Given:



A

E

D





A

C

B

.

∠AED≅∠ACB.


Prove:



A

B

C





A

D

E

∠ABC≅∠ADE.


Given: AEDACB.AEDACB.Prove: ABCADEABCADE.

Answers

Answer 1

The triangles have a common vertex angle, and a given pair of

corresponding and congruent angles, they are therefore similar triangles.

∠ABC ≅ ∠ADE  (CASTC)

Reasons:

The given parameters are;

∠AED ≅ ∠ACB

By observation, we have that ΔAED and ΔACB have ∠A = ∠DAE and ∠A =

∠BAC in common.

Therefore, ∠DAE ≅ ∠BAC, by reflexive property.

Two angles of ΔAED (∠AED and ∠DAE) are congruent to two angles in

ΔACB.

(∠ACB and ∠BAC), which gives that ΔAED and ΔACB are similar by AA

Angle-Angle similarity postulate, and by Corresponding Angles of Similar

Triangles are Congruent CASTC we have;

∠AED ≅ ∠ACB

∠DAE ≅ ∠BAC

∠ABC ≅ ∠ADE

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Related Questions

Leticia spends $18.45 on a shirt. She spends at least $3.00 more than Humberto spends. If h represents the amount Humberto spends, which symbol can be used to complete the inequality below to represent this situation?

18.45 blank 3 + h
>
<
Greater-than-or-equal-to
Less-than-or-equal-to

Answers

Answer:

>

Step-by-step explanation:

28.45 >3+hgydnjsjsjjsjkso

HELP PLS " A circle’s circumference is approximately 76 cm. Estimate the area of the circle"

Answers

Answer: if the circumference is 76 the area is 38

Step-by-step explanation:

A scrapyard had 200 tons of recycled steel. They sold 15 tons per day for several days. If there are 80 tons left at the scrapyard, how many days have passed?

Please explain fully.

Answers

Answer:

8 days

Step-by-step explanation:

200-80= 120

120 ÷ 15 = 8 days

Answer:

SAME AS WHAT HE SAYS

Step-by-step explanation:

guys pls help me!!!!!!!

Answers

Answer:

36°

Step-by-step explanation:

it's the same as the given number.

lines l, m, and n are parallel to each other and the same line is intersecting all three of them. since the 36° angle is in the same placement as the x° angle, they are the same.

have a lovely day <3

Avery and Carmen both have summer jobs. Avery gets paid $360 every 4 weeks. Carmen gets paid $480 every 6 weeks. summer break lasts a total of 12 weeks. who will earn more money during summer break?

Answers

Answer:

Avery

Step-by-step explanation:

12/4=3 so Avery will be paid 3 times

360×3= $1080

12/6=2 Carmen will be paid twice

480×2=$960

Avery earns more

360/4 = $90 a week

480/6 = $80 a week

80 x 12 = 960

90 x 12 = 1080

1080 > 960

So Avery will earn more.

1
Mr. Johnson wants to fill up his car's gas tank. The car has a 25 gallon gas tank and there are 4 gallons of gas already in the tank. Gas costs $3.04 for each gallon. Mr. Johnson has $50 to spend on gas. Will he have enough money. Show your work and justify your answer.

Answers

Based on the cost of filling of the car, we can infer that Mr. Johnson does not have enough to spend on gas.

The car can take 25 gallons of gas and already has 4 liters inside it. The quantity of gas Mr. Johnson has to buy is:

= 25 - 4

= 21 gallons

The price of a gallon is $3.04. The price of 21 gallons would be:

= Price of gas x Number of gallons

= 3.04 x 21

= $63.84

In conclusion, Mr. Johnson does not have enough to spend on gas because he has only $50 yet the gas will cost $63.84.

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Graph the following features:
Y-intercept = -2
Slope = 1

Answers

Answer:

Follow the steps below!

Step-by-step explanation:

If you're provided with a graph then use that, but if not, draw it with a scale of 1 unit per 1 tick and all four quadrants.

Start at -2 on your y-axis (two ticks down from the origin the vertical line) and draw a dot or cross. Then, go to the right one tick and up one tick and draw another dot or cross. If you do this again, you should have made a mark on the x-axis (horizontal line). All you need to do is draw a straight line connecting the points you plotted with arrows on the end. You can use a ruler  or other straight edge if straight lines are a challenge to draw.

How much will it cost for him to buy 3 dozen using the rate $12.00 for 20 cookies?

Answers

3 dozen = 36 cookies

20/12 = 1.666666666666667

1.666666666666667 = 1 cookie

(x36)

36 x 1.666666666666667 = 60

It will cost him $60 for 3 dozen cookies

If PS= RS= 38 and PQ, what is QR?
a)83
b)64
c)38
d)46

Answers

Answer:

first of all tell in the clear manner that anyone can easily understand

Answer:

C is your answer

Two sides of a triangle have lengths 6 and 16. Which inequalities represent the possible

lengths for the third side, x?

Answers

Answer:

22 > x > 10

Step-by-step explanation:

By the triangle inequality, the length of the 3rd side must be less than the sum of the two other sides and greater than the positive difference of the other two sides.  Thus, 6 + 16 > x > 16 - 6

22 > x > 10

Choose the grid reference number for the mine shown. A. 621333 B. 136233

PLEASE HELP ASAP!!!

Answers

Answer:

A.621333

Step-by-step explanation:

◑◑◑◑◑◑◑◑

Answer:

631226

Step-by-step explanation:

An oil tanker can be emptied by the main pump in 5 hours. An auxiliary pump can empty the tanker in 7 hours. If the main pump is started at 7 PM​, when should the auxiliary pump be started so that the tanker is emptied by PM​?
Suppose you have entered 103 ​-mile biathlon that consists of a run and a bicycle race. During your​ run, your average velocity is 5 miles per​ hour, and during your bicycle​ race, your average velocity is26 miles per hour. You finish the race in 8 hours. What is the distance of the​ run? What is the distance of the bicycle​ race?

Answers

Answer:

so the answer will be 1

Step-by-step explanation:

An oil tanker can be emptied by the main pump in 5 hours.

An auxilary pump can empty the tanker in 14 hours.

If the main pump is started at 7pm, when should the auxilary pump be started

so that the tanker is emptied by 11pm?

:

Let t = no. of hrs to run the Aux pump

:

The main pump will run 4 hr (7 - 11 pm)

:

Let the completed job = 1; (an empty Tanker)

:

The shared work equation

4%2F5 + t%2F14 = 1

Multiply equation by 70 to get rid of the equation, results:

14(4) + 5t = 70

56 + 5t = 70

5t = 70 - 56

5t = 14

t = 14%2F5

t = 2.8 hrs to run the aux pump

:

2.8 hr = 2 + .8(60) = 2 hrs 48 min

:

Subtract 2:48 from 11:00 = 8:12 PM start the aux pump

;

;

Check solution

4/5 + 2.8/14 =

.8 + .2 = 1

A group of 15 people dines at your restaurant, and their total bill is $315. They decide to split the bill evenly between each person, and each person presents a coupon for $5 off their meal. How much does each diner pay?? $16 $21 $26 $48 $54

Answers

315 * 15 = $21
$21 - 5 = $16
$16 x 15 people
= 240
They each pay $16

Please mark brainelist

Please help me !!!!!!

Answers

Answer:

2

Step-by-step explanation:

-2+4=2

–3.8p + 4.5p − 6.67 = –9.57 + 0.2p how do u solve p?

Answers

Answer: p = - 5.8

Step-by-step explanation:

0.7p - 0.2p = -9.57 + 6.67

0.5p = -2.9

p =  [tex]\frac{-2.9}{0.5}[/tex]

p = - 5.8

please give me a brainliest answer

Here is a linear equation in two variables: 2x+4y−31=123

Answers

Answer:

y=−11x+77/2

Step-by-step explanation:

The procedure for solving simultaneous linear equations now called Gaussian elimination appears in the ancient Chinese mathematical text Chapter Eight: Rectangular Arrays of The Nine Chapters on the Mathematical Art. Its use is illustrated in eighteen problems, with two to five equations.[4]

Systems of linear equations arose in Europe with the introduction in 1637 by René Descartes of coordinates in geometry. In fact, in this new geometry, now called Cartesian geometry, lines and planes are represented by linear equations, and computing their intersections amounts to solving systems of linear equations.

The first systematic methods for solving linear systems used determinants, first considered by Leibniz in 1693. In 1750, Gabriel Cramer used them for giving explicit solutions of linear systems, now called Cramer's rule. Later, Gauss further described the method of elimination, which was initially listed as an advancement in geodesy.[5]

In 1844 Hermann Grassmann published his "Theory of Extension" which included foundational new topics of what is today called linear algebra. In 1848, James Joseph Sylvester introduced the term matrix, which is Latin for womb.

Linear algebra grew with ideas noted in the complex plane. For instance, two numbers w and z in {\displaystyle \mathbb {C} }\mathbb {C}  have a difference w – z, and the line segments {\displaystyle {\overline {wz}}}{\displaystyle {\overline {wz}}} and {\displaystyle {\overline {0(w-z)}}}{\displaystyle {\overline {0(w-z)}}} are of the same length and direction. The segments are equipollent. The four-dimensional system {\displaystyle \mathbb {H} }\mathbb {H}  of quaternions was started in 1843. The term vector was introduced as v = x i + y j + z k representing a point in space. The quaternion difference p – q also produces a segment equipollent to {\displaystyle {\overline {pq}}.}{\displaystyle {\overline {pq}}.} Other hypercomplex number systems also used the idea of a linear space with a basis.

Arthur Cayley introduced matrix multiplication and the inverse matrix in 1856, making possible the general linear group. The mechanism of group representation became available for describing complex and hypercomplex numbers. Crucially, Cayley used a single letter to denote a matrix, thus treating a matrix as an aggregate object. He also realized the connection between matrices and determinants, and wrote "There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants".[5]

Benjamin Peirce published his Linear Associative Algebra (1872), and his son Charles Sanders Peirce extended the work later.[6]

The telegraph required an explanatory system, and the 1873 publication of A Treatise on Electricity and Magnetism instituted a field theory of forces and required differential geometry for expression. Linear algebra is flat differential geometry and serves in tangent spaces to manifolds. Electromagnetic symmetries of spacetime are expressed by the Lorentz transformations, and much of the history of linear algebra is the history of Lorentz transformations.

The first modern and more precise definition of a vector space was introduced by Peano in 1888;[5] by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged. Linear algebra took its modern form in the first half of the twentieth century, when many ideas and methods of previous centuries were generalized as abstract algebra. The development of computers led to increased research in efficient algorithms for Gaussian elimination and matrix decompositions, and linear algebra became an essential tool for modelling and simulations.[5]

Vector spaces

Main article: Vector space

Until the 19th century, linear algebra was introduced through systems of linear equations and matrices. In modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general (not limited to the finite-dimensional case), and conceptually simpler, although more abstract.

A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations satisfying the following axioms. Elements of V are called vectors, and elements of F are called scalars. The first operation, vector addition, takes any two vectors v and w and outputs a third vector v + w. The second operation, scalar multiplication, takes any scalar a and any vector v and outputs a new vector av. The axioms that addition and scalar multiplication must satisfy are the following. (In the list below, u, v and w are arbitrary elements of V, and a and b are arbitrary scalars in the field F.)[7]

Heba ate 1/12 of a box of cereal. Now the box is 3/4 full
What fraction of a full box was there before Heba ate?

Answers

Answer:

5/6

Step-by-step explanation:

1/12 + 3/4 = 9/12

9/12 + 1/12 = 10/12

simplify 10/12

= 5/6

Heres the answer
Hope it helps

Directions: Find the specified term of the geometric sequences given the first term and the common ratio.​

Answers

Step-by-step explanation:

As you know

[tex] a_{n} = a_{1} \times {r}^{n - 1} [/tex]

1.

[tex]3 \times {3}^{4} = {3}^{5} \\ 3 \times {3}^{6} = {3}^{7} \\ 3 \times {3}^{8} = {3}^{9}[/tex]

2.

[tex]2 \times {2}^{4} = {2}^{5} \\ 2 \times {2}^{6} = {2}^{7} \\ 2 \times {2}^{8} = {2}^{9}[/tex]

3.

[tex] - \frac{1}{2} \times {( - 6)}^{4} = { \frac{ - 1}{2} } \times {6}^{4} \\ - \frac{1}{2} \times {( - 6)}^{6} = { \frac{ - 1}{2} } \times {6}^{6} \\ - \frac{ 1}{2} \times {( - 6)}^{8} = { \frac{ - 1}{2} } \times {6}^{8} [/tex]

IF YOU DONT KNOW THE QUESTION, PLEASE DONT ANSWER IT FOR THE PONIS. I REALLY NEED IT

Answers

Answer:

- 3x^2 + 2x - 13

Step-by-step explanation:

f (x) + g (x) = ( - 4x^2+5x-9) + (x^2 - 3x - 4)

= ( - 4x^2 + x^2) + (5x-3x) + (-9-4)

= - 3x^2 + 2x - 13

What is the Prime factorization of 321411?

Answers

Answer:

The determined equation for number 321411 factorisation is 3 * 107137.

Which of the following numbers can be exposed as repeated decimals? 5/7 4/5 7/9 5/8

A. 7/9 and 5/8
B. 5/7 and 4/5
C. 5/7 and 7/9
D.4/5 and 5/8

Answers

Answer:

C.

Step-by-step explanation:

5/7=.714285714 and so on

7/9=.777777778 and so on

8 kg of potatoes and 5 kg of carrots cost $28 whereas 2 kg of potatoes and 3 kg of carrots cost $11.20. Find the cost of 1 kg of each item.
also give the explanation.​

Answers

Answer:

Step-by-step explanation:

Cost of 1 kg of Potatoes = $ 2

Cost of 1 kg of Carrots = $ 2.40

Let the cost of 1 kg of Potatoes = x

Let the cost of 1 kg of Carrots = y

ATQ , 8x + 5y = 28 - 1)

2x + 3y = 11.20 - 2)

Multiplying 2) by 4

8x + 12y = 44.80 - 3)

Applying Elimination method in 1) and 3)

8x + 5y = 28.00

8x + 12y = 44.80

0 + -7y = - 16.80

y = 16.8/7

y = 2.4

Putting the value of "y" in 1)

8x + 5(2.4) = 28

8x + 12 = 28

8x = 16

x = 16/8

x = 2

What is the relationship between the radius of a circle and its diameter?

Question 2 options:

Answers

Answer:

B

Step-by-step explanation:

Diameter is across a circle or a circular object. The Radius is half of the diameter. For example if the diamter was 6, the radius would be 3. You can always find radius by dividing the diameter by 2.

Select the shapes that are similar to shape A

Answers

Answer:

purple in the top left

Step-by-step explanation:

um I don't know, it looks right, lol I'm sorry I hope this helps you let me know if its right

i think it is the pink one that is similar to A

3x - 5y = 4, -2x + 6y = 18 (system of equations)

Answers

Answer:

(x, y) = (57/4, 31/4)

Step-by-step explanation:

-2x + 6y = 18

-2x = 18 - 6y

x = -9 + 3y

3(-9 + 3y) - 5y = 4

-27 + 9y - 5y = 4

4y = 31

y = 31/4

x = -9 + 3(31/4) = 57/4

Answer:

Step-by-step explanation:

-5y=4-3x

y=(4/-5)-(3/-5x)

2x+6y=18

6y=18-2x

y=18/6-(2/6x)

y=y

(4/-5)-(3/-5x)=18/6-(2/6x)

0.93x=3.8

x=3.8/0.93

x=4.09

sub 4.09 for the 3x-5y=4

which will give you y=1.65

sub 4.09 for -2x+6y=18

which will give you y=4.36

help please because I feel like my brain is gonna rot from this (please look at the image)

Answers

Answer:

124.3

Step-by-step explanation:

42.15+20.00=1/2x

62.15=1/2x

62.15*2

124.3 is the total of her paycheck.

42.1<20.00+x

Can someone please help me with number 35?

Answers

Answer:

4

Step-by-step explanation:

Find f(0), f(3), and f(5) for the following function: f(x) = 3x + 1
f(0) =
f(3) =
f(5) =

Answers

Answer:

1, 10, 16

Step-by-step explanation:

Substitute the given values of x into f(x)

f(0) = 3(0) + 1 = 0 + 1 = 1

f(3) = 3(3) + 1 = 9 + 1 = 10

f(5) = 3(5) + 1 = 15 + 1 = 16

James has a piece of construction paper with a length of 9/10 feet and a width of 2/3 feet.

What is the area of James's piece of construction paper?

Answers

Area = length x width

When you multiply fractions, multiply top number by top number and bottom number by bottom number:

9/10 x 2/3 = (9 x 2) / (10 x 3) = 18/30 this can be reduced by dividing both numbers by 6:

18/30 reduces to 3/5

Answer: 3/5 square feet

Can someone tell me the answer to this?

Answer choice B is incorrect

Answers

Answer:

B) or C)

Step-by-step explanation:

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