candy that sells for $1.75 per lb and 6 pounds of candy that sells for $1.25 per lb to obtain 20 lbs of a mixture that sells for $1.60 per lb.
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-x^2+6x-2=0 solve using quadratic formula and explain why you used this method
Answer:
x = 3 + √7
x = 3 - √7
Step-by-step explanation:
To solve the quadratic equation -x² + 6x - 2 = 0, we can use the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation, a, b, and c represent the coefficients of the quadratic equation in the form ax² + bx + c = 0.
Comparing the given equation -x² + 6x - 2 = 0 with the standard form, we can determine the values of a, b, and c:
a = -1
b = 6
c = -2
Substituting these values into the quadratic formula, we have:
x = (-6 ± √(6² - 4(-1)(-2))) / (2(-1))
Simplifying further:
x = (-6 ± √(36 - 8)) / (-2)
x = (-6 ± √(28)) / (-2)
x = (-6 ± √(4 * 7)) / (-2)
x = (-6 ± 2√7) / (-2)
Now, we can simplify the expression further:
x = (6 ± 2√7) / 2
Dividing both the numerator and denominator by 2:
x = 3 ± √7
Therefore, the solutions to the quadratic equation -x² + 6x - 2 = 0 are:
x = 3 + √7
x = 3 - √7
We used the quadratic formula because it is a reliable and systematic method for solving quadratic equations. It works for any quadratic equation, regardless of whether the equation has real or imaginary solutions. By substituting the coefficients of the quadratic equation into the formula, we can determine the roots of the equation accurately.
21. The heights of two different children were recorded in the chart.
Age (months)
Child 1 Height
(Inches)
21.7
26.4
29.9
31.5
33.9
34.6
37.4
38.1
40.6
42.5
43.3
0
6
12
18
24
30
36
42
48
54
60
Child 2 Height
(Inches)
18.5
21.5
23.9
30.4
34.2
35.1
38.3
39.5
42.1
43.5
44.0
What type of visual display could be used to compare the two data
sets?
A type of visual display that could be used to compare the two data sets is a line graph or scatter plot.
One type of visual display that could be used to compare the two data sets is a side-by-side bar graph.
A side-by-side bar graph would allow for a direct comparison of the average heights of the two children at each age group.
The x-axis would represent the age (in months) and the y-axis would represent the height (in inches).
Two vertical bars would be placed side by side for each age group, one representing the average height of child 1 and the other representing the average height of child 2.
The height of each bar would correspond to the respective average height for that age group.
By comparing the heights of the bars at each age group, it would be possible to see which child was taller on average at each age.
Another type of visual display that could be used is a line graph.
A line graph would allow for a more detailed view of the individual data points for each child's height over time.
Each child's height would be plotted on the y-axis with age (in months) on the x-axis.
A separate line would be drawn for each child, with different colors or symbols used to distinguish between the two.
By comparing the trends of the lines over time, it would be possible to see how each child's height changed as they grew older, as well as identify any differences or similarities between the two.
A scatter plot is another option, where each data point is plotted on a graph, with child 1's data points in one color or symbol and child 2's data points in another color or symbol.
This would allow for a more detailed view of the distribution of heights for each child at each age group and also allow for identifying any outliers or differences between the two children.
This type of graph may not be as effective in directly comparing the two data sets as the side-by-side bar graph or line graph.
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what transformations are applied to the graph of the function f(x)=10ft o produce the graph of the funvtiong(x)=3(10)x-2
The transformations applied to f(x) are a vertical dilation of scale factor 3 and a traslation down of 2 units.
What are the transformations applied?Here we start with the exponential function:
f(x) = 10ˣ
Now let's define the transformations used.
A vertical dilation of scale factor k is written as:
g(x) = k*f(x)
And a translation down of N units is written as:
g(x) = f(x) - N
Then if we apply a vertical dilation of scale factor 3, we will get:
g(x) = 3*f(x)
And a translation down of 2 units we will get:
g(x) = 3*f(x) - 2
Replacing f(x) we will have:
g(x) = 3*10ˣ - 2
That is the transformed function.
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8. Where are the corresponding angles in the diagram below?
O2 and 4
1 and 3
12
3 4
5 6
78
All the pairs of corresponding angles are,
⇒ 2 and 6
⇒ 4 and 8
⇒ 1 and 5
⇒ 3 and 7
We have to given that;
Parallel lines are shown in figure.
Now, We know that;
All the Corresponding angles are formed in matching corners or corresponding corners with transversal when two parallel lines are intersected by any other line.
Hence, We get;
By definition of corresponding angles, All the pairs of corresponding angles are,
⇒ 2 and 6
⇒ 4 and 8
⇒ 1 and 5
⇒ 3 and 7
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Using the strategy to select the best integration techniques, evaluate the integral
The integral of the function is determined as -cos (2x + 3) + C.
option A.
What is the integral of the function?The integral of the function is calculated as follows;
The given function is;
= ∫ 2sin (2x + 3) dx
We will use substitution method to evaluate the integral as shown below;
Let u = 2x + 3
du/dx = 2
dx = du/2
Using the substitution method, the integral is evaluated as follows;
∫ 2sin (2x + 3) dx
= ∫ 2sin u (du/2)
= -cos u + C
Replace u with its initial value;
-cos u + C = -cos (2x + 3) + C
∫ 2sin (2x + 3) dx = -cos (2x + 3) + C
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Calculate the area of a rectangle, two sides of which are equal to 8 centimeters, and the other two are equal to 4 centimeters
which type of savints institution offers a range of services to its customers, including savings accounts, checking accoungs, and money market accounts, and also makes loans and investments and buys government bonds? A savings and loan institution B credit union C savings bank D commercial banks
The correct answer is D) commercial banks. Commercial banks are financial institutions that offer a wide range of services to their customers, including savings accounts, checking accounts, and money market accounts.
Commercial banks are versatile financial institutions that offer a diverse range of services to their customers. They provide savings accounts, checking accounts, and money market accounts to help individuals manage their finances. Additionally, commercial banks offer loans to individuals and businesses, allowing them to fund various ventures and projects. These banks also engage in investments, using their expertise to manage and grow clients' assets.
Furthermore, they participate in the buying and selling of government bonds, which helps in financing government operations. With their comprehensive suite of services, commercial banks play a crucial role in facilitating economic activities and serving as a trusted financial partner for individuals and businesses alike.
So, The correct answer is D) commercial banks.
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A company's investors make an initial contribution of $10,000 to start a company. In its first year of operations, the company has $2,000 in revenues and $500 in expenses. Before the first year ends, the company pays a $600 dividend back to its owners. What is the company's total Stockholders' Equity at the end of its first year of operations?
Retained Earnings of the company is $900.
Retained Earnings -
We calculate the retained earnings by the subtracting the total earnings by the sum of all the expenses of the company.
The company has $2,000 in revenues; hence the earnings of the company are given as follows:
$2,000.
Expenses:
$500 in basic expenses.
$600 dividend paid back to owners.
Total expenses:
500 + 600 = $1100.
Retained Earnings are given as follows:
2000 - 1100 = $900.
Hence the company's Retained Earnings at the end of the first year of operations is given as follows: $900.
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What is the 20th term of the following series
Answer:
84
Step-by-step explanation:
a_20=84
Triangle PQR has vertex coordinates at P(4, 0), Q(5, 4), R(5, 1). If the triangle is translated so that Q′(0, 4), determine the translation direction and number of units.
5 units down
5 units up
5 units to the right
5 units to the left
The translation direction is 5 units to the left.
To determine the translation direction and number of units, we can compare the original coordinates of point Q (Q(5, 4)) with the new coordinates of Q' after the translation (Q'(0, 4)).
By comparing the x-coordinates, we can see that the x-coordinate of Q' is smaller than the x-coordinate of Q, which means the triangle was translated to the left.
By comparing the y-coordinates, we can see that the y-coordinate of Q' is the same as the y-coordinate of Q, which means there was no vertical translation.
Therefore, the translation direction is 5 units to the left.
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