The width of the single slit is 0.00135 mm and the second minimum will be at angle of 69.9º.
To find the width of the single slit, we can use the formula:
w = λL/d * sinθ
where w is the width of the single slit, λ is the wavelength of light, L is the distance from the slit to the screen, d is the distance between the slits and θ is the angle at which the first minimum is observed. By substituting the given values, we get:
w = (633*10^-9 m) (2L) / (d) * sin(28.0º) = 0.00135 mm
The angle of the second minimum can be found by using the formula: θn = sin^-1(nλ/w)
where θn is the angle at which the nth minimum is observed, n is the order of the minimum and λ and w are the wavelength and width of the single slit respectively. Substituting the values we get: θ = sin^-1(2*(633*10^-9 m) / (0.0175 mm)) = 69.9º
It is important to note that the above explanation is based on the assumption that the width of the single slit is much smaller than the distance between the slit and the screen (L) and the distance between the slits (d).
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I don’t understand my homework
The Seed, where the range is 100, is the initial value of an algorithm used to produce a set of numbers.
Describe Range.Difference between the greatest and lowest value is referred to as the range. To get the range, find the variable's greatest observed value and deduct its lowest observed value. The data points in the center of the distribution are not taken into account; the range only considers these two values. Between the lowest and greatest values, there is a range of values. Values at each end of the range make up the range. Use the data set 4, 6, 10, 15, 18 as an example. Its range is 18-4 = 14, and its minimum and maximum values are 4, 4, and 4.
The term "seed" refers to the initial value of an algorithm used to produce a set of integers.
[tex]20, 25, 30, 45, 55, 90, 110,115,120[/tex]
Range = 120 - 20 = 100
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What are angles for Grade 6?
In Grade 6, students typically learn about angles and their properties. Some of the key concepts that students may study include:
Understanding that an angle is formed by two rays with a common endpoint called the vertex.Identifying and labeling angles, using the vertex and the two rays that form the angle.Understanding that angles can be measured in degrees (°).Measuring angles with a protractor.Classifying angles as acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), or straight (exactly 180°).Identifying and drawing complementary and supplementary angles.Understanding the relationship between adjacent angles formed by parallel lines and transversals.Using angle properties to solve problems and prove geometric theorems.These are some of the key concepts that students may learn about angles in Grade 6, but the specific curriculum can vary depending on the school district and state.
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On March 13, 2013, a Japanese printer presented the smallest book known at that date entitled "flowers of the four seasons". This square book has 22 pages of 0.75 mm on each side.
1) Calculate the area in m², of a page of this book answer : ???
The area of a page of the book, "flowers of the four seasons". would be = 5.6× 10^-⁷ m²
How to calculate the area of a book?To calculate the area of a book, the length and weight of the book must be determined which is then multiplied to give it's area in square metres or mm².
The number of pages that makes up the book, "flowers of the four seasons". = 22 pages.
Since the book has a square shape, the length and width is the same = 0.75 mm
To convert 0.75 mm to meter, divide by 1000= 0.00075m
The area of a page = Length× width = 0.00075×0.00075
= 0.0000005625= 5.6× 10^-⁷ m²
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Please answer asappp!!
Ty
Aiden's bank account has $160 in it. He plans to deposit a certain amount, m, each month
for the next year.
Aiden wants to have $400 at the end of the year. Which equation can he solve to find
the amount he should deposit each month?
160+12m = 400
160 + m = 12(400)
12(160+ m) = 400
160m | 12 = 400
The equation to find the amount deposited each month is 160 + 12m = 400.
The amount deposited each month is $20.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
Amount in account = $160
Amount at the end of the year = $400
Now,
There are 12 months in a year.
The amount deposited each month = m
Now,
160 + 12m = 400
Solve for m.
12m = 400 - 160
12m = 240
m = 20
Thus,
The equation is 160 + 12m = 400.
The amount deposited each month is $20.
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Andre says he can find the length of the third side of triangle ABC and it is 13 units. Mai disagrees and thinks that the side length is unknown. Who do you agree with? Show or explain your reasoning
On soloing the provided question we can say that - Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area. A = 210-123 = 87 sq unit
what is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
the sum of the areas of the circle, the triangle, and the square.
Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area.
A = 210-123 = 87 sq unit
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a shipment contains 10 televisions, of which two are defective. a sample of three televisions is selected at random. what is the probability that the sample contains no defective televisions?
The combination of samples is 80% likely to contain no defective televisions.
A combination appears to be a statistical technique for estimating the number of potential configurations in a collection of objects where the sequence of anything like the option is immaterial. Organize the elements in every order to choose. Permutations & combinations are commonly misunderstood.
Evaluate just non-faulty TVs to identify the same amount of ways in which the picked TVs are not defective. Because there are two faulty televisions out of 16, the amount of non-faulty sets is two.
= 10 - 2
= 8
Two non-defective televisions must be picked from a pool of twelve. There are several ways to accomplish this:
= ((10 × 9 × 8 × 7 ....) ÷ ((2 × 1) × (8 × 7 × 6...)) = 8!/2!((10- 2)!) = 80.
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how many times does 5 go into 2.5
Answer:
.5
Step-by-step explanation:
2.5/5 = .5
everything in the picture
The measure of m∠6 is 123° and is equal to m∠1 because there are corresponding angles formed by parallel lines cut by a transversal.
What are corresponding anglesCorresponding angles are the angles that are formed when two parallel lines are cut or intersected by the transversal and they are equal.
The angles 1, 2, 3, 4, 5, 6, 7, and 8 all lie on a transversal line that cuts the parallel lines, hence m∠1 and m∠6 are corresponding angles are they are equal.
so;
m∠1 = (15x + 3)° = m∠6 = (10x + 43)°
collect like terms, we have;
15x - 10x = 43° - 3°
5x = 40°
divide through by 5
x = 40°/5
x = 8
m∠6 = [10(8) + 43]°
m∠6 = (80 + 43)°
m∠6 = 123°
Therefore, the corresponding angle m∠6 have the measure of 123°.
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Solve the inequality.
-4i + 28 > 8
The value of i for given inequality is i < 5.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a b indicates that an is smaller than b.
When a > b is used, it indicates that an is bigger than b.
A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.
Given,
-4i + 28 > 8
Dividing the equation by 4
-i + 7 > 2
Subtracting 7 from both sides,
- i > -5
i < 5
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Are the following two functions inverses of each other? Use function composition to explain your answer.
To determine whether two functions are inverses of each other, we can use function composition to check if the composition of the two functions is the identity function. The identity function is a function that always returns its input.
What does the term "inverse function" mean?
A function that reverses the effects of another function is called an inverse function. When y=f(x) and x=g, a function g is the inverse of a function f. (y). Applying f and then g is equivalent to doing nothing, in other words. This can be expressed as g(f(x))=x in terms of the relationship between f and g.
The composition of two functions f and g is denoted by f(g(x)) or f o g.
If f(g(x)) = x and g(f(x)) = x for all x in the domain of the functions, then f and g are inverse functions.
In this case,
f(g(x)) = f((x-2)/5) = 5((x-2)/5) + 2 = x
so, f and g are inverse functions.
and also
g(f(x)) = g(5x+2) = (5x+2-2)/5 = x
so, f and g are inverse functions.
Therefore the functions f(x)= 5x+2 and g(x) = x-2/5 are inverses of each other.
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m
0
Find the quotient 2+
27
4/²/7
13
317
土
1
3
You can use the model to help.
7
2/3
2
+
3
Answer: (D) --> 4 2/3
Step-by-step explanation:
1st --> Turn the problem into an improper fraction using the reciprocal
2nd --> Turn the improper fraction into a mixed answer
what is the image of the point (-5,-4) after the rotation of 180 degrees counter clockwise?
Please help me ASAP!!!
Answer:
(5, 4 )
Step-by-step explanation:
under a counter- clockwise about the origin of 180°
a point (x, y ) → (- x, - y ) , then
(- 5, - 4 ) → (- (- 5), - (- 4) ) → (5, 4 )
find 9 f(x) dx 0 if f(x) = 7 for x < 7 x for x ≥ 7 .
The function is 130/2.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.
According to question,
[tex]\int\limits^9_0 {f(x)} \, dx \\ \int\limits^7_0 {f(x)} \, dx+\int\limits^9_7 {f(x)} \, dx\\ \int\limits^7_0 {7} \, dx + \int\limits^9_7 {x} \, dx\\ (7x)^{7} _{0} + (\frac{x^{2} }{2})^{9} _{7}[/tex]
7x7 - 7x0 + 81/4 - 49/4
49 + 32/2
130/2
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Here are some fractions.
9/12 6/8 18/24 10/16 15/20
One of these fractions is not equivalent to 3/4
Which fraction?
Fraction 10/16 is not equivalent to 3/4 among the other given fractions.
What is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given some fractions.9/12, 6/8, 18/24, 10/16, and 15/20.
Simplifying this given fraction by taking the common term out
[tex]\frac{9}{12}, \frac{6}{8} , \frac{18}{24} , \frac{10}{16} , \frac{15}{20}[/tex]
[tex]\frac{9/3}{1/3}, \frac{6/2}{8/2} , \frac{18/6}{24/6} , \frac{10/2}{16/2} , \frac{15/5}{20/5}[/tex]
Thus we will get
3/4, 3/4, 3/4, 5/8, 3/4
Therefore, Among the other fractions listed, fraction 10/16 is not equal to fraction 3/4.
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What does the AAS triangle congruence theorem tell you about triangles?
The AAS Triangle Congruence Theorem states that if two angles and the side between them of one triangle are equal to two angles and the side between them of another triangle, then the two triangles are congruent.
The AAS Triangle Congruence Theorem states that if two angles and the side between them of one triangle are equal to the two angles and the side between them of another triangle, then the two triangles are congruent. This theorem is an important tool in geometry that can be used to determine if two triangles are congruent and to find missing side lengths or angles. This theorem is based on the idea that if two sides and the included angle of one triangle are equal to the two sides and the included angle of another triangle, then the two triangles must be congruent. This is because the third side of the triangle, and the remaining angles must also be equal in order for the triangles to be congruent. Therefore, the AAS Triangle Congruence Theorem can be used to determine if two triangles are congruent, and to find missing side lengths or angles.
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Represent and connect Andre wrote the expression 15(1.5x-3) to represent the relationship shown in the table. Write two other expressions that represent the relationship shown in the table .
X ..................value of expression
0 ..............................-45
2 ............. ...................0
5 ................ ................. 67.5
8 ......................................135
The two expressions which are similar to the given expressions are 45 (0.5x - 1) and 22.5 ( x - 2 ) .
What is linear Equation ?
linear equation can be defined as the equation in which the highest degree is one.
Given expression,
15(1.5x-3)
expression 15(1.5x-3) can also written as 15 (15/10 -3)
that is
15 ( 3/2 - 3 )
15 * 3 (1/2 x -1 )
45 (0.5x - 1)
And
45 ( 0.5x -1 )
45 (x-2/2)
22.5 ( x - 2 )
Hence , The two expressions which are similar to the given expressions are 45 (0.5x - 1) and 22.5 ( x - 2 ) .
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What is the result when the number 63 Is decreased by 1.3%
Answer:
62.18
Step-by-step explanation:
The new value =
63 - The value of the percentage decrease =
63 - (1.3% × 63) =
63 - 1.3% × 63 =
(1 - 1.3%) × 63 =
(100% - 1.3%) × 63 =
98.7% × 63 =
98.7 ÷ 100 × 63 =
98.7 × 63 ÷ 100 =
6,218.1 ÷ 100 =
62.181 ≈
62.18
1/5/2023
7:00PM
13 Jitesh made a square using 8 toothpicks of the same length as shown below. Arun made a bigger square. He also used some toothpicks of the same length. Which of these could be the number of toothpicks Arun used to make his square? A. 14 B. 16- D. 22
The number of toothpicks Arun could have used to make his bigger square than Jitesh's 8-toothpick square was B. 16.
How is the number of toothpicks determined?We are told that Jitesh made a square using 8 toothpicks.
The toothpicks have the same length as Arun's. We also know that Arun made a bigger square than Jitesh.
The same number of toothpicks must be on the four sides to make a square. Otherwise, it cannot form a perfect square.
Thus, it is unlikely that 14 toothpicks can make a square because 14 is not evenly divisible by 4, just like 22. However, 16 is evenly divisible by 4 and forms a perfect square of 4, giving each side an equal size.
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Find the area of the following trapezoid:
22cm, 12cm, 10cm, and 8cm
Answer:
Area of a Trapezoid = [tex]136cm^{2}[/tex]
Step-by-step explanation:
Area of a Trapezoid = [tex]\frac{1}{2} X(a+b)h[/tex]
Area of a Trapezoid = [tex]\frac{1}{2} X(12+22)8[/tex]
Area of a Trapezoid = [tex]\frac{1}{2} X34X8[/tex]
Area of a Trapezoid = [tex]136cm^{2}[/tex]
if 8x ≤ g(x) ≤ 4x4 − 4x2 + 8 for all x, evaluate lim x→1 g(x).
If 8x ≤ g(x) ≤ 4x4 − 4x2 + 8 for all x, x will be evaluated as lim x→1 g(x), 1 is 8.
To evaluate the limit of g(x) as x approaches 1, we must first examine the given inequality. It states that if 8x is less than or equal to g(x), and g(x) is less than or equal to 4x4 - 4x2 + 8, then this is true for all x.
Calculating the limit of g(x) as x approaches 1, we start by substituting x = 1 into the given inequality. This gives us 8(1) ≤ g(1) ≤ 4(1)4 - 4(1)2 + 8. Simplifying, this gives us 8 ≤ g(1) ≤ 8, so g(1) must be equal to 8.
Therefore, the limit of g(x) as x approaches 1 is 8.
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29. After a reflection in the y-axis, the quadratic function listed below would have which of the
following formulas?
f (x) = 2x² - 8x +3
A. y=-2a² + 8x - 3
B. y=-2x²8x+3
C. y = 2x² + 8x +3
D. y=2x² +8x-3
Answer:
After a reflection in the y-axis, the quadratic function would have the following formula:
y = -(2x² - 8x + 3)
= -2x² + 8x - 3
Therefore, the answer is option D: y=2x² +8x-3.
Step-by-step explanation:
How do you find the third side of an inequality of a triangle?
To find the third side of an inequality of a triangle, you must first use the Triangle Inequality Theorem.
This theorem states that for any triangle, the sum of any two sides of the triangle must be greater than the third side. This means that in order to find the length of the third side, you must subtract the sum of the two known sides from the smaller of the two sides, then the length of the third side will be equal to the difference between these two numbers. For example, if two sides of a triangle have lengths of 4 and 3, the third side must be greater than 1 (4 + 3 = 7 and 4 - 3 = 1). Therefore, the length of the third side must be greater than 1.
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if a wave has a wavelength of 25.4 cm and a frequency of 1.63 khz, its speed is closest to
Its speed is closest to 414m/s
given that
A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is typically defined in wireless systems in metres (m), centimetres (cm), or millimetres (mm) (mm). The wavelength is more frequently described in nanometers (nm), which are units of 10-9 m, or angstroms (), which are units of 10-10 m, for infrared (IR), visible light (UV), and gamma radiation ().
Frequency, which is defined as the quantity of wave cycles per second, and wavelength have an inverse relationship. The wavelength of the signal decreases with increasing signal frequency.
a wave has a wavelength = 25.4cm
a frequency = 1.63khz
now, we need to find speed of the wave
speed = wavelength × frequency
speed = 25.4 × 16.3
= 414m/s
speed = 414m/s
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Find the area of the shaded figure
The area of shaded figure is 272 square units
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.
Area of trapezium = (1/2)(a+b)*h
a=18 , b= 34, h - 16
So, area of trapezium = (1/2)(18+34)*16 = 52*8 = 416 square units
Area of unshaded triangle = (1/2) * base*height
= (1/2) * 18*16 = 18*8 = 144 square units
Area of shaded figure = area of trapezium - Area of unshaded triangle
= 416 - 144
= 272 square units
So, the Area of shaded figure = 272 square units
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13
5
L
N
M
Enter the ratio equivalent to tan(L).
tan (L) =
For right triangle LMN, the required ratio equivalent to tan(L) is 5 /13.
What is right angle triangle?The triangle is a geometric shape with three sides, and the sum of the interior angles should not exceed 180°.A right triangle also known as right-angled triangle, or more formally an orthogonal triangle, generally known as a rectangled triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.In this case, in order to find the ratio equivalent to tan (L).
tan(L) = opposite / adjacent side
tan(L) = NM /LN
Here given
NM = 5cm
LN = 13cm
We already know that tan(L) = perpendicular / adjacent
from given,
tan (L) = 5 / 13
As a result, the required ratio for triangle LMN is 5/13.
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The points (2, u) and (3, 10) fall on a line with a slope of 8. What is the value of u?
Please I have a unit test tomorrow I need help.
Answer:
u = 2
Step-by-step explanation:
The slope of a line between points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is equal to [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], so, given our slope of 8, we need to find the first y-coordinate:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\8=\frac{10-u}{3-2}\\\\8=\frac{10-u}{1}\\\\8=10-u\\\\-2=-u\\\\2=u[/tex]
Hence, the value of "u" is 2.
Answer:
To find the value of u, you can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
In this case, (x1, y1) = (2, u) and (x2, y2) = (3, 10). Plugging these values into the formula gives:
slope = (10 - u) / (3 - 2)
Simplifying this expression gives:
slope = (10 - u) / 1
Since the slope is 8, we can set this expression equal to 8 and solve for u:
8 = (10 - u) / 1
8 = 10 - u
u = 10 - 8
u = 2
Therefore, the value of u is 2.
Certainly! The slope of a line is a measure of how steep the line is. It is calculated by finding the ratio of the difference in the y-coordinates of two points on the line to the difference in the x-coordinates of those same two points. For example, in the line you gave, the two points are (2, u) and (3, 10). The difference in the x-coordinates of these two points is 3 - 2 = 1, and the difference in the y-coordinates is 10 - u. The slope of the line is then (10 - u) / 1. We know that the slope of this line is 8, so we can set the expression for the slope equal to 8 and solve for u. This gives us the value of u, which is 2. I hope this helps! Let me know if you have any questions.
Mia's family wants to go on a tour to Brazil. A tour company charges $150 bus rental fee plus $35 per person for private group tours. If the total charge can be modeled by the function, where represents the amount of people, identify each of the following.
Create a function that models Sidney's earnings
Function that represents the expression is f (y) = $150 + $35Y
what is function?
In mathematics, function is an expression that creates a relationship between an independent variable and a dependent variable.
The set of values of independent variable is called input and the set of values for dependent variable is called output.
What is the function that can represent the above statement?
given, bus rental fee = $150
fee for private group tour per person = $35
let, the amount of people included in this tour = Y
total fee for private group tour for Y people= $35Y
Therefore, the total charge for the Brazil tour = bus rental fee + fee for private group
total charge = $150 + $35Y
if total charge for Brazil tour can be modelled by a function
then function f (y) = $150 + $35Y
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Find the slope-intercept equation of the line that passes through (1,-2) and has an undefined slope.
The slope - intercept equation of a line that would pass through (1,-2) and has an undefined slope, is y = -2 x
How to find the slope intercept equation?The slope - intercept equation takes the form:
y = mx + b
m = slope
b = y - intercept
When the slope is undefined, it means that there is no y - intercept as the slope is a vertical line which crosses the x - axis alone. The slope would therefore be :
y = mx
- 2 = 1 x
m = - 2
The slope - intercept form is:
y = -2 x
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Given the Square JKLM, if the area of JKLM is 64 sq in.., what is the length of the diagonal KM?
The length of diagonal KM of square is 11.31 inch.
What is square?
A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can also be explained as a rectangle with two adjacent sides that are of equal length.
A square has four equal sides, four vertices, and is a closed, two-dimensional shape. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width.
Given:
The Square JKLM, the area of JKLM is 64 sq in.
We have to find the length of diagonal KM.
Since,
Area of square = (side)^2
64 = (side)^2
Side = 8
Length of each side of square is 8 in.
By using the Pythagorean theorem,
(KL)^2 + (LM)^2 = (KM)^2
8^2 + 8^2 = (KM)^2
64 + 64 = (KM)^2
128 = (KM)^2
KM = 11.31
Hence, the length of diagonal KM of square is 11.31 inch.
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In ABDC shown below, point E is on CD, and point F is on BD so that
ZBCD ZEFD. If FD=30, BC = 77, and EF = 35, find the
length of CD. Figures are not necessarily drawn to scale.
The length of the CD is 66.
What are similar triangles?Similar triangles are triangles that have the same shape but can be different sizes. Two triangles are similar if and only if the corresponding angles are congruent and the corresponding side lengths are in proportion. The symbol for similarity is '~' . Similarity can be determined by using the Angle-Angle (AA) similarity, the Side-Angle-Side (SAS) similarity, or the Side-Side-Side (SSS) similarity. If two triangles are similar, the ratio of the corresponding side lengths is called the scale factor. If this scale factor is k, then the ratio of any pair of corresponding sides is k.
In ΔBCD and ΔEFD,
side BC ≈ side EF ....(given E is on CD)
∠ BCD ≅ ∠EFD .....(given)
side CD ≈ side FD ......( given F is on BD)
∴ΔBCD ≈ ΔEFD ....(By Side Angle Side criteria)
[tex]\frac{BC}{EF} = \frac{CD}{FD}[/tex]
∴ [tex]\frac{77}{35} = \frac{CD}{30}[/tex]
∴ CD = 77 × 30/ 35
∴ CD = 66
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