Answer:
D. 5/6
Step-by-step explanation:
The given fractions have decimal values of ...
2/3 ≈ 0.67
6/7 ≈ 0.86
The answer choices are approximately 0.60, 0.50, 0.43, and 0.83.
The last choice (5/6) is between 2/3 and 6/7.
Using a common denominator of 42, these three fractions are ...
2/3 = 28/42
5/6 = 35/42
6/7 = 36/42
The fraction 5/6 lies between 2/3 and 6/7.
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It is useful to memorize the decimal equivalents of fractions with denominators of 10 or less. There are some patterns involved that make it easier.
Answer:
1.
centre(h,k)=(-13,9)
radius (r)=6
we have
equation of the circle is
(x-h)²+(y-k)²=r²
(x+13)²+(y-9)²=6²
x²+26x+169+y²-18y+81=36
x²+y²+26x-18y+169+81-36=0
x²+y²+26x-18y +214=0
is a required equation of the circle.
2.
centre(h,k)=(1,-1)
radius (r)=11
we have
equation of the circle is
(x-h)²+(y-k)²=r²
(x-1)²+(y+1)²=11²
x²-2x+1+y²+2y+1=121
x²+y²-2x+2y=121-2
x²+y²-2x+2y=119
is a required equation of the circle.
The area of an equilateral triangle of side "s" is s^2*sqrt(3)/4. So the volume of the slices in your problem is
(x - x^2)^2 * sqrt(3)/4.
Integrating from x = 0 to x = 1, we have
[(1/3)x^3 - (1/2)x^4 + (1/5)x^5]*sqrt(3)/4
= (1/30)*sqrt(3)/4 = sqrt(3)/120 = about 0.0144.
Since this seems quite small, it makes sense to ask what the base area might be...integral from 0 to 1 of (x - x^2) dx = (1/2) - (1/3) = 1/6. Yes, OK, the max height of the triangles occurs where x - x^2 = 1/4, and most of the triangles are quite a bit shorter...
Answer:
x < -5
Step-by-step explanation:
- 2x - 7 > x+ 8
Add 2x to each side
- 2x+2x - 7 > x+2x+ 8
-7 > 3x+8
Subtract 8 from each side
-7-8 > 3x+8-8
-15 > 3x
Divide by 3
-15/3 > 3x/3
-5 >x
x < -5
Answer:
Step-by-step explanation:
ok so this is a vetical angle. so they are equal to 180. so if 1 measurement is found the other is the difference of 180 and that angle measeurement.
so y is the same as 110
and 180 - 110 is 70, so x and z are equal to 70.
i hope this helped you :)
