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Answer:

1) x = 50 m

2) Max area = 22500 m²

3) Max area of each pen = 1500 m²

4) y = 150 m

5) dimensions of pen are 50m and 30m

6) Graph is attached

Step-by-step explanation:

Area of a rectangle is length × width

Let length be y and let width be x

Thus;

A = xy

Fencing material is 600m

Thus,perimeter = 600

Perimeter is; P = 6(length) + 2(width)

Thus;

600 = 6x + 2y

y = (600 - 6x)/2

y = 300 - 3x

Thus,

A = x(300 - 3x)

A = -3x² + 300x

We can see that the coefficient of x² is negative. This means that the parabola will open downward and has a maximum value at the vertex.

The vertex formula is;

x = -b/2a

a = -3

b = 300

Thus;

x = -300/(2 × -3)

x = 50 m

Since y = 300 - 3x, then;

y = 300 - 3(50)

y = 150 m

Maximum area of entire garden = xy = 50 × 150 = 7500 m²

There are 5 pens, thus;

Max area of each pen = max area of entire garden/5 = 7500/5

Max area of each pen = 1500 m²

Dimensions of each pen will be;

x and y/5

>> x = 50 m and y/5 = 150/5 = 30m

The value of x from the similar triangles is x = 9 and the length of CE of the triangle ACE is CE = 35

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔACE

Let the second triangle be represented as ΔBDC

The measure of side AB = 6

The measure of side BC = x - 5

The measure of side AC = x + 1

The measure of side CD = 14

The measure of side DE = 2x + 3

The measure of side CE = 2x + 17

Now , ΔACE and ΔBDC are similar

So , the corresponding sides of similar triangles are in the same ratio

Substituting the values in the equation , we get

AC / CE = BD / CD

( x + 1 ) / ( 2x + 17 ) = ( x - 5 ) / 14

On simplifying the equation , we get

14x + 14 = 2x² - 10x + 17x - 85

Subtracting 14x + 14 on both sides of the equation , we get

2x² - 7x - 99 = 0

On factorizing the equation , we get

x = 9 or x = -11/2

Substituting the value of x in the equation , we get

The length of line segment CE = 2x + 17

The length of line segment CE = 2 ( 9 ) + 17

The length of line segment CE = 35

Hence , the length of CE is 35

To learn more about similar triangles click :

https://brainly.com/question/29378183

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Answer:

option (C) W + 180° is right answer

Answer:

Model 2

Step-by-step explanation:

1.56 + 0.33 = 1.89

Answer:

He is incorrect. He would need 225g of cocoa powder

Step-by-step explanation:

1. Lets calculate how much powder do we need per one cupcake, so 60 divided by 20, since 60g makes 20 cupcakes, 60/20 = we get 3g of cocoa powder per one cupcake.

2. Now we can multiply that by 75, 75*3=225, and 225g is more than 210g

Step-by-step explanation:

A(-5,1) and B(0,4)

[tex]m \: = \: \frac{y2 - y1}{x2 - x1} [/tex]

X1=0 , Y1=4 X2= -5 , Y2=1

[tex]m \: = \: \frac{3 }{5} [/tex]

[tex]y - y1 = m(x - x1)[/tex]

y - 4 = ⅗(x-0) ==> y - 4 = ⅗ X ==> y = ⅗ X + 4

C is the answer

A. Angle E = 113°

B. x = 16°

Number A

92 + 70 + 85 + ? = 360

162 + 85 + ? = 360

247 + ? = 360

? = 360 - 247

? = 113°

Number B

108 + 84 + ( x + 30 ) + ( 2x + 18 ) = 360

(180 + 84 + 30 + 18) + (x + 2x) = 360

312 + 3x = 360

3x = 360 - 312

3x = 48

x = 48/3

x = 16°

#LearnWithBrainly

9514 1404 393

Answer:

  150°

Step-by-step explanation:

The rule here is that the external angle is half the difference of the arcs subtended. That relation is used to form an equation, which can then be solved for whatever measure is of interest.

  (RB -EC)/2 = D

  ((13x +7) -(60))/2 = (5x -10)

  13x -53 = 10x -20 . . . . . . . . . . multiply by 2

  3x = 33 . . . . . . . . . . . . . . add 53-10x to both sides

  x = 11 . . . . . . . . . . . . divide by 3

  RB = 13x +7 = 13·11 +7 = 150

The measure of arc RB is 150°.

Answer:

618.2203≈618.22

Step-by-step explanation:

618.2203≈618.22

Answer:

Required equations are:

Solving the first, we get:

Solving the second we get:

Answer:

Always the product of any number and zero will be zero.

Step-by-step explanation:

Answer: Always the product of any number and zero will be zero.

HOPE THIS ANSWER HELPS YOU....

Answer:

x = 32.6°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{13}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{7}{13}[/tex] ) ≈ 32.6° ( to the nearest tenth )

Step-by-step explanation:

4x^2-9

=(2x)^2 -3^2

=(2x+3) (2x-3)

Hope this helps you.

Answer: since there is no table shown you can’t really tell but the closest would be the number that shows up the most amount of time but you would have to take into consideration of the increase of the number

Step-by-step explanation:

Answer:

Step-by-step explanation:

Percent increase:

Answer:

37

Step-by-step explanation:

10x40 = 400

2(39+42)+ 40 x 4 + 41 + X = 400

162 + 160 + 41 = 400 - X

400 - 363 = X

X= 37

Answer:i dont know sr

Step-by-step explanation:

Answer:

The last one

Step-by-step explanation:

Answer:

it's a translation

Step-by-step explanation:

it just moved (3,0). If it were a rotation the y-axis wouldn't be the same. If it were a reflection you would be able to flip the blue triangle onto the red triangle.

Answer:

C

Step-by-step explanation:

Answer:

Multiply all the cm and u will get the answer.

Answer:

D.4 3/4

Step-by-step explanation:

hope it helps you

Answer: I Don't Know

Answer:

3

Step-by-step explanation:

5.5 litres paint needed for 1 stool

1  litres paint needed for  1/ 5.5

20 litres paint needed for  20/5.5

= 3.636

And now comes the twist, you can't paint 3.6 stools. also You can't paint 4 stools. You need to round down to 3

Answer:

There are 42 dogs and 105 cats at the shelter. To find the number of rabbits, subtract these numbers from the total number of animals at the shelter. So there are 21 rabbits at the shelter.

Step-by-step explanation:

Because there are 168 animals at the shelter and [tex]\frac{1}{4}[/tex] of the animals are dogs, you can infer that there are [tex]\frac{168}{4}[/tex] or 42 dogs at the shelter. The question says that [tex]\frac{5}{6}[/tex] of the remaining animals are cats, which you can get two things from this statement: #1, [tex]\frac{5}{6}[/tex] of the remaining animals (not including dogs) are cats in the shelter. #2, [tex]\frac{1}{6}[/tex] of the remaining animals (not including dogs) are rabbits in the shelter, since that is the remaining number of animals left that aren't cats or dogs. Using this, you can get the number of cats is the number of dogs subtracted by the total number of animals at the shelter and multiplied by [tex]\frac{5}{6}[/tex], which would be  [tex]\frac{5}{6}[/tex](168 - 42) = [tex]\frac{5}{6}[/tex]*126 = 5 * 21 = 105 cats at the animal shelter. Since the number of rabbits is [tex]\frac{1}{5}[/tex] the number of cats in the shelter ([tex]\frac{5}{6}[/tex] = [tex]\frac{1}{6}[/tex] * 5), that means there are [tex]\frac{105}{5}[/tex] or 21 rabbits at the animal shelter, and that we'd need to subtract the number of cats and dogs from the total number of animals at the shelter to find the number of rabbits.

Solve the equation replacing x with 2 and the 6:

-2^2 + 2(2) + 2 = 4 + 4 + 2 =10

-6^2 + 2(6) + 2 = 36 + 12 + 2 = 50

Difference between the answers: 50-10 = 40

Difference between 2 and 6 = 6-2 = 4

Average rate of change = 40/4 = 10

The answer is 10

Answer:

a = -4

Step-by-step explanation:

a + c = 6

substitute 10 for 'c'

a + 10 = 6

a = -4

Answer:

a has to be a negative since c is equal to 10 so a is -4 because -4 + 10= 6

Step-by-step explanation:

hope this helps.

Answer:

75

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

3(5^2) = 3(25) = 75

Answer:

60 math problems.

Step-by-step explanation:

30/2.5=12

12*5=60