Given: ​ ​△ACE,BD¯¯¯¯¯∥AE¯¯¯¯¯​ ​ Prove: BACB=DECD A triangle with vertices labeled as A, C, and E, with base A E. Sides C A and C E contain midpoints B and D, respectively. A line segment parallel to base A E is drawn from point B to D. Angle C A E is labeled as 4 and angle C E A is labeled as 3. Angle C B D is labeled as 1 and angle C D B is labeled as 2. Drag an expression or phrase to each box to complete the proof. Statement Reason ​△ACE,BD¯¯¯¯¯∥AE¯¯¯¯¯​ Given Response area Corresponding Angles Postulate △ACE∼△BCD Response area CACB=CECD Definition of similar triangles ​CA=CB+BACE=CD+DE​ Segment Addition Postulate ​CB+BACB=CD+DECD​ Substitution Property of Equality ​CBCB+BACB=CDCD+DECD​ ​ Addition of fractions ​1+BACB=1+DECD​ Simplification of fractions Response area Subtraction Property of Equality

Step-by-step explanation:

EC = 165 cm (Given) Tangent of circle also makes 90°.

a) sind = Perpendicular Hypotenuse = CD = EC 165 => 0 = Sin = 0.519 ~ 0.52 =29.7448 ~ 29.75° =<E

By angle sum property of triangle. <D+<E+ <C = 180°

90° + 29.75 + LC = 180°

<C = 180-90-29.75 = 60.25° <C= 60.25°

<DCE = <C = 60.25 x π/180 = 1.052 radians.

(b) Area of triangle DCE = 1/2 x b x h = 1/2 x ED X 4

ED² + CD² = EC² ED² + 4² = (√65)² => EC² = 65-16 = 49 ED=7

Area = 1/2 x 7 x 4 = 14 cm²

Area of sector a π x 4²x 60.25/360 = 8.4125 cm2

Area of shaded region= Area ADCE Area of sector -

= 14-8.4125 = 5.5875 cm²

(a) <DCE = 1.052 radians b) Area shaded of region = 5.5875cm²

The sum of squares of two sides is equal to the square of the third side.

Finding the Third Side of a Triangle with Two Sides

Let's assume that the triangle is right-angled, as the third side of a right-angled triangle can only be found when the other two sides are known.

A right-angle triangle is what?

This particular sort of triangle adheres to the Pythagoras theorem and may be calculated using the trigonometry tool.

We are aware that the right-angled triangle follows Pythagoras' Theorem.

According to the Pythagorean Theorem, the third side's square equals the sum of the first two sides' squares.

More about the right-angle triangle link is given below.

brainly.com/question/3770177

#SPJ4

The complete question should be:

What is the length of 3rd side of a triangle?

A guy wire is attached to an upright pole 6 meters above the ground. If the wire is anchored to the ground 5 meters from the base of the pole 7.81 m long is the wire. This can be solved by using the concept of Pythagoras theorem.

The widely accepted geometric principle known as the Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs (the side opposite the right angle).

The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem. The perpendicular, base, and hypotenuse of this triangle are its three designated sides.

Let, assume ΔABC is a right-angled triangle

where, AC = 6m be the pole.

AB = 5m is the length of a guy wire and is attached to stake B

By Pythagoras theorem,

BC² = AB² + AC²

or, BC² = (5)² + (6)²

or, BC² = 36 + 25

or, BC =  √61 m

or, BC = 7.81 m

To know more about Pythagoras theorem refer to:

https://brainly.com/question/343682

#SPJ1

We refer to the enlargement or reduction of one of two figures as a similarity transformation. For example: When one of two figures can be produced from the other and the ratio of their corresponding sides is equal, we say that the two figures are comparable. Similar figures come in a variety of sizes and shapes.

Either a geometric similarity or a matrix transformation that produces a likeness are referred to as "similarity transformations" in this context. Space items are changed into comparable things by similarity transformations. Fractals and iterated function systems are based on essential principles such as similarity transformations and the idea of self-similarity.

know more about geometry here

https://brainly.com/question/13419413#

#SPJ4

The missing term of the arithmetic sequence is 2 1/2

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the arithmetic sequence be represented as A

Now , the equation will be

A = 1 3/8 , 1 3/4 , 2 1/8 , x , 2 7/8

The first term a₁ = 1 3/8

The second term a₂ = 1 3/4

The common difference d of the arithmetic sequence d = second term - first term

Common difference d = 1 3/8 - 1 3/4 = 3/8

Now , the fourth term of the arithmetic sequence is given by

Tn = a + (n - 1) d

Substitute the values in the equation , we get

a₄ = 1 3/8 + ( 4 - 1 ) ( 3/8 )

a₄ = 11/8 + 9/8

a₄ = 20/8

a₄ = 2 4/8

a₄ = 2 1/2

Therefore , the fourth term is 2 1/2

Hence , it is an arithmetic sequence and the fourth term is 2 1/2

To learn more about arithmetic sequence click :

https://brainly.com/question/1522572

#SPJ1

Answer: Hello your question is vague hence I will give a more general answer

answer : Tate spending $100 to purchase virus protection will help protect his computer from Viruses that can cause Damages worth more than $100. therefore he should purchase the virus protection.

Step-by-step explanation:

Virus protection software ( i.e. Anti-virus software) is a set of computer programs written into the computer or any other electronic Gadget like a Phone with the purpose of protecting, detecting and removing  malicious software ( computer viruses ) from the computer

Answer:

Step-by-step explanation: Two quarters, 50 pennies: N = 52 (N+1 = 53) One quarter, 75 pennies: N = 76 (N+1 = 77) 100 pennies, N = 100 (N+1 = 101) 6 nickels, 70 pennies: N = 76 (N+1 = 77)

Answer:

2 quarters, 2 dime's, 1 Nickel, 2 penny's

Step-by-step explanation:

Well u well need to quarters because 2 quarters are $25 cent then u well need 2 dimes because when your counting dime's that 10 20 30 40 50 so to dime's and 1 Nickel that makes $75 cents so u need 2 penny's and that makes 77

Answer:

(5,0)

Step-by-step explanation:

-6x-8y=10

(2)   2x-4y=10      (2)

4x-8y=20

add the systems

2x=10

divide 10 by 2

x=5

substitute 5 into x

2(5)-4y=10

10-4y=10

-4y=

y=0

Answer:

354acres

Step-by-step explanation:

Total acre = 59000

Percentage of old oak acre trees is 0.6%

Therefore, the acres of old trees are calculated:

59000 * (0.6÷100) = 354acres

Answer:

x = $25,400 [the original price of the Junko car]

Step-by-step explanation:

The price Ben paid, $23,622, is after the 7% discount.  Let x be the original price of the Jinko car.   Ben's prices reflect a 7% discount:

 x*(1-0.07) = $23,622  [The expression (1-0.07) means the original price, 1, is reduced by 7%, -0.07, to give the final price]

(0.93)x = $23,622

x = $25,400

Answer:

this is B 4

Step-by-step explanation:

Answer:

18 is the answer

Step-by-step explanation:

because you times 2 my 9

Answer:

18

Step-by-step explanation:

9 x 2 9 + 9 ? u good people ?

Answer:

x = 6

Step-by-step explanation:

x:(x + 3) = 2:3

[tex] \frac{ \\ x}{x + 3} = \frac{2}{3} [/tex]

cross multiply

3x = 2(x + 3)

3x = 2x + 6

subtract (2x) from both sides

3x – 2x = 2x – 2x + 6

x = +6

x = 6

Answer:

(n - 6)(n -4)

Step-by-step explanation:

Find two numbers that add to - 10 and multiply to +24.
In this case, -6 * -4 satisfies these requirements.

Answer:

31.5 ft

Step-by-step explanation:

Use the Pythagorean Theorem

a² + b² = c²

Plug in the knowns

a² + 23² = 39²

Subtract 23² from both sides

a² = 39² - 23²

a² = 1521 - 529

a² = 992

Take the square root of both sides

a = 31.496031496

Rounded

a = 31.5 ft

The bottom of the ladder from the bottom of the building will be equal to 31.5 ft.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given instructions in the question,

Use the equation of Pythagoras's theorem

a² + b² = c²

Put in the known values in the above equation,

a² + 23² = 39²

a² = 39² - 23²

a² = 1521 - 529

a² = 992

a = √992

a = 31.496 or,

a = 31.5 ft

To know more about the expression:

https://brainly.com/question/14083225

#SPJ2

Given:

The expression is:

[tex]6x^2+3x+21[/tex]

To find:

The factor of the given expression by GCF.

Solution:

We have,

[tex]6x^2+3x+21[/tex]

Here, 3 is the greatest common factor (GCF) of [tex]6x^2,3x,21[/tex].

Taking out GCF, we get

[tex]6x^2+3x+21=3(2x^2+x+7)[/tex]

Therefore, the required factor form of the given expression is [tex]3(2x^2+x+7)[/tex].

Answer:

y >_ 2x-2

the 3rd one

Step-by-step explanation:

Please mark as brainliest if answer is right  

Have a great day, be safe and healthy  

Thank u  

XD

Answer:

the measure of vertex angle is 32°

Answer:

32°

Step-by-step explanation:

An isosceles triangle has 2 congruent base angles, both 74° , then

vertex angle = 180° - (74 + 74)° = 180° - 148° = 32°

Explanation is[tex]^{}[/tex] in a file

bit.[tex]^{}[/tex]ly/3gVQKw3

Answer:

m<FDG = 120 degrees

Step-by-step explanation:

90 + 150 + x = 360

subtract 90 and 150 from both sides

x = 120

The answer is $112.70  The Question is a simple Sales tax rate calculating problem.

Multiplying the purchase price by the sales tax rate will provide the sales tax. Don't forget to round the sales tax rate from percent to decimal. The price of the purchase is increased after the sales tax has been calculated. The entire cost is what the client pays as a result.

Sales tax rate = Sales tax percent / 100.

Sales tax = List price x Sales tax rate.

Given,

Rate of sandwich is = $4. 00

Rate of drink is = 94$

The rate of a meal that Her grandson ordered is =$6. 35.

What was the total price of all three items when 8% sales tax was added?

Total price of all three items without tax = 4 + 94 + 6.35

= $104.35

Total price of all three items with tax = (100% + tax) * Price

= (100% + 8%) * 104.35 = 108% * 104.35

= 1.08 * 104.35 = 112.698

≅ $112.70

The estimation to check if the result is reasonable by putting the answer in the original equation.

E.g. x + 4 = 10; x = 10 - 4

We get that x = 6

Plug in x = 6 in x + 4 = 10.

6 + 4 = 10.

To know more about sales tax problems visit:

brainly.com/question/9437038

#SPJ4

AnswerNo nin

Step-by-step explanation:

dsfsfsdffsfsfsfs is bad

Answer: 39%

Step-by-step explanation:

Given

The ratio of the number of teachers to the number of students is 1:15.

and the ratio of the number of male and female students is 7:5

Suppose the number of teachers is x. So, students become 15x

For the ratio of male to female, assume male is 7y, so female is 5y

The sum of the male and female students comprises the whole student community

[tex]\therefore 15x=7y+5y\\15x=12y\\5x=4y[/tex]

The percentage of female students on the trip is

[tex]\Rightarrow \dfrac{5y}{x+15x}\times 100\\\\\Rightarrow \dfrac{5y}{16x}\times 100\\\\\Rightarrow \dfrac{5\times \frac{5}{4}x}{16x}\times 100\\\\\Rightarrow \dfrac{625}{16}=39\%[/tex]

In function notation, the function is represented as f(x) = (3/4)x + 7.

In function notation, the function is represented by the letter "f" followed by the input value inside parentheses. The input value is typically represented by the letter "x". In this case, the function takes "x" as its input and performs the operation of multiplying it by 3/4 and then adding 7 to get the output. We can represent this function using the equation f(x) = (3/4)x + 7.

It's worth noting that the function notation is a way to express a mathematical relationship between two variables, the input variable (x) and the output variable (f(x)), in which every input value of x corresponds to exactly one output value. This equation represents the same function regardless of the input value, and it can be used to find the output for any input value by simply substituting it in the equation.

Learn more about function notation here:

https://brainly.com/question/27915724

#SPJ4

Total distance travelled by the family in the truck is 497.98 miles

An equation is an expression that shows the relationship between two or more numbers.

The rental of the truck has a base cost of $49.95, and $1.19 per mile. The average gas mileage is 18 miles per gallon.

Let us assume the total distance travelled was x miles, hence:

Total gas consumed = x miles / 18 miles per gallon = x/18 gallons

The cost is $3.89 per gallon, hence:

Total cost of gas = $3.89 per gallon * x/18 gallons = 3.89x/18

Total cost of journey = 1.19x + 3.89x/18 + 49.95 = 2531x/1800 + 49.95

If $724.85 was charged, hence:

724.85 = 2531x/1800 + 49.95

x = 497.98

Total distance is 497.98 miles

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1