express answer in exact form.

find the area of one segment formed by a square with sides of 6" inscribed in a circle.

(hint: use the ratio of 1: 1: √2 to find the radius of the circle.)

4.5 pi in.^2 - 9 in.^2

Step-by-step explanation:

First, bisect the chord (one side of the square) in half. Draw a line from the middle of the chord to the center of the circle. This will bisect the 90o (o = degree sign) central angle in half, creating a 45o angle.  

So, you have a 45-45-90 triangle. Use the rules for 45-45-90 triangles to determine that the hypotenuse is 3 sqrt 2.  

The hypotenuse of the triangle is the radius of the circle. So now you can find out the area of the circle: A = pi * r^2 --> A = 18 pi in.^2.  

From this information, you can figure out the area of the sector. Do 90o (since the sector angle is 90o) divided by 360o: 90/360. You should get 1/4 (this shows that the sector is a quarter of the square). Next, do 1/4 times the area of the circle --> 1/4 * 18 pi = 4.5 pi in.^2.  

Finally, find out the area of the triangle by using the formula for the area of triangles: A = 1/2 * b * h ---> A = 1/2 * 6 * 3 (we know the base and height from earlier calculations with the 45-45-90 triangle). So --> A = 9 in.^2.  

Lastly, to find the area of one segment, do the area of the sector - the area of the triangle: 4.5 pi in.^2 - 9 in.^2 (This is in exact form. The approximate form would be 5.14 in.^2).

Hope this helps! :)

answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation:

here is me explaining it:

the pizza would be delivered around 5, give or take 15 minutes. this means it could be delivered anywhere from 4: 45 to 5: 15

let's say 5: 00 is equivalent to 0 on a number line and x represents time. 4: 45 would be equal to -15x because we are 15 minutes behind our starting point, 5: 00. 5: 15 would be equal to 15x because we are 15 minutes ahead of your starting point (which means you're late on the pizza delivery! )

absolute value is very confusing. the basic definition is how far you are from your starting point. if we deliver the pizza at 4: 45 (15 minutes before the starting point) we would be -15. this means we are 15 away from our starting point, 5: 00. that's the absolute value. |-15| (absolute value of negative fifteen) is equal to 15. if you did not understand this i suggest rereading this paragraph.

the normal way you would write this scenario would be 4.75 (4 and 3 quarters, or 4: 45. you can also write as a fraction.) is less than x and x is less than 5.25 (5 and 1 quarter or 5: 15). 4.75< x< 5.25 the reason why i am using numbers is because you cannot represent typical time as values on a graph, number line, or in an equation.

another way to write this scenario is with absolute value. we can write this as |x| being less than or equal to .25 (remember, this just means 15 minutes).           |x| ≤ .25.

sorry if the end was confusing. because we are talking about time this whole question is 10x harder. like i said earlier, you cannot represent time as, well, time, in a graph, equation, or number line. i set the values as follows: 1/4 or .25 for 15 minutes, and 1 for 1 hour. this is just a common way to set up graphs involving time.

|x| ≤ .25

i hope this ! : )

tell me if you need more assistance