If triangle KMN is congruent with triangle LMN, then:
1) KM must be congruent with LM→KM=LM→
x+2y=3x-y→x+2y-x-2y=3x-y-x-2y→0=2x-3y→2x-3y=0 (1)
2) KN must be congruent with LN→KN=LN→
5x+3y=8x-7→5x+3y-5x-3y+7=8x-7-5x-3y+7→7=3x-3y→3x-3y=7 (1)
We have a system of two equations and two unkowns:
(1) 2x-3y=0
(2) 3x-3y=7
Subtracting equation (1) from equation (2)
(3x-3y)-(2x-3y)=7-0
3x-3y-2x+3y=7
x=7
Replacing x=7 in equation (1)
(1) 2x-3y=0→2(7)-3y=0→14-3y=0→
14-3y+3y=0+3y→14=3y→14/3=3y/3→14/3=y→y=14/3
The length of the hypotenuse is:
KN=5x+3y=5(7)+3(14/3)=35+14→KN=49
or
LN=8x-7=8(7)-7=56-7→LN=49
Answer: Option C. 49
Answer:
6.7 = 6 
-0.92= -
-0.1= -
-5.05=-5
Step-by-step explanation:
:-)
First rewrite the decimal as a number with 1 in the denominator.
2nd multiply to remove 2 decimal places by (100/100)
3rd reduce the result of the multiplication
Then simplify the improper fraction
-Alex :-)
Answer:
d
Step-by-step explanation:
Hope this helps! Good luck!
Answer:
The green would take 4 and the blue would take 16 times respectivly. I did it by finding the volumes of the cups in terms of pi, then dividing it by the volume of the sink.
Step-by-step explanation:
So the volume of the whole half sphere is 512pi.
Now we have to find the volumes of the cup.
Equation: 
Blue cup:
It would take 16 times to drain it completly.
Green cup:
It would take 4 times to drain it completly.
A trig identity is <span>asinucosu=<span>a/2</span>sin(2u)</span>So you can write your equation as<span>y=sin(x)cos(x)=<span>1/2</span>sin(2x)</span>Use the crain rule here<span><span>y′</span>=<span>d/<span>dx</span></span><span>1/2</span>sin(2x)=<span>1/2</span>cos(2x)<span>d/<span>dx</span></span>2x=cos(2x)</span>The curve will have horizontal tangents when y' = 0.<span><span>y′</span>=0=cos(2x)</span>On the interval [-pi, pi], solution to that is<span><span>x=±<span>π4</span>,±<span><span>3π</span>4</span></span></span>
