Answer:
21870 km^2
Step-by-step explanation:
Area of sector=1/2r^2(theta)
Where r=18 km and theta=135
Area of sector=1/2(18)^2(135)
=1/2(324)(135)
=1/2(43740)
=21870 km^2
Answer:
The system has one solution.
Step-by-step explanation:
To find the number of solutions of the system, we equal both equations for y.
If we have ax = b, in which both a and b are different of 0, we have one solution.
If both a and b are 0, we have infinite solutions.
If a is 0 and b is not, there are no solutions.
y=6/7x-8 and y=7/9x+10/9
So
Both a and b are different of 0, so the system has one solution.
Answer:
there are 2 right angles
Step-by-step explanation:
Given:
4log1/2^w (2log1/2^u-3log1/2^v)
Req'd:
Single logarithm = ?
Sol'n:
First remove the parenthesis,
4 log 1/2 (w) + 2 log 1/2 (u) - 3 log 1/2 (v)
Simplify each term,
Simplify the 4 log 1/2 (w) by moving the constant 4 inside the logarithm;
Simplify the 2 log 1/2 (u) by moving the constant 2 inside the logarithm;
Simplify the -3 log 1/2 (v) by moving the constant -3 inside the logarithm:
log 1/2 (w^4) + 2 log 1/2 (u) - 3 log 1/2 (v)
log 1/2 (w^4) + log 1/2 (u^2) - log 1/2 (v^3)
We have to use the product property of logarithms which is log of b (x) + log of b (y) = log of b (xy):
Thus,
Log of 1/2 (w^4 u^2) - log of 1/2 (v^3)
then use the quotient property of logarithms which is log of b (x) - log of b (y) = log of b (x/y)
Therefore,
log of 1/2 (w^4 u^2 / v^3)
and for the final step and answer, reorder or rearrange w^4 and u^2:
log of 1/2 (u^2 w^4 / v^3)
Answer:
The answer is below
Step-by-step explanation:
The Angle Addition Postulate states that the measure of an angle formed by two or more angles which are placed side by side is the sum of the measures of the two angles.
Therefore:
∠MON = ∠MOP + ∠NOP (angle addition postulate)
Substituting values gives:
124 = (2x + 1) + (2x + 1)
124 = 2x + 2x + 1 + 1
124 = 4x + 2
subtracting 2 from both sides of the equation:
124 - 2 = 4x + 2 - 2
4x = 122
Dividing through by 4:
4x / 4 = 122 / 4
x = 30.5
Therefore ∠MOP = 2x + 1 = 2(30.5) + 1 = 62°, ∠NOP = 2x + 1 = 2(30.5) + 1 = 62°
∠MOP = 62°, ∠NOP = 62°
