Answer:
x < -3 is the solution for the given inequality - 8 > 8x + 16.
Step-by-step explanation:
Here, the given inequality is - 8 > 8x + 16
Now, we know if equal (positives) are added, subtracted multiplied or divided on both sides of in equality, the signs remain unchanged.
⇒ - 8 > 8x + 16 is equivalent to - 8 + 8 > 8x + 16 + 8
or, 0 > 8x + 24
⇔ -8x > 8x + 24 - 8x
⇔ -8 x > 24
or, 
(REVERSE SIGN as dividing by a a negative number)
or, x < -3
or, x < -3 is the solution for the given inequality.
Answer:
B or 31r-71
Step-by-step explanation:
First, use distributive property to expand the first term.
30r-66-(5-r)
Remove the parenthesis of the third term:
30r-66-5+r
Combine like terms
31r-71
1. You have that the Standard form for the equation of a circle when its center is at the origin, is:
x²+y²=r²
2. You must calculate the radius. Then:
r=√(x²+y²)
x=24
y=32
3. When you substitute the values of "x" and "y" into the equation r=√(x²+y²), you obtain:
r=√(x²+y²)
r=√(24²+32²)
r=√(576+1024)
r=√1600
r=40 feet
4. Therefore, the diameter (D) of the circle, is:
D=2r
D=2(40 feet)
D=80 feet
Recall that
cos²(<em>x</em>) + sin²(<em>x</em>) = 1
Then in the equation
1 - cos(<em>x</em>) = 2 - 2 sin²(<em>x</em>)
we can rewrite as
1 - cos(<em>x</em>) = 2 (1 - sin²(<em>x</em>))
1 - cos(<em>x</em>) = 2 cos²(<em>x</em>)
2 cos²(<em>x</em>) + cos(<em>x</em>) - 1 = 0
Factorize the left side as
(2 cos(<em>x</em>) - 1) (cos(<em>x</em>) + 1) = 0
so that
2 cos(<em>x</em>) - 1 = 0 <u>or</u> cos(<em>x</em>) + 1 = 0
cos(<em>x</em>) = 1/2 <u>or</u> cos(<em>x</em>) = -1
On the interval (-<em>π</em>, <em>π</em>) (note that this interval is open, so we don't allow <em>x</em> = <em>π</em>), we have
• cos(<em>x</em>) = 1/2 for <em>x</em> = <em>π</em>/3 and <em>x</em> = -<em>π</em>/3
• cos(<em>x</em>) = -1 for <em>x</em> = <em>π</em>
The answer is 93. Add all the sides and subtract 267 (which is what you get adding all the sides you have together) from 360.
