Finding dilations geometry

lisov135 [29]

$\sqrt{8} + 3 \sqrt{32} - \sqrt{50}$

$= \sqrt{4 \times 2} + 3 \sqrt{16 \times 2} - \sqrt{25 \times 2}$

$= 2\sqrt{ 2} + 12 \sqrt{2} - 5\sqrt{ 2}$

$= 9\sqrt{ 2}$

6 0

3 years ago

a 1ft long piece of wire needs to be divided into two pieces which will form the shape of a circle and a square. Determine the l

yan [13]

Answer:

Length of wire for circle is 0.44 ft

Length of wire for square is 0.56 ft

Step-by-step explanation:

Let x is circumference of the circle

then

(1-x) = perimeter of the square

Find the radius of the circle

r = (x/2.π)

Find the area of the circle

a = π(x/2π)^2

a = π(x^2/4π^2)

Cancel π

a = x^2/4π

Find the area of the square:

a = (1-x/4)^2

a = (1-2x+x^2)/16

Total area

A = (x^2/4π)+(1-2x+x^2/16)

A = 4x^2+3.142-6.284x+3.142x^2

A = 7.142x^2-6.284x+3.142

Find the axis of symmetry [x = -b/(2a)]

x = -(-6.284)/{2.(7.142)}

x = 6.284/14.284

x = 0.44 ft, the piece of wire creating a circle

and

1 - 0.44 = 0.56 ft, the piece of wire creating the square

These lengths should give minimum area of the circle and square together

7 0

3 years ago

What is 12 divided by 2/3<br><br><br><br> What is 2/3 divided by 12

Alex777 [14]

12 divided by 2/3 = 18
2/3 divided by 12 = 0.5

8 0

3 years ago

Someone please pass the answers to this

arsen [322]

Answer/Step-by-step explanation:

1. The figure is composed of a triangle and a rectangle.

Area of the triangle = ½*base*height

base = 4 ft

height = 12 - 8 = 4ft

Area of triangle = ½*4*4 = 8 ft²

Area of rectangle = length * width

Length = 8 ft

Width = 4 ft

Area of rectangle = 8*4 = 32 ft²

✔️Area of the figure = 8 + 32 = 40 ft²

2. The figure is composed of a semicircle and a triangle

Area of the semicircle = ½(πr²)

radius (r) = 3 cm

π = 3

Area = ½(3*3²) = 13.5 cm²

Area of triangle = ½*base*height

base = 3*2 = 6 cm

height = 6 cm

Area = ½*6*6 = 6 cm²

✔️Area of the figure = 13.5 + 6 = 19.5 cm²

5 0

3 years ago

A(n - 3) +8= bn for n please help me

Papessa [141]

Given equation: A(n - 3) +8= bn.

Solution: On the left side of the equation we have A(n-3).

We don't have any sign in between A and parenthesis (n-3).

So, we need to multiply A and (n-3).

We need to apply distributive property to multiply A and (n-3).

Distributing A over (n-3), we get

A(n-3) = A*n - 3*A = An -3A.

Substituting this value in original equation,

An -3A +8= bn.

We need to solve it for n, so we get n terms on a side.

We have An on left side, we need to get rid n from left side.

Subtracting An from both sides, we get

An -3A +8-An= bn-An.

-3A +8 = bn - An.

We can see n is a common factor on rigth side in bn-an.

Factoring out n on right side from bn-an.

-3A +8 = (b - A)n.

Dividing both sides by (b-A),

$\frac{(-3A+8)}{(b-A)} = \frac{(b-A)n}{(b-A)}$

On right (b-A) paranthiss cancelled and we get n on right side.

$\frac{(-3A+8)}{(b-A)} =n$ Final answer.

So, that would be our final answer

n = (-3A+8)/(b-A)

7 0

4 years ago

Finding dilations geometry​

Finding dilations geometry