The doghouse shown has a floor but no windows. Find the total surface area of the doghouse including the door.

A) Identify the center of rotation: What points in the rotated image correspond with

Phoenix [80]

Answer:

the rotated image correspond is angle DEF

5 0

3 years ago

The length of a rectangle is the sum of the width and 3. The area of the rectangle is 54 units. What is the width, in units, of

zimovet [89]

Answer:

Let a be the width and b the length

a+3=b

a*b=54

a(a+3)=54

a^2+3a-54=0

a=6

8 0

3 years ago

A company sells its printers to customers in order to make a profit of 25% calculate the price the company paid for a printer wh

ioda

The company paid $2000 for the printer

Step-by-step explanation:

Let x be the price of the printer for which the company bought it.

If x is the price of printer, then 25% of x will be the profit made by the company.

That is:

0.25x

According to the statement,

The cost and profit earned by company are equal to 2500

So,

$x+0.25x = 2500\\1.25x = 2500$

Dividing both sides by 1.25

$\frac{1.25x}{1.25} = \frac{2500}{1.25}\\x = 2000$

Hence,

The company paid $2000 for the printer

Keywords: Percentage, Profit

Learn more about percentage at:

#LearnwithBrainly

7 0

3 years ago

Find the length of a side of an equilateral triangle given its altitude is six inches long.

vampirchik [111]

An equilateral triangle has three 60 degree angles.
The altitude divides it into two 30 60 90 triangles.
The altitude is the "middle side" of such a triangle.
When that is the case, the middle side divided by the square root of 3 = the short side and multiplied by (2/sq root (3)) equals the hypotenuse.
The hypotenuse is the side of the equilateral triangle.
So, 6 * 2 / (sq root of 3) = 6.9282032303 

Source:
http://www.1728.org/trig2.htm

8 0

3 years ago

1. Create a circle. Show and explain the difference between the following:

liberstina [14]

1.
a.
A secant line is a line which intersects the circle at 2 different points.

A tangent line is a line which has only one point in common with the circle.

Check picture 1: The orange line s is a secant line, the blue line t is a tangent line.

b.
An inscribed angle is an angle formed by using 3 points of a circle.

The main property of an inscribed angle is that its measure is half of the measure of the arc it intercepts.

Check picture 2: If $m(\angle KML)=\beta$ , then the measure of arc KL is $2 \beta$ .

A central angle is an angle whose vertex is the center of the circle, and the 2 endpoints of the rays are points of the circle.

The main property is: the measure of the central angle is equal to the measure of the arc it intercepts.

Check picture 2

2.
To construct the inscribed circle of a triangle, we first draw the 3 interior angle bisectors of the triangle.
They meet at a common point called the incenter, which is the center of the inscribed circle.
We open the compass, from the incenter, so that it touches one of the sides at only one point. We then draw the circle. (picture 3)

To draw the circumscribed circle, we first find the midpoints of each side. We then draw perpendicular segments through these (the midpoints.) They meet at one common point, which is the circumcenter: the center of the circumscribed circle.
We open the compass from the circumcenter to one of the vertices of the triangle. We draw the circle, and see that it circumscribes the triangle.

(picture 4)

3.

Given an equation of a circle: $x^2-2x+y^2+6y+6=0$ .

To determine the center and the radius of the equation we must write the above equation in the form :

$(x-a)^2+(y-b)^2=r^2$ .

Then, (a, b) is the center, and r is the radius of this circle. We do this process by completing the square.

Note that $x^2-2x$ becomes a perfect square by adding 1, and
$y^2+6y$ becomes a perfect square by adding 9.

Thus we have:

$x^2-2x+y^2+6y+6=0\\\\(x^2-2x+1)+(y^2+6y+9)-4=0\\\\(x-1)^2+(y+3)^2=2^2$

Thus, the center is (1, -3), and the radius is 2.

4. Not complete

5.

The radius of the pizza is $\displaystyle{ \frac{131}{2}ft=65.5ft$ .

The surface of a circle with radius r is given by the formula $\displaystyle{ A=\pi r^2$ ,
and the circumference is given by the formula C=2πr.

Thus, the area of the whole pizza is given by $\displaystyle{ A=\pi r^2= \pi\cdot65.5^2=4290.25 \pi$ (square ft).

Each of the 50 slices, has an area of $\displaystyle{ \frac{4290.25 \pi}{50} =85.805 \pi$ (square ft)

Notice that the perimeter (the crust) of a slice is made of 2 radii, and the arc-like part.
The arc is 1/50 of the circumference, so it is $\displaystyle{\frac{2 \pi r}{50} = \frac{2\cdot65.5\cdot \pi }{50}= 2.62 \pi$ .

So the perimeter of one slice is 65.5+65.5+2.62π=131+2.62π

7 0

3 years ago