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3 years ago

What is a simplified expression for the perimeter of the polygon?

Mathematics

2 answers:

serious [3.7K]3 years ago

7 0

Answer:

D. 5x^2 + 2y^2 + 12x + 5y

Step-by-step explanation:

6x + 2y + y^2 + 6x + 2y + y^2 + 4x^2 + x^2 + y

6x + 6x = 12x

12x + 2y + y^2 + 2y + y^2 + 4x^2 + x^2 + y

2y + 2y + y = 5y

12x + 5y + y^2 + y^2 + 4x^2 + x^2

y^2 + y^2 = 2y^2

2y^2 + 4x^2 + x^2 + 12x + 5y

4x^2 + x^2 = 5x^2

2y^2 + 5x^2 + 12x + 5y

5x^2 + 2y^2 + 12x + 5y

alexandr1967 [171]3 years ago

3 0

Answer:

$5 {x}^{2} + 2 {y}^{2} + 12x + 5y$

Step-by-step explanation:

Add all of the sides of the polygon:

$6x + 2y + {y}^{2} + 6x + 2y + {y}^{2} + 4 {x}^{2} + {x}^{2} + y$

Combine like terms.

$12x + 5y + 2 {y}^{2} + 5 {x}^{2}$

$5 {x}^{2} + 2 {y}^{2} + 12x + 5y$

You might be interested in

Compare the value of √(100/25) to the value of √100/√25.

olga2289 [7]

Answer:

4 16 2.000

5 25 2.236

6 36 2.449

7 49 2.646

Step-by-step explanation:

7 0

3 years ago

5. You are making your Halloween costume this year. You have 6 yards of fabric and the pattern says that you need to cut it in t

REY [17]

Answer:

The shorter side piece of fabric = x = 8 feet

The longer side piece of fabrics = (x + 2) = 10 feet

Step-by-step explanation:

Total yards of fabrics = 6 yards

you need to cut it in two pieces where one is two feet longer than the other.

First piece= x feet

Second piece= x+2 feet

Convert 6 yards to feet

6 yards = 18 feet

First piece + second piece = total piece of fabrics

x + (x+2) = 18

x + x + 2 = 18

2x + 2 = 18

2x = 18 - 2

2x = 16

Divide both sides by 2

x = 16 / 2

x = 8 feet

8 feet = 2.66667 yards

x + 2

= 8 + 2

= 10 feet

10 feet = 3.33333 yards

The shorter side piece of fabric = x = 8 feet

The longer side piece of fabrics = (x + 2) = 10 feet

7 0

3 years ago

Solve the differential. This was in the 2016 VCE Specialist Maths Paper 1 and i'm a bit stuck

Nimfa-mama [501]

$\sqrt{2 - x^{2}} \cdot \frac{dy}{dx} = \frac{1}{2 - y}$
$\frac{dy}{dx} = \frac{1}{(2 - y)\sqrt{2 - x^{2}}}$

Now, isolate the variables, so you can integrate.
$(2 - y)dy = \frac{dx}{\sqrt{2 - x^{2}}}$
$\int (2 - y)\,dy = \int\frac{dx}{\sqrt{2 - x^{2}}}$
$2y - \frac{y^{2}}{2} = sin^{-1}\frac{x}{\sqrt{2}} + \frac{1}{2}C$

$4y - y^{2} = 2sin^{-1}\frac{x}{\sqrt{2}} + C$
$y^{2} - 4y = -2sin^{-1}\frac{x}{\sqrt{2}} - C$
$(y - 2)^{2} - 4 = -2sin^{-1}\frac{x}{\sqrt{2}} - C$
$(y - 2)^{2} = 4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C$

$y - 2 = \pm\sqrt{4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C}$
$y = 2 \pm\sqrt{4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C}$

At x = 1, y = 0.
$0 = 2 \pm\sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$
$-2 = \pm\sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$

$4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C > 0$
$\therefore 2 = \sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$

$4 = 4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C$
$0 = -2sin^{-1}\frac{1}{\sqrt{2}} - C$
$C = -2sin^{-1}\frac{1}{\sqrt{2}} = -2\frac{\pi}{4}$
$C = -\frac{\pi}{2}$

$\therefore y = 2 - \sqrt{4 + \frac{\pi}{2} - 2sin^{-1}\frac{x}{\sqrt{2}}}$

6 0

3 years ago

There are less than 200 apples in a box. It is known that 2, 3, 4, 5, or 6 kids can share these apples evenly. How many apples c

Sedaia [141]

Answer:

There can be 180 apples in that box.

Step-by-step explanation:

1. Let's review the information given to answer the question correctly:

Number of apples in a box < 200

2. It is known that 2, 3, 4, 5, or 6 kids can share these apples evenly. How many apples can be in that box?

The answer is that the number of apples that can be in the box is the highest multiple of 2, 3, 4, 5, and 6 that is close to 200.

The common multiples for this set of numbers are 60, 120, 180, 240, 300 and so on with 60 as the constant.

Therefore, the highest number that is multiple for this set of numbers and at the same time lower than 200 is 180.

There can be 180 apples in that box.

5 0

3 years ago

Functions please helpp

rodikova [14]

Answer:

Functions:

3. The chart with arrows

4. The graph

Not Functions:

1. (1,1), (2,2), (3,3), (1,4)

2. (1,17), (0,16), (0,15), (-2,17)

Step-by-step explanation:

Functions do not have repeating domains (x-coordinates).

Hope it helps!

8 0

2 years ago