Answer:
w= 7/4 +1/4 √89 OR w= 7/4 -1/4 √89
Step-by-step explanation:
2w^2-8w-1= (w-2)^2
Multiply (w-2)^2 by (-1)
2w^2-8w-1= -w+2^2
Add w to both sides
2w^2-7w-1= 4
Add 1 to both sides therefore that -1 cancels
2w^2-7w=5
Get the equation equal to 0 by subtracting 5 from both sides
2w^2-7w-5=0
Use the quadratic formula to solve
x= -(-7) plus or minus √(-7)-4(2)(-5)/2(2)
7 plus or minus √89/4
A proper fraction is a fraction such as 3/5, or 2/4, any fraction where the numerator is less than the denominator. Then it says "the whole is divided into an even number of equal parts, and an odd number of those parts exists." Such as 1 3/5. From my understanding, you then divide by 2, which would give you 0.8, which could then be turned into 0.4 if that's what your teacher wants you to do. In the end, there will be no odd number.
Octagon, stop sign.
Eight isoscles triangles. It looks like we're told the side is 9.9 and the height to the side (also called the apothem) is 12.
So each isosceles triangle has area (1/2)(9.9)(12) and we have eight of them,
area = 8(1/2)(9.9)(12) = 475.2
Answer: 475.2
Usually we wouldn't be told 9.9 -- this is the baby version. We know each of those isoscles triangles has unique angle 360/8=45 degrees, so the apothem and half the side of the octagon are a right triangle with acute angle 22.5 degrees.
The area of the right triangle with long leg 12, short leg x,
tan 22.5 = x/12 or
x = 12 tan 22.5
Twice that is what we're told is 9.9; let's check:
2x = 24 tan 22.5 = 9.941125496954282
The area of the little right triangle is
(1/2) 12 × 12 tan 22.5
and there are 16 of these
16 (1/2) 12 × 12 tan 22.5 ≈ 477.174
Answer:
n/4 - 3 OR 1/4n - 3
Step-by-step explanation:
First, let's assign a variable to Emily's number. Let is be <em>x</em>.
Now all we have to do is go through the problem step by step.
"She finds 1/4 of the number..."
There are two ways you can do this. You can either multiply n by 1/4 (1/4n), or you can divide by 4 (dividing by four is the same as finding 1/4 of a number). For this example let's divide by four
n/4
"...and then subtracts 3."
All we have to do is subtract 3 from n/4
n/4 - 3
REMEMBER: like I said, there are two possible options. You can either have n/4 or 1/4n. They mean the same thing
