Part 1: Use transformations to prove congruency.
1. Given: ;
Prove: CBF EDF using isometric (rigid) transformations.
F
D
E
B
C
Outline the necessary transformations to prove CBF EDF using a paragraph proof. Be sure to name specific sides or angles used in the transformation and any congruency statements.
Part 2: Use congruency theorems to prove congruency.
1. The congruency of rMNO and rXYZ can be proven using a reflection across the line bisecting . However, this congruency can also be proven using geometric postulates, theorems, and definitions. Prove that the triangles are congruent using a two-column proof and triangle congruency theorems.
Given: M X
N Y
Prove: rMNO rXYZ
Answers
The two triangles CBF and EDF are congruent.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
The two triangles are congruent by the conditions are given;
CB // ED and both BD and CE are transversals
The point E will be the image of point C by rotation 180° around point F
The point D will be the image of point B by rotation 180° around point F
Rotation is a kind of transformation;
ΔCBF ≅ ΔEDF
Part 2;
Definition of congruent line segments;
Symmetric property of congruence;
Addition and substitution properties of equality;
Segment addition theorem;
Definition of congruent line segments;
AAS congruence postulate;
The addition property says if A=B, then A+C=B+C. The substitution property says if C=D, then A+C=B+D (D can be substituted for C). IMO, both properties are needed together to get from A=B and C=D to A+B=C+D;
Hence, the triangles CBF and EDF are congruent.
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Related Questions
The product of two consecutive natural numbers is 1. 5 times the square of the lesser number.
Answers
The two consecutive natural numbers are 2 and 3.
Let x be the smaller number. Hence, the larger number will be x + 1.
The product of these two consecutive natural numbers is x(x + 1). It is stated in the problem that this product is 1.5 times as big as the square of the smaller number, x². So we can set up the equation:
x(x + 1) = 1.5x²
Expanding and simplifying the equation:
x² + x = 1.5x²
0.5x² - x = 0
x(0.5x - 1) = 0
x = 0 or 0.5x - 1 = 0
x = 0 or 0.5x = 1
x = 0 or x = 2
The smaller number cannot be 0, so the solution for the smaller number is x = 2 and the larger number is x + 1 = 2 + 1 = 3.
Therefore, the two consecutive natural numbers are 2 and 3.
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Select the GCF of these numbers. 2^5 · 5· 11 and 2^3· 5^2 · 7
2 2 · 3
3 2
13 · 19 3 ·23 2
2 3 ·5
2· 11 2
Answers
The GCF of these numbers. 2^5 · 5· 11 and 2^3· 5^2 · 7 is D. 2³.5
What is GCF?The greatest common factor is the largest number that can divide evenly into two or more other numbers (GCF). The highest common factor is another name for this (HCF). A factor is a smaller number that could divide into a larger one evenly.
Before determining the greatest common factor, enumerate the prime factors of each integer. The greatest common factor of two or more integers is the biggest integer that is a factor of each.
In this case, 2 appears three times as the most frequent factor and 5 only once as the most frequent factor among the numbers.
Hence 2³.5 is the GCF of the given number.
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How do you graph vertical and horizontal shifts?
Answers
To graph a vertical shift, take the original graph and move it up or down on the y-axis. To graph a horizontal shift, take the original graph and move it left or right on the x-axis.
Vertical shifts can be graphically represented by taking the original graph and moving it up or down on the y-axis. This is accomplished by adding a constant value to every y-value in the equation. For example, if the equation is y = x + 2, shifting the graph up two units on the y-axis would change the equation to y = x + 4. Horizontal shifts can be graphically represented by taking the original graph and moving it left or right on the x-axis. This is accomplished by adding a constant value to every x-value in the equation. For example, if the equation is y = x + 2, shifting the graph two units to the right on the x-axis would change the equation to y = x - 2. When graphing vertical or horizontal shifts, it is important to remember that the overall shape of the graph remains the same, only the position of the graph changes.
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Which ongle in this triangle is a right ongle?
O angle B
O angle C
O angle D
Answers
Answer:
Angle D
Step-by-step explanation:
Angle D because it has that little square on it. That little square means that the angle is 90 or it is a right angle.
Cheers!
How to solve 5x 9 5 3x?
Answers
The value of x in the equation 5x+9=5+3x is 2.
When we have an equation, we can divide it into two parts, the left and right sides. In short, we call the equation LHS and RHS.
If we get both LHS and RHS as equal values, we can say that the equation is true; otherwise, the equation does not hold for at least some real-number values.
Given that,
5x+9=5+3x
Bring x terms to LHS and constants to RHS
5x-3x=5-9
we get,
2x=-4
taking 2 to RHS
in LHS we multiply with two so it becomes divided on RHS
so
x=4/-2
x=-2
Thus, the value of x in the equation 5x+9=5+3x is 2.
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What is the solution of 2x y is equal to 7?
Answers
There is no single solution to this equation, as it is an indeterminate equation. To solve it, you must introduce a third variable and use algebraic manipulation to solve for the three variables.
An indeterminate equation is one where there is no single solution. This equation, 2x y = 7, is an example of an indeterminate equation. To solve this equation, a third variable must be introduced, and then the equation must be manipulated using algebraic laws. The manipulation of the equation will result in an equation with three variables, which can then be solved using standard methods of solving equations. This process can be used to solve any indeterminate equation, regardless of the complexity of the equation. It is important to remember that an indeterminate equation has no single solution, and the only way to solve it is to introduce a third variable and use algebraic manipulation to solve for the three variables.
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find the length (in cm) of an arc of a circle with radius 6 cm if the arc subtends a central angle of 60
Answers
The length (in cm) of an arc of a circle 5π
60°=π/3 radians
A unit circle's arc length is expressed in radians.
We may get the length of an arc using the following formula given an angle and a circle's diameter: ArcLength = (angle / 360) * (2 * pi * radius) Pi equals 22/7, diameter equals 2 * radius, and angle is in degrees.
If a unit circle's arc length is π/3,
(that is a circle with a radius of 1)
For a circle with a radius of 15, the arc length for the same angle would be
X15xπ/3
=5π
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Jordan can buy 2 tires for $108. How much does it cost to buy 4 tires?
Answers
Answer:
216
Step-by-step explanation:
108/2 = 54 per tire
54 x 4 = 216
Answer:
Step-by-step explanation:
108 times 2 is 216
so it costs 216
also if u needed the individual cost of each tire divide 108 by 2
A store's profit P varies directly with the number of items n that they purchase from a warehouse. Greg's gadgets buys 75 Wacky Widgets from Gadget Supply Warehouse. The store's profit for this purchase is -190. 50. How do I write a direct variation equation on that
Answers
The required equation will be k=-2.54n
The profit P of a retailer is said to be directly correlated with the quantity n of goods it purchases from a warehouse.
Since y is directly proportional to x and k is a constant of variation, we know that two proportional numbers have the form y=kx.
The result of inserting our provided variables is:
P=kn
We are also informed that Gadget Supply Warehouse sells 75 Wacky Widgets to Greg's Gadgets. The sale resulted in a loss of 190.50 for the retailer.
Let's determine the proportionality constant.
-190.50=k *75
k=-2.54n
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Given: AABC=AAED
Prove:
Answers
If two angle in one triangle are congruent to two angles of a second triangle, and also if the included sides are congruent, then the triangles are congruent.
Is there sufficient evidence to infer that the two triangles are congruent?If two angles in one triangle are congruent with two angles in another triangle, and the included sides are likewise congruent, then the triangles are congruent. Making use of labels: Triangle ABC is congruent to triangle DEF if angle A = angle D, angle B = angle E, and AB = DE in triangles ABC and DEF.
If the triangle ABC is an isosceles triangle, then AB=AC; similarly, if the triangle ACB is an isosceles triangle, then AC=AB. As a result, each triangles will have one equal angle and two included equal sides, making them congruent.
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When a quadratic function is in factored form what information about the graph can be easily determined?
Answers
Equations may be solved and x-intercepts can be found very quickly when a quadratic expression is in factored form and equal to 0. Vertices, as well as the expression's maximum and minimum values, can also be identified.
A polynomial equation of degree 2 is a quadratic equation. A quadratic equation has the conventional form a[tex]x^2[/tex] + bx + c=0, where a, b, and c are all real values and a[tex]\neq[/tex]0.
The quadratic function y=a[tex]x^2[/tex] + bx + c, whose graph will be a parabola, is obtained if we substitute 0 with y.
The solutions to the equation a[tex]x^2[/tex]+bx+c=0 will be at the spots where the graph intersects the x-axis. In other words, if the polynomial a[tex]x^2[/tex]+bx+c can be factored to (x-p)(x-q), then (x-p)(x-q)=0 or (x-p)(x-q)=0 according to the zero product property. As a result, p and q are the x-intercepts of the quadratic equation and the solutions to the equation a[tex]x^2[/tex] + bx + c=0.
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need help asap on this zearn
Answers
The value of k for the given expression is, 2.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ 8 (k + 10) = 48k
Now, We can solve the expression for k as;
⇒ 8 (k + 10) = 48k
Divide by 8,
⇒ k + 10 = 48k/8
⇒ k + 10 = 6k
Subtract k,
⇒ 10 = 6k - k
⇒ 10 = 5k
⇒ 5k = 10
Divide by 5;
⇒ k = 10/5
⇒ k = 2
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• Texas: 2. 69 x 10 5 square miles • Rhode Island: 1. 21 x 10 3 square miles Determine the difference, in square miles, between the area of Texas and the area of Rhode Island. Write your answer in scientific notation. (2019)
Answers
The difference between the area of Texas and Rhode Island in square miles and scientific notation = (2.68 × 10⁵) square miles.
How to calculate area and perimeter of square?Square Area = Side x Side. The square's area is therefore equal to Side2 square units. and a square's perimeter equals four side units.
As a result, the square's perimeter will be as follows: perimeter = 4 x side = 4 area units.
A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It may alternatively be explained as a rectangle with two neighbouring sides that are of equal length.
A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.
Area of Texas = (2.69 × 10⁵) square miles = 269000 square miles
Area of Rhode Island = (1.21 × 10³) square miles = 1210 square miles
Difference between the Area of the Texas and Rhode Island = 269000 - 1210 = 267,790 square miles = (2.68 × 10⁵) square miles.
The difference between the area of Texas and Rhode Island in square miles and scientific notation = (2.68 × 10⁵) square miles.
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a crew of mechanics at the highway department garage repair vehicles that break down at an average of 3 vehicles every 12 minutes (approximately poisson in nature). the mechanic crew can service an average of 3 vehicles every 10 minutes with a repair time distribution that approximates an exponential distribution. the crew cost is approximately $150 per hour. the cost associated with lost productivity from the breakdown is estimated at $50 per hour. which is cheaper, the existing system with one service crew or a revised system with two service crews? note that the average waiting time for adding the second crew is 0.01.
Answers
Total cost in single service crew is greater than double service crew. So, double service crew is cheaper.
We have, a crew of mechanics at the highway department garage repair vehicles. In case of poisson distribution,
λ = 3 vehicles every 12 minutes
= 3×60/12 = 3× 5
λ = 15 vehicles per hour
When time distribution is approximates an exponential distribution,
The mechanic crew can service an average, μ = 3 vehicles every 10 minutes
μ = 3×60/10 = 18 vehicles per hour
Cost for one service crew =$150 per hour
Cost associated with lost productivity from the breakdown or wait cost
=$50 per hour
For single crew, number of vehicles out of cost, Lₛ = 15/(18 - 15) = 15/3 = 5
Single service crew cost = $150 per hour
wait cost = $5×50 = $250 per hour
Total cost = $400 per hour
For double service crew, Number of vehicles out of service cost = 15/(36 - 15)
= 15/21 = 0.7143
Double service crew cost = 2× $150
= $300
Wait cost = $0.7143×50 = $35.715
Total cost = $335.715 per hour
As we see, the double service crew is cheaper.
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what are the solutions of X2 + 6x - 16 = 0
Answers
Answer:
x = 2
Step-by-step explanation:
combine like terms :2x + 6x -16 = 0
Rearrange the terms : 8x - 16 =0
divided both sides: 8x =16
simplify: x 16/18
Hope this helps
I need to know this pleaseeeeeeeeeeee
ax+ 5y = bx-3y
Answers
Answer:a=bx−8y/x
Step-by-step explanation:
Answer:
x=-8y/a-b
Step-by-step explanation:
If tangent of x degrees equals four-thirds, what is the value of b? triangle lmn in which angle m measures 90 degrees, angle l measures x degrees, lm measures 10.5 units, and nm measures 2b units b = 4 b = 5 b = 6 b = 7
Answers
The value of b is equal to seven
if the tangent of x degrees is equal to four-thirds, the triangle's area is 10.5 units, and the length of the NM is 2b units. In this case, b = 7, hence the last choice is right.
Triangles are described as having right angles.Has three sides in the normal sense, where the total of any two sides is always greater than the third side. One kind of triangle is the right angled triangle.
A right angle triangle is one that has angle
between its two sides .
We also have a number of sides.
NM = 2b, LM = 10.5 length of side
x's tangent, tan x = 4/3
We must figure out what b is worth.
triangular base = LM = 10.5
As is common knowledge, the tangent of any angle equals the perpendicular to base ratio.
=>4/3 = 2b / 10.5
Tan x = 4/3 = LM/NM, thus.
=>4x 10.5 = 2b x 3
> b= 42 0/6
=> b=7
Therefore, the needed value is 7.
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How do you solve 4 more than 5?
Answers
The answer of 4 more than 5 is 9.
The answer of 4 more than 5 is 9 which can be derived using simple mathematical calculations.
To find 4 more than 5, you can add 4 to the original number 5.
5 + 4 = 9
It's a simple arithmetic operation where you add a specific number, in this case, 4, to the original number.
An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.
Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.
Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.
Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.
Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.
Therefore, The answer of 4 more than 5 is 9.
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What is the inverse of 9?
Answers
Answer: -9
Step-by-step explanation:
A $ suit is marked down by %. Find the sale price.
Question content area bottom
Part 1
The sale price is $
168. (Round to the nearest dollar as needed.)
Answers
The sale price of the suit is $168.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
The cost of the suit is $240 and the discount is 30%.
The sale price of the suit is:
240 - 30% of 240
= 240 - 30 × 240/100
= 240 - 72
= 168.
Therefore, $168 is the price of the suit.
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The complete question;
A $240 suit is marked down by 30%. Find the sale price.
You and your three best friends went out for pizza. Together you ordered a large pizza for $23.75, some cheese sticks for $6.88, and a pitcher of soda for $4.85. You split the total cost evenly. What was your share of the bill?
Answers
Answer:
$8.87
Step by Step explanation:
You+ 3 friends = 4 people.
= 23.75 + 6.88 + 4.85( All the food)
= 35.48(Total Cost of dinner)
= 35.48/ 4(amount of people)
= $8.87(per person)
What is the process of substituting the value of a variable to the given expression?
Answers
To evaluate an expression, we first replace the variable with the given number, then we use the order of operations to simplify the expression.
What is a mathematical expression?
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. This mathematical operation may be addition, subtraction, multiplication, or division.
Term is defined as a constant, a single variable, or a combination of a variable and a constant combined with multiplication or division. Algebra Expression Example: 3x + 9, 5x + 10
What are an equation and an expression?
In mathematics, an expression is a word or phrase that combines variables, operators, and numbers to represent the value of something. Two expressions are assigned equal to one another in a mathematical statement known as an equation.
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Edith and Rashida are shooting free throws. Complete the ratio tables. who has a better ratio of basket to shots
Answers
Edith has a better ratio of the basket to shots.
What is ratio?
The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, Edith and Rashida are shooting free throws.
For Edith
B 1 2 3 4 5
S 3 6 9 12 15
ratio = 3/1
the ratio of Edith's shots = 3
For Rashida
B 2 4 6 8 10
S 5 10 15 20 25
Ratio = 5/2
The ratio of Rashida's shots = 2.5
Therefore, Edith has the better ratio of the basket to shots
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Complete question:
how many 7 letter words can be made from mathisfun if each word must have 4 consonants and 3 vowels?
Answers
There are 5040 possible combination of 7 letter words using 3 vowels and 4 consonants.
We know that the word must have 4 consonants and 3 vowels. We have the following vowels in "mathisfun" : i, a, and u.
We have 7 letters that can be used as consonants: m,t,h,s,f,n.
First we need to find the number of ways to choose the 4 consonants out of 7 possible letters, which is 7C4 = 35.
Then we need to find the number of ways to arrange the 4 consonants and 3 vowels, which is 4!*3! = 144
Finally, we multiply those two values together: 35 * 144 = 5040.
So there are 5040 7 letter words that can be made from "mathisfun" if each word must have 4 consonants and 3 vowels.
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2(x-y)=4 3x+y=10 use elimination
Answers
Answer: x=3 y=1
Step by step solution
A television and DVD player cost a total of $1140. The cost of the television is two times the cost of the DVD player. Find the cost of each item.
Answers
Answer:
television is 760 and the dvd player is 380
Step-by-step explanation:
1140/3 then multiply the 380 x two times the cost sorry if I didn’t explain it right
a degree can be further divided into arcminutes and arcseconds. one degree contains 60 arcminutes, and one arcminute contains 60 arcseconds. given this information, how many degrees is 15 arcseconds?
Answers
There are 0.00416667 degrees in 15 arcsecond.
Define arcseconds?
A unit of angular measure equal to 1/60 of an arc minute, or 1/3600 of a degree. The arc second is denoted. (not to be confused with the symbol for inches).This is a tiled collection of the 3D Elevation Program (3DEP) and is 1 arc-second (approximately 30 m) resolution. The elevations in this Digital Elevation Model (DEM) represent the topographic bare-earth surface.There is a simple relationship between a star's distance and its parallax angle: d = 1/p. The distance d is measured in parsecs and the parallax angle p is measured in arcseconds. This simple relationship is why many astronomers prefer to measure distances in parsecs.The angular resolution of the human eye typically ranges between 40 arcseconds and 1 arcminute. To perceive two separate points, at least three photoreceptors arranged in a row are require.To learn more about arcsecond refers to:
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PLEASE HELP I WILL GIVE BRAIN LIST
Mrs. hool is planting a garden In her backyard this summer. it must be fenced in to keep out animals. she only has 60 feet of fencing. she would like the garden to be at least 10 feet long and at least 5 feet wide. what is the graph showing the possible dimensions of her garden could be?. Name two possible dimensions for her garden
Answers
The garden will be in the shape of rectangle with length=18feet, breadth=12feet or length=20 feet, breadth=10 feet.
What is a rectangle?
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length which makes it different from a square.
For example, if one side of a rectangle is 20 cm, then the side opposite to it is also 20 cm.
Perimeter of a Rectangle:-
The perimeter of a rectangle is defined as the total distance covered by the outer boundary of the rectangle. It is measured in unit length. The formula of perimeter is given by:
Perimeter, P = 2 (Length + Width)
Now,
Total fencing available=60feet
that means perimeter should be 60 feet of the garden.
Hence,
two dimensions of the rectangle could be length=18feet, breadth=12feet or length=20 feet, breadth=10 feet.
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2.86 + (-14.6,) is i need help
Answers
Answer: -11.74
Step-by-step explanation: The reason for this is if you minus 14.6 from 2.86 you get -11.74.
Find the length of the third side. If necessarry, round to the nearest tenth
Answers
Answer:
Step-by-step explanation: 6*6 + 7*7=C
36+49=85
The square root of 85 is 9.21
9.21 rounded to the nearest tenth is 9.2