The dimensions of the smaller prism are each multiplied by the factor of 1/3 for length, 1/4 for width, and 1/4 for height to produce the corresponding dimensions of the larger prism.
To determine the factor by which the dimensions of the smaller prism are multiplied to produce the corresponding dimensions of the larger prism, let's consider the relationship between the two prisms.
A prism is a three-dimensional shape with two parallel, congruent bases connected by rectangular faces. Since the problem specifies that the dimensions of the smaller prism are being multiplied to obtain the dimensions of the larger prism, we can infer that the prisms are similar, meaning they have the same shape but possibly different sizes.
Let's denote the dimensions of the smaller prism as length, width, and height, and the corresponding dimensions of the larger prism as L, W, and H.
To find the factor by which the dimensions are multiplied, we need to compare the corresponding sides of the two prisms. Based on the information provided, we can establish the following relationships:
L = 3 × length
W = 4 × width
H = 4 × height
We can rewrite these relationships as:
length = L/3
width = W/4
height = H/4
Now, let's compare the ratios of corresponding sides:
length/L = (L/3)/L = 1/3
width/W = (W/4)/W = 1/4
height/H = (H/4)/H = 1/4
From these ratios, we can observe that each dimension of the smaller prism is one-third (1/3) the size of the corresponding dimension of the larger prism in terms of length, one-fourth (1/4) in terms of width, and one-fourth (1/4) in terms of height.
Therefore, the dimensions of the smaller prism are each multiplied by the factor of 1/3 for length, 1/4 for width, and 1/4 for height to produce the corresponding dimensions of the larger prism.
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These shapes are similar.
Find X.
X
5
9
27
15
21
The value of X is 7.
Given that the set of number are in pattern,
X, 5, 9, 27, 15, 21.
To find the value of X such that given numbers are in pattern.
The next three number are three times of first three numbers respectively.
Let a, b, c is the first three numbers then 3a, 3b, 3c are next three numbers.
Consider the given set of numbers, X, 5, 9, 9 × 3, 5 × 3, 21.
By using the data and the pattern set gives,
3X = 21.
Divide by 7 on both sides,
X = 7.
Hence, the value of X is 3
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Need some help on this question!!!!!
The greater number of packages that can fit in the truck is 24000.
The volume of the part of the truck that is being filled is 375 cubic feet.
We have,
To determine the greater number of packages that can fit in the truck, we need to calculate the volume of both the packages and the part of the truck that is being filled.
The volume of a cube-shaped package:
The side length of the cube-shaped package is 1/4 feet.
The volume of a cube is given by V = s³, where s is the side length.
Therefore, the volume of each package is (1/4)³ = 1/64 cubic feet.
The volume of the part of the truck being filled:
The dimensions of the rectangular prism-shaped part of the truck are:
Length = 8 feet
Width = 6(1/4) feet = 6.25 feet
Height = 7(1/2) feet = 7.5 feet
The volume of a rectangular prism is given by V = length × width × height.
Therefore, the volume of the part of the truck being filled is:
8 × 6.25 × 7.5
= 375 cubic feet.
To calculate the greater number of packages that can fit in the truck, we divide the volume of the part of the truck by the volume of each package:
= 375 cubic feet / (1/64 cubic feet)
= 375 × 64
= 24000 packages.
Therefore,
The greater number of packages that can fit in the truck is 24000.
The volume of the part of the truck that is being filled is 375 cubic feet.
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(-20,13) (16,15)
Can some find the slop for this question
a triangle has angle measurements of 51 89 and 40 what kind of triangle is it?
(20 points, please answer quick)
The correct classification for this triangle is an acute triangle.
How to solveThe angle measures given are 51, 89, and 40 degrees.
There are no angles that are either equal to or greater than 90 degrees among those mentioned. Consequently, the triangle does not contain any angles that are either right or obtuse.
To categorize a triangle according to its angles, the total of the angles within the triangle, which is invariably 180 degrees, is taken into account.
51 + 89 + 40 = 180
Given that the total of the angles is 180 degrees, we can deduce that this particular triangle is acute in nature. An acute-angled triangle is a type of triangle that has three angles which are each smaller than 90 degrees.
Therefore, the correct classification for this triangle is an acute triangle.
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100 Points! Multiple choice geometry. Photo attached. Thank you!
8. Option (A) is correct as line XB is a radius
9. Option (D) is correct as line BD is a tangent line
What is the radius and tangent of the circleThe radius is the straight line from the center of the circle to the circumference and according to the tangent to a circle theorem, a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency
8. The only option that represents a radius is the line from the center X to the point B on the circle circumference.
9. The line from the point B to the point D is called is a tangent to the circle
Therefore, line XB is a radius and line BD is a tangent line.
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Use table values to graph the Quadratic function.
y = x^2 - 2x + 4
What is the meaning of "A function f is one-to-one if f(x) = f(y) implies x = y"?
The meaning of the sentence is that for an one-to-one function, each input makes an unique output.
What is the meaning of the sentence?Here we want to find the meaning of "A function f is one-to-one if f(x) = f(y) implies x = y"
That is a definition of an one-to-one function.
In simpler words, an one to one function is a function that for each input x, the output y is unique.
So the sentence says that if:
f(x) = f(y) (we have two equal outputs)
Then x = y (then the inputs must be equal)
So that is the meaning of the sentence.
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Given the number pattern: 20; 18: 14; 8;
a) Determine the nth term of this number pattern.
b) Determine the value of T12 in this number pattern.
c) Which term in this number pattern will have a value of - 36?
A quadratic number pattern has a second term equal to 1, a third term equal to -6 and a fifth term equal to - 14.
a) Calculate the second difference of this quadratic number pattern.
b) Hence, or otherwise, calculate the first term of this number pattern.
Answer:
tn = -n² +n +20; t12 = -112; t8 = -362; 10Step-by-step explanation:
You have two problems involving quadratic sequences. For the sequence that starts 20, 18, 14, 8, ..., you want the n-th term, the 12-th term, and the term number of -36. For the sequence with terms 2, 3, and 5 having values 1, -6, and -14, you want the second difference and the first term.
1. 20, 18, 14, 8The first attachment shows the first and second differences of this sequence each begin with -2. The first of differences at level n can be put into a formula for the n-th term:
∆0 +(n -1)(∆1 +(n -2)/2(∆2 + ...))
We have (∆0, ∆1, ∆2) = (20, -2, -2), so the expression for the n-th term is ...
tn = 20 +(n -1)(-2 +(n -2)/2(-2))
(a) tn = -n² +n +20
Listing the first 12 terms, we find the 12th term is ...
(b) t12 = -112
Locating the term -36 in the list, we find ...
(c) -36 is term 8
2. x, 1, -6, y, -14For a quadratic sequence the third differences are zero. The second attachment shows us the third differences for this sequence are ...
-3(y +11) = 0 ⇒ y = -11
y -x +21 = 0 ⇒ x = 10
That attachment also shows us the second differences are x-8 (or y+13):
x -8 = 10 -8 = 2
(a) The second difference is 2.
(b) The first term is 10.
__
Additional comment
The ability of this free calculator app to perform arithmetic symbolically and to find differences of successive list elements is very helpful for solving questions related to sequences. The linear and quadratic regression capabilities can also be useful for some questions. It pays to know your tools.
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Here is the histogram of a data distribution.
5
4
لیا
3-
2-
1 2 3 4 5 6 7 8 9 10
What is the shape of this distribution?
OA. Unimodal skewed left
B. Uniform
OC. Unimodal symmetric
D. Unimodal skewed right
E. Bimodal
W
The given histogram is bimodal, which is the last option/ option E, as bimodal distribution means that the data set has two distinct peaks or modes. In a bimodal histogram, the bars are grouped in a way that shows two prominent peaks or modes in the data.
Each bar in the histogram represents a specific range of values, and the height of the bar indicates the frequency or count of data points falling within that range. In a bimodal histogram, there will be two relatively high bars that correspond to the two modes of the data. The bimodal histogram is useful for visualizing and analyzing data sets that exhibit two distinct groups or clusters. It provides a clear visual representation of the two modes and their frequencies, which can help in identifying patterns and understanding the underlying characteristics of the data.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer: Area = = 38.5 - Perimeter - 29.6819.
Step-by-step explanation:
To find the perimeter and area of a triangle with vertices L(5,5), M(-2,-4), and N(5,-6), we can use the distance formula and the formula for the area of a triangle.
Perimeter:
The perimeter of a triangle is the sum of the lengths of its sides. We can find the lengths of each side using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can calculate the lengths of LM, MN, and NL:
LM = √((-2 - 5)^2 + (-4 - 5)^2)
= √((-7)^2 + (-9)^2)
= √(49 + 81)
= √130
MN = √((5 - (-2))^2 + (-6 - (-4))^2)
= √((7)^2 + (-2)^2)
= √(49 + 4)
= √53
NL = √((5 - 5)^2 + (-6 - 5)^2)
= √((0)^2 + (-11)^2)
= √(0 + 121)
= √121
= 11
The perimeter of the triangle is the sum of these three sides:
Perimeter = LM + MN + NL
= √130 + √53 + 11 = 29.6819
Area:
To calculate the area of the triangle, we can use the formula for the area of a triangle using the coordinates of its vertices. The formula is given by:
Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Using the coordinates of L(5,5), M(-2,-4), and N(5,-6), we can calculate the area:
Area = 0.5 * |5(-4 - (-6)) + (-2)(-6 - 5) + 5(5 - (-4))|
= 0.5 * |5(2) + (-2)(-11) + 5(9)|
= 0.5 * |10 + 22 + 45|
= 0.5 * |77|
= 38.5
Therefore, the perimeter of the triangle is given by √130 + √53 + 11 = 29.6819 units, and the area of the triangle is 38.5 square units.
A set of twins purchase a small, oddly shaped plot of land for their retirement. They want to divide the parcel along the grid lines into two identical plots. Can they do it and how?
The ability of the twins to divide the oddly shaped plot into two Identical plots along the grid lines depends on the presence of a line of symmetry.
To determine whether the set of twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need to consider the characteristics of the plot and the conditions required for the division.
For the division to be possible, the plot needs to have a line of symmetry that can be used to create two identical halves. A line of symmetry divides an object into two equal and mirrored parts.
If the plot of land has a line of symmetry, the twins can divide it by drawing a line along the symmetry axis. This line should cut the plot into two equal halves, ensuring that both plots are identical.
However, if the plot does not have a line of symmetry, it may not be possible to divide it into two identical plots along the grid lines. In this case, the twins would need to consider alternative methods of division or compromise on the goal of having two identical plots.
To determine if the plot has a line of symmetry, the twins can examine its shape and characteristics. They can look for any symmetrical patterns, such as equal sides or mirrored shapes, that indicate the presence of a line of symmetry.
If the plot does not have an obvious line of symmetry, the twins might need to explore other options, such as dividing the plot into two equal areas based on other criteria, such as the length or width of each half.
the ability of the twins to divide the oddly shaped plot into two identical plots along the grid lines depends on the presence of a line of symmetry. If such a line exists, they can divide the plot by drawing a line along the symmetry axis. However, if the plot lacks symmetry, they may need to consider alternative methods of division or adjust their expectations.
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Note the full question may be :
To determine whether the twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need more specific information about the shape and dimensions of the plot. the shape of the plot (rectangular, triangular, irregular), the lengths of its sides, any existing grid lines or divisions within the plot.
Define the variables
a. The variables are x and y which represents 2 shots and 3 shots respectively.
b. The system of equations are;
x + y = 11
2x + 3y = 29
What are the variables to this problem?a. Let's define the variables to write the system of equations:
Let x be the number of two-point shots Noah made.
Let y be the number of three-point shots Noah made.
b. We can write a system of equations that model this problem.
Equation 1: x + y = 11
This equation represents the total number of shots Noah made, which is 11.
Equation 2: 2x + 3y = 29
This equation represents the total number of points Noah scored, which is 29. Since each two-point shot is worth 2 points and each three-point shot is worth 3 points, we can multiply the number of two-point shots (x) by 2 and the number of three-point shots (y) by 3 and sum them up to get the total score of 29.
The system of equations that can be used to determine the number of two-point shots Noah made and the number of three-point shots he made is:
x + y = 11
2x + 3y = 29
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Un atleta parte desde el reposo en una competencia al cabo de 30 segundos su velocidad es de 2m/s ¿cuál es la aceleración del atleta?
The required acceleration is 0.0666 [tex]m^{2}[/tex]/s.
Given that the velocity of the object is 2m/s and time is 30s.
Acceleration is the rate of change of velocity with respect to time.
To find the acceleration by using the formula.
acceleration (a) = velocity (v) / time (t).
By using data and formula gives,
acceleration (a) = velocity (v) / time (t).
acceleration (a) = 2 / 30
acceleration (a) = 0.0666 [tex]m^{2}[/tex]/s.
Hence, the required acceleration is 0.0666 [tex]m^{2}[/tex]/s.
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Enter the number that belongs in the green box. 4 51° 109°
The answer choice which belongs in the green box and is the longest side of the triangle as required is; 11.06.
What is the length of the longest side?It follows from the task content that since the sum of angles in a triangle is; 180°, the missing angle measure is; 180 - 51 - 109° = 20°.
Consequently, it follows from the sine law that;
4 / sin 20° = x / sin 109°
x = 4 sin 109° / sin 20°
x = 11.06.
Ultimately, the number that belongs in the green box is; 11.06.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
ABC forms a right-angled triangle
Let the distance between AB = x
Using Pythagoras theorem
Sin 30 = Opposite / Hypoteneuse
Sin 30 = 12 in/ x
However, From the equilateral triangle, all sides are = 2 and the angles are all = 60 degrees. Then we take a right-angled triangle out of it. This means that the base equals 1, and the top side is halved and equals 30 degrees.
Using Pythagoras' theorem, Sin 30 = 1/ 2
Substituting back into the equation, we get:
1/ 2 = 12 in / x
Cross multiplying, we get:
x = 24 in
Recall x = AB
AB = 24 inches
To remember the angles and their respective formula, use SOHCAHTOA
Where sin x = Opposite / Hypoteneuse
Cos x = Adjacent / Hypoteneuse
Tan x = Opposite / Adjacent
Find the probability of not rolling factors of 5 on both dice
The probability of not rolling factors of 5 on both dice is 25/36
Calculating the probability of not rolling factors of 5 on both diceFrom the question, we have the following parameters that can be used in our computation:
Rolling two number cubes
Using the above as a guide, we have the following:
Sample space, S = {1, 2, 3, 4, 5, 6}
In the above sample space, we have
Not factors of 5 = {1, 2, 3, 4, 6}
So, we have
P(Not rolling factor of 5) = 5/6 * 5/6
Evaluate
P(Not rolling factor of 5) = 25/36
Hence, the probability is 25/36
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Question
Two six sided dice are rolled.
Find the probability of not rolling factors of 5 on both dice
If you are traveling 14 miles per hour, how many inches would you travel in 3 seconds? (1 mile = 5280 feet; 1 foot = 12 inches) (Convert 3 seconds to inches)
1. What will the coordinates of Triangle RST be after it is translated 4 units down and 3 units left?
--5-5
R
Da
4
64
5-
4
3-
bo
24
4
10
=arpy 5
-3
--5-
1 2 3 4 5 6 x
O Re(-7,-2), Sc(2, -1), Tc(-1,-9)
ORE(-1,-2), Sc(8,-1), Tc (5,-9)
ORE(-1,6), Sc(8,7), TC(5, -1)
O Re(-7,-2), Sc(8,-1), Tc(-1,-1)
The coordinates of the Triangle RST after it is translated 4 units down and 3 units to the left is the option;
R¢(-7, -2), S¢(2, -1), T¢(-1, -9)
What is a translation transformation?A translation transformation is one in which the location of the pre-image is transformed from its initial location to the destination location.
The coordinates of the vertices of the triangle RST are; R(-4, 2), S(5, 3), T(2, -5)
The translation transformation that is applied on the triangle RST includes;
A vertical translation 4 units downwards
An horizontal translation 3 units to the left
The translation transformation is therefore; T₍₋₃, ₋₄₎
Therefore, applying each transformation, we get;
R(-4, 2) ⇒ T₍₋₃, ₋₄₎ ⇒ R¢(-4 -3, 2 - 4) = R¢(-7, -2)
S(5, 3) ⇒ T₍₋₃, ₋₄₎ ⇒S¢(5 - 3, 3 - 4) = S¢(2, -1)
T(2, -5) ⇒ T₍₋₃, ₋₄₎ ⇒ T¢(2 - 3, -5 - 4) = T¢(-1, -9)
The correct option is therefore, the first option
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
A. 1.78cm².
B. 331.34 square meters.
Step-by-step explanation:
The area of the shaded region in a circle if the radius and central angle is given can be calculated using the following formula:
Area of shaded region = (θ/360) * πr²
Where:
θ is the central angle in degrees. r is the radius of the circle. π is the mathematical constant pi, approximately equal to 3.14.A.
If the radius is 2 meters and the central angle is 51 degrees, then the area of the shaded region is:
Area of shaded region = (51/360)*π*2² = 0.357π m²
≈ 1.78 square meters
Therefore, the area of the shaded region is approximately 1.78square meters.
Therefore, the area of the shaded region is 1.78cm².
B.
If the radius is 12.5 meters and the central angle is 243 degrees, then the area of the shaded region is:
Area of shaded region = (243/360)*π*12.5² = 105.47π m²
≈ 105.47π square meters
Therefore, the area of the shaded region is approximately 331.34 square meters.
100 Points! Geometry question. Photo attached. Find x and y. Please show as much work as possible. Thank you!
The values of given x and y is,
x = 6 and y = 13/2
Since we know that,
Basic proportionality theorem,
The basic proportionality theory was developed by Thales, a great Greek mathematician; hence, it is also known as the Thales theorem. According to the great mathematician, the ratio of any two matching sides of any two equiangular triangles is always the same. The basic proportionality theorem (BPT) was suggested based on this premise.
Since we know that,
In the figure we that,
⇒ 2x + 1 = x +7
⇒ x = 6
Similarly
⇒ 3y - 8 = y +5
⇒ y = 13/2
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Given the following Mayan Number, write the equivalent Base-10 number in the Answer Box. Each
row (place value) is separated with white space.
> Next Question
Your Answer:
:|| :||- €
The Mayan number || :||- € is equivalent to the base-10 number 1021.
How to find Mayan number?To convert a Mayan number to base-10, use the following steps:
Read the number from bottom to top, starting with the ones place.Assign a value to each digit, based on its position.Multiply each digit by its place value.Add the products together to get the final value.In this case, the values of the digits are as follows:
Ones: 1
Twentys: 0
Four-hundreds: 2
Eight-thousands: 1
The place values are as follows:
Ones: 1
Twentys: 20
Four-hundreds: 400
Eight-thousands: 8000
The final value is calculated as follows:
1 × 1 + 0 × 20 + 2 × 400 + 1 × 8000 = 1021
Therefore, the Mayan number || :||- € is equivalent to the base-10 number 1021.
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What is the range of g(x) = |x + 3| + 2? A. [-3, ∞) B. (-∞, 2] C. [2, ∞) D. (-∞, ∞)
Answer:
C. [2, + ∞)-----------------
Given function:
g(x) = | x + 3| + 2We know that absolute value is non-negative, hence |x + 3| has a minimum value of 0 when x = - 3. Then the function has a minimum value of 2.
The range is the set of output values. As we see given function has a minimum value of 2 and no maximum value.
It can be shown as:
g ∈ [2, + ∞)The matching choice is C.
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Answer:
D. Alternate Interior Angles Converse
Edplanation:
13 ~= 12
13 altenated angle to nr.10
13 is parpendicular to nr.15 and 15 is alternate to 12
Show your work HELPPPP DUE TOMORROW!!
Answer:
10
Step-by-step explanation:
[tex]2\frac{3}{8}[/tex]+[tex]1\frac{3}{4}[/tex]+[tex]5\frac{7}{8}[/tex]=
[tex]2\frac{3}{8} +1\frac{6}{8} +5\frac{7}{8}[/tex]=
[tex]8\frac{16}{8} =10[/tex]
Graph the line with y-intercept 4 and slope 2.
Answer is in the file atttached.
Question 8 (2 points)
What is the area of this figure?
6 yd
4 yd
4 yd
4 yd
4 yd
Answer: The figure you are describing seems to be a rectangle with a length of 6 yards and a width of 4 yards. The area of a rectangle is calculated by multiplying its length by its width. So, the area of this rectangle would be 6 yd * 4 yd = 24 square yards.
Answer: Total Area = 36yd
Step-by-step explanation:
You have to find the area of both square and triangle.
Area Triangle = .5x5x8= 20yd
Area Square = 4x4 = 16yd
Triangle + Square - 20yd+16yd = 36yd
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Answer:
∠ 1 and ∠ 3 = 180°
Step-by-step explanation:
∠ 1 and ∠ 3 are same- side interior angles and sum to 180° , that is
∠ 1 + ∠ 3 = 180
A surveyor is standing 30 feet from the base of a tall building. The surveyor measures the angle of elevation from the ground to the top of the building to be 65 degrees. Find the height of the building to the nearest foot
Answer:
Height = 64 feet
Step-by-step explanation:
(***It's very important to model these kinds of problems. I attached a picture modeling the problem so show how modeling makes it easier to solve the problem)
We know that the building is vertical, and the ground is horizontal. Thus, the ground and the building make a right angle.
Therefore, the top of the building, the base of the building, and the surveyor form a right triangle, where
The distance between the surveyor and the building is a leg of the triangle,The height, h of the building (aka distance between the top of the building and the base) is another leg of the triangle,and the distance between the top of the building and the surveyor is the hypotenuse.Because we're working with a right triangle, we can now find h, the heigh of the building using one of the trigonometric ratios.
We know that the angle of elevation is made by the ground and the distance between the surveyor and top of the building.
When the 65° (angle of elevation) is our reference angle, the height of the building is the opposite side and the distance between the base of the building and the surveyor is the adjacent side.
Thus, we can use the tangent ratio, which is: tan (θ) = opposite / adjacent:
We can now plug in 65 for θ and 30 for the adjacent side. This will allow us to find the opposite side, which is the heigh of the building:
tan (65) = h / 30
30 * tan(65) = h
64.33520762
64 = h
Thus, the height of the building to the nearest foot is 64 feet.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer: D
Step-by-step explanation: -135
please help fast !!!
The coordinate of vertices of DEF are;
D = ( -4, -3)
E = ( -7, 4)
F =( -7, -3)
Here, we have,
Reflection in the y-axis: The reflection of point (x, y) across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse (x,y)→( -x,y) .
First, triangle ABC is reflected across the y axes.
So, we have:
(x,y)→( -x,y)
then, translated down 5 units.
so, transformation rule on ABC, we have:
(x,y)→( -x , y - 5)
so, the coordinate of vertices of DEF are;
D = ( - 4, 2 - 5) = ( -4, -3)
E = ( -7, 9 - 5) = ( -7, 4)
F = (-7 , 2 - 5) = ( -7, -3)
Hence, the coordinate of vertices of DEF are;
D = ( -4, -3)
E = ( -7, 4)
F =( -7, -3)
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