Given parallelogram ABCDABCD, diagonals ACAC and BDBD intersect at point E. AE=2x, BE=y+10, CE=x+2AE=2x, BE=y+10, CE=x+2 and DE=4y−8DE=4y−8. Find yy.

Answers

Answer 1

Answer:

y = 6

Step-by-step explanation:

Given a parallelogram ABCD with diagonals AC and BD.

Kindly refer to the diagram attached for the given parallelogram.

[tex]AE=2x\\BE=y+10\\CE=x+2\\DE=4y-8[/tex]

To find:

The value of y = ?

Solution:

First of all, let us consider a property of parallelogram and its diagonals.

The intersecting point of diagonals of a parallelogram bisect the diagonals in two equal parts.

Let us consider the given parallelogram ABCD which has its diagonals BD and AC intersecting at point E.

As per the property stated above:

AE = CE and

DE = BE

Putting the values of AE, CE, DE and BE as given in the question statement and solving for [tex]x[/tex] and [tex]y[/tex]:

[tex]2x = x+2\\\Rightarrow \bold{x = 2}[/tex]

and

[tex]y+10=4y-8\\\Rightarrow 4y-y = 10+8\\\Rightarrow 3y=18\\\Rightarrow y =\dfrac{18}{3}\\\Rightarrow \bold{y= 6}[/tex]

So, the answer is:

y = 6

Given Parallelogram ABCDABCD, Diagonals ACAC And BDBD Intersect At Point E. AE=2x, BE=y+10, CE=x+2AE=2x,

Related Questions

Simplify this expression.

20x - 8 - 15x - 10

[?]x + [?]

Enter the numbers that go in the box.​

Answers

Answer:

5x-18

Step-by-step explanation:

Answer:

3x+2y=4

Step-by-step explanation:

bro it says wait till 20 sec to send this brruuhhhhh

Olivia is tracking the growth rate of a population of termites, x, living in a mound. When the population is x = 400, it is the 0th hour. Initially, it takes f(x) = 1 hour for the population to grow by 400 termites. When the population grows by another 400 termites, the total time taken is f(x) = 1.585 hours. The time taken keeps decreasing to model the same incremental growth. Does the equation for f(x) or the graph of g(x) correctly model the situation?

Answers

Answer:

Based on the information in the problem statement, the function must pass through points (400 , 0), (800 , 1), and (1,200 , 1.585). Notice that the graph of function g(x) passes through these points.

Next, check the graph of f(x). Plot the function using the given equation to see which points it passes through.

The equation indeed starts at (400 , 0), but it doesn’t pass through the other two required points. So, the graph of g(x) fits the situation, but the equation for f(x)does not.

How do I do this, im not sure what im supposed to do

Answers

Answer:

Step-by-step explanation:

3<x<7

the set will contain all elements greater than 3 and less than 7

Roster form ={4,5,6}

b) Roster form :{-6,-5,-4,-3......}

set builder form is all numbers greater than -6

I hope it is right


how to do splitting method of x square- 2x -8​

Answers

Answer:

x^2+2x+1=0

x^2+(1+1)X+1=0

x^2+X+X+1=0

X(X+1)+1(X+1)=0

(X+1)(X+1)=0

X=-1,X=-1

hope it helps :)

please mark it the brainliest!

Answer:

Hey mate

kindly see attached picture:)

hope it helped you ☺️

Point P is located at (-3,5)
Point P' is the image of P after a translation three units to the left, then a reflection using the x-axis.
Find the coordinates of P'

Answers

Answer:

P' (- 7, - 5 )

Step-by-step explanation:

A translation of 3 units to the left means subtractin 3 from the x- coordinate with no change to the y- coordinate, thus

P(- 3, 5 ) → (- 3 - 4, 5 ) → (- 7, 5 )

Under a reflection in the x- axis

a point (x, y ) → (x, - y ), thus

(- 7, 5 ) → P'(- 7, - 5 )

For g(x)= (x+7)^2 + 6x determine the input of x when the output of g(x) =13

Answers

Answer:

x = -2 or -18.

Step-by-step explanation:

(x+7)^2 + 6x = 13

x^2 + 14x + 49 + 6x - 13 = 0

x^2 + 20x + 36 = 0

(x + 2)(x + 18) = 0

x = -2, -18.

1. Solve for x, 5 (2x + 3) + 3 (x - 4) = 25 And one more question 2. The perimeter of a rectangle is 40m. The length of the rectangle is 4 m less than 5 times its breadth. Find the length of the rectangle.

Answers

Answer:

Step-by-step explanation:

1) 5(2x + 3) + 3(x -4) = 25

Use distributive property

5*2x + 5 *3 + 3*x - 3*4 = 25

10x + 15 + 3x - 12 = 25

Add like terms

10x + 3x +15 - 12 = 25

13x + 3 = 25

Subtract 3 form both sides

13x = 25 - 3

13x = 22

x = 22/13

x = [tex]1\frac{9}{13}[/tex]

2) Breadth = b m

Length = 5b - 4

Perimeter of rectangle = 40 m

2*(length + breadth) = 40    { Plug in the values of breadth & length}

2* (5b - 4 + b) = 40

2 * ( 6b - 4 ) = 40  

2*6b - 2 *4 = 40

12b - 8 = 40  { add 8 to both sides}

12b - 8 + 8 = 40 + 8

   12b = 48  { divide both sides by 12}

  12b/12 = 48/12

b = 4 m

Breadth = 4m

Length = 5*4 - 4 = 20 - 4 = 16 m        

Answer:

16cm

Step-by-step explanation:

5(2x+3) + 3 (x-4)= 25

10x+15+3x-12=25

(combine the like terms)

13x+3=25

13x= 22

x= 1 and 9/13

perimeter= 40m

length=5a-4

breadth=a

5a-4+a+5a-4+a= 40

12a-4-4 = 40

12a-8=40

12a= 48 a= 4cm

the breadth is 4cm, the length is 5×a-4= 20-4 =16cm

your welcome!

What is the approximate value of tan C?

Please help! Urgent!

Answers

Hey there! I'm happy to help!

Tan means tangent. The tangent is the ratio of the opposite side of the angle to the adjacent side of the angle.

If we look across from angle C, we see that the opposite side is 5.

The adjacent side is the one next to the angle, and it can't be the hypotenuse (the diagonal one). Our adjacent side is 13.

So, the tangent of C is 5/13, and we can divide these, giving us about D. 0.38.

Have a wonderful day! :D

Answer:

0.38

Step-by-step explanation:

took a p e x test

Solve for n
3n-2=2n
N=

Answers

Answer:

Hey there!

3n-2=2n

n-2=0

n=2

Let me know if this helps :)

3n - 2 = 2n

n =?

3n - 2n = 2

n = 2 ✔️

PLEASEEEEEE Which system of equations does not have a real solution? y = x 2 + 3 x - 5 and 4 x + 5y = 20 y = x 2 + 3 x - 5 and x + y = -10 y = x 2+ 3 x- 5 and x + y = -9

Answers

Answer:

[tex]\Large \boxed{y = x^2 + 3 x - 5 \ \ \mathrm{and} \ \ x + y = -10}[/tex]

Step-by-step explanation:

y = x² + 3 x - 5 and x + y = -10 are the system of equations that do not have a real solution.

When the two equations are graphed and if they do not intersect, then there are no real solutions for the system of equations.

Answer:

Step-by-step explanation:

Leonel computed the average rate of change in the depth of a pool over a two week interval to be zero. Which statement is true

Answers

Statement a is true I took the test

-2 3/4 divided by 5/-9 = ? in the simplest form

Answers

Answer:

Read Exp:

Step-by-step explanation:

Exact Form:  

- 99/20

Decimal Form:  

- 4.95

Mixed Number Form:

- 4 19/20

Answer:

Step-by-step explanation:

[tex]-2\frac{3}{4}[/tex]  ÷  [tex]\frac{5}{-9}[/tex]  = [tex]\frac{-11}{4}[/tex] ÷ [tex]\frac{5}{-9}[/tex]

                 [tex]=\frac{-11}{4}*\frac{-9}{5}\\\\\\=\frac{99}{20}\\\\\\= 4\frac{19}{20}[/tex]

One morning, the temperature in Oakdale was -4°F. By noon, a strong wind had caused the temperature to drop another 3°F. What was the temperature at noon in Oakdale?​

Answers

Answer:

-7°F

Step-by-step explanation:

if -4 was it's original number and the number has dropped means subtraction and by that means subtracting 3 to -4.

Answer: -7

Step-by-step explanation: if -4 was it's original number and the number has dropped means subtraction and by that means subtracting 3 to -4.

I need help ASAP
integrated math ll

Answers

Answer:

Its most likely A

sorry If I get it wrong

Joseph built a model of a pyramid where the base of the pyramid is a square. If the base has an area of 49 cm2 (squared), what is the side length of the base?

Answers

Answer:

7 cm

Step-by-step explanation:

We are told that the pyramid has a square base of an area of 49 cm².

Therefore, the side length of the base of the pyramid is still the same as the side length of a square having an area of 49 cm².

Area of a square = s², where s is the side length of the square.

The side length of the base can be gotten using the following equation,

[tex] s^2 = 49 [/tex]

Solve for s by looking for the share root of both sides.

[tex] \sqrt{s^2} = \sqrt{49} [/tex]

[tex] s = 7 [/tex]

The side length of the base = 7 cm

A bag contains 7 red marbles and 4 blue marbles.
A marble is taken at random from the bag and replaced.
Another marble is taken from the bag.
Work out the probability that the two marbles
taken from the bag are the same colour.

Answers

Answer:

calculate the probability that the marbles are the same color, then subtract this probability from 1 to find the probability they are different colors. P(2 of the same) = P(2 green) + P(2 yellow) + P(2 red) = 1/26 + 5/26 + 2/26 = 8/26 = 4/13. P(2 different) = 1 - P(2 of the same) = 1 - 4/13 = 9/13.

Step-by-step explanation:

HELP PLEASE. Solve. 6(x+20)=168

Answers

Answer:

x=8

Step-by-step explanation:

6(x+20)=168

Divide each side by 6

6/6(x+20)=168/6

x+20 =28

Subtract 20 from each side

x+20-20 = 28-20

x =8

Answer: x=8

Step-by-step explanation: 168/6=28. x+20=28. 8+20=28.

6(8+20)=168

what is the width?
2w + 2(w+6) = 84

Answers

Answer: w = 18

Step-by-step explanation:

2w + 2(w+6) = 84

Distribute: 2w + 2w + 12 = 84

4w + 12 = 84

4w=72

PLEASE ANYONE HEEELLLLPP.......I NEED HELP I DONT UNDERSTAND!!!

Answers

Answer:

[tex]\large \boxed{\mathrm{Option \ 4}}[/tex]

Step-by-step explanation:

The area has to be found for the floor.

The whole rectangle = length × width = x × (x-4), has an area of x(x-4).

The area x(x-4) has to be subtracted from the area of the stage and closet.

Area of stage = area of triangle : base × height × 1/2

(x-4) × 8 × 1/2

(0.5) × (8) × (x-4)

Area of closet = area of rectangle : length × width

(3) × (7)

The area of the floor = x(x-4) - 0.5(8)(x-4) - 3(7)

Answer:

i don’t understand it either

Step-by-step explanation:

If f(x) = 2x + 7 and g(x)= 3x² -1, what expression represents (f(g(x)) ?
A 6x2 +5
B 6x2 +12
C 3x2 - 2x -8
D 3x2 + 2x + 6

Answers

Answer:

A. 6x^2+5

Step-by-step explanation:

The expression that represents the function (f(g(x))) is 6x² + 5, option A is correct.

Given expressions are f(x) = 2x + 7 and g(x) = 3x² - 1

To find (f(g(x))), we substitute g(x) into f(x):

f(g(x)) = 2(g(x)) + 7

Substituting g(x) = 3x² - 1:

f(g(x)) = 2(3x² - 1) + 7

Distributing the 2:

f(g(x)) = 6x² - 2 + 7

Combining like terms:

f(g(x)) = 6x² + 5

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ2

Q={(-2,4), (0,2), (-1,3), (4,-2)} Domain and range

Answers

Answer:

Read exp:

Step-by-step explanation:

Domain: {(-2,0), (-1,4)}

Range: {(4,2), (3,-2)}

How are the properties of segments and angles used to determine their measures

Answers

Answer:

See below

Step-by-step explanation:

Use of following postulates and properties of line segments and angles will help in measuring them.

The Segment Addition Postulate

It states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC

The Angle Addition Postulate

It states that if B is in the interior of AOC , then m∠AOB+m∠BOC=m∠AOC. That is, the measure of the larger angle is the sum of the measures of the two smaller ones.

NEED HELP ASAP ALGEBRA 1

There are approximately 330,000,000 people that live in the United States. There
are approximately 33,000,000 people that live in California. How many times
bigger is the population of the United States than the population of California?​

Answers

Answer:

330,000,000/33,000,000=10

10 times bigger

Step-by-step explanation:

Complete the conditional statement. If -2a > 6, then _____.

Answers

Answer:

a < -3

Step-by-step explanation:

-2a > 6

Divide each side by -2, remembering to flip the inequality

-2a/-2 < 6/-2

a < -3

Step-by-step explanation:

[tex]-2a > 6 \\ a > \frac{6}{ - 2} \\ a > - 3[/tex]

Hope this helps

Which of the following can not be used to express the number -6?

negative six
six below zero
six less than zero
six above zero

Answers

Answer: six above zero

explanation: six is negative meaning it can’t be above zero

If he pays $16.80 for one year. He receives one magazine each month for 12 months. Find the dollars he pays for each
magazine

Answers

Answer:

About $1.40 per each monthly magazine.

Step-by-step explanation:

16.80 / 12 = 1.4

Your sock drawer has two white socks, four brown socks, and two black socks. You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right foot. Find the probability of this occuring.

Answers

Answer:

The probability of this occurring is 1/7

Step-by-step explanation:

Okay, here is a probability question.

From the question, we can identify the following;

Total number of socks = 2 + 4 + 2 = 8 socks

Since we are not given the order in which the socks was worn, we can assume any order.

Let’s say the right leg socks was worn first.

From the question, the socks on the right leg is a brown one.

So now let’s calculate the probability of selecting a brown socks out of the mix

That would be ;

number of brown socks/ total number of socks = 4/8 = 1/2

Now, for the left foot, we are having white sock here.

Kindly recall that since we already have a sock on the right foot, we have 7 socks left to pick from.

Now we need the probability of picking a white sock from the total 7. That would be ; 2/7

So the probability of both action occurring is simply the product of both probabilities and that is ;

1/2 * 2/7 = 1/7

Jordan's football team gained 12 yards on their first play. On the second play, the team
lost 8 yards. Which expression could be used to describe the total yards gained by
Jordan's team?

Answers

Answer:

4 yards

Step-by-step explanation:

they gained 12 yards and then lost 8

that can be expressed as 12-8=4

Answer:

12+(−8)

Step-by-step explanation:

Solve for 20 points, 5stars and brainliest

Answers

Hey there!

Functions are basically like machines you put a number into and they give you a new one as an output. This f represents this machine. f(x) represents whatever the output is because it is the x after it has gone through the function machine.

We want to figure out what x is when f(x)=12. Well, we can simply replace f(x) with 12 in the first equation and solve for x!

12=-16x+8

We flip the equation so x is on the left side.

-16x+8=12

We subtract 8 from both sides.

-16x=4

We divide both sides by -16.

x=-1/4

Have a wonderful day! :D

Answer:

f(x) = -16x + 8

F(x) = 12

=> f(12) = -16x + 8

=> 12-8 = -16x + 8 - 8

=> 4 = 16x

=> 4/16 = 16x/16

=> 1/4 = x

So, the answer is 1/4.

You can just keep 0 as the whole number to answer this question.

Which expression is equivalent to 3(3x + 8) ? A B С C D 9x = 21​

Answers

Answer: it would be D.

Step-by-step explanation: you'd multiply the 3 by the 3x then multiply the 3 with the 8.

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