I'm pretty sure the answer is "A matrix separates rational and irrational numbers." (Note: I'm not that great with memorizing definitions, but I'm pretty sure.) Hope this helps :)
Answer:
6x²y(9 - 2y)
Step-by-step explanation:
Step 1: Factor out GCF
6(9x²y - 2x²y²)
Step 2: Factor out <em>x²</em>
6x²(9y - 2y²)
Step 3: Factor out <em>y</em>
6x²y(9 - 2y)
And we have our factored answer.
1. 60,30,90 right triangle. y will be hypotenuse/2, x will be
hypotenuse*sqrt(3)/2. So x = 16*sqrt(3)/2 = 8*sqrt(3), approximately 13.85640646
y = 16/2 = 8
2. 45,45,90 right triangle (2 legs are equal length and you have a right angle).
X and Y will be the same length and that will be hypotenuse * sqrt(2)/2. So
x = y = 8*sqrt(2) * sqrt(2)/2 = 8*2/2 = 8
3. Just a right triangle with both legs of known length. Use the Pythagorean theorem
x = sqrt(12^2 + 5^2) = sqrt(144 + 25) = sqrt(169) = 13
4. Another right triangle with 1 leg and the hypotenuse known. Pythagorean theorem again.
y = sqrt(1000^2 - 600^2) = sqrt(1000000 - 360000) = sqrt(640000) = 800 5. A 45,45,90 right triangle. One leg known. The other leg will have the same length as the known leg and the hypotenuse can be discovered with the Pythagorean theorem. x = 6. y = sqrt(6^2 + 6^2) = sqrt(36+36) = sqrt(72) = sqrt(2 * 36) = 6*sqrt(2), approximately 8.485281374
6. Another 45,45,90 triangle with the hypotenuse known. Both unknown legs will have the same length. And Pythagorean theorem will be helpful.
x = y.
12^2 = x^2 + y^2
12^2 = x^2 + x^2
12^2 = 2x^2
144 = 2x^2
72 = x^2
sqrt(72) = x
6*sqrt(2) = x
x is approximately 8.485281374
7. A 30,60,90 right triangle with the short leg known. The hypotenuse will be twice the length of the short leg and the remaining leg can be determined using the Pythagorean theorem.
y = 11*2 = 22.
x = sqrt(22^2 - 11^2) = sqrt(484 - 121) = sqrt(363) = sqrt(121 * 3) = 11*sqrt(3). Approximately 19.05255888
8. A 30,60,90 right triangle with long leg known. Can either have fact that in that triangle, the legs have the ratio of 1:sqrt(3):2, or you can use the Pythagorean theorem. In this case, I'll use the 1:2 ratio between the unknown leg and the hypotenuse along with the Pythagorean theorem.
x = 2y
y^2 = x^2 - (22.5*sqrt(3))^2
y^2 = (2y)^2 - (22.5*sqrt(3))^2
y^2 = 4y^2 - 1518.75
-3y^2 = - 1518.75
y^2 = 506.25 = 2025/4
y = sqrt(2025/4) = sqrt(2025)/sqrt(4) = 45/2
Therefore:
y = 22.5
x = 2*y = 2*22.5 = 45
9. Just a generic right triangle with 2 known legs. Use the Pythagorean theorem.
x = sqrt(16^2 + 30^2) = sqrt(256 + 900) = sqrt(1156) = 34
10. Another right triangle, another use of the Pythagorean theorem.
x = sqrt(50^2 - 14^2) = sqrt(2500 - 196) = sqrt(2304) = 48
'A' is the square root of 25. That's 5, so take A=5 with you
as you go to the next step.
B is A³. A³ means (A x A x A). We know that 'A' is 5, so 'B' is (5x 5 x 5) = 125 .
Take B=125 with you to the next step.
'C' is B - 25. We know that 'B' is 125. So C = (125 - 25) = 100 .
Take C=100 with you to the next step.
'D' is the square root of 'C'. We know that C=100, so D = √100 .
The square root of 100 is 10, so D=10.
Take D=10 with you to the next step .
'E' is D+39. We know that D=10. So E=(10+39) = 49 .
Take E=49 with you to the last step.
'F' is the square root of 'E'. We know that E=49.
<span><span>27100</span>(60)=<span>815</span>=16<span>15</span></span>
The 16 is how many minutes you have. If you were not given the seconds, we would have to say that we have a remainder of (1/5) of a minute. Since 1 minute is (1/60), one-fifth of that is (1/300). Now we would need to see how many seconds that gives us. 1 second is (1/3600) of a degree, so we would need to divide (1/300) by (1/3600). Doing this gives us:
<span><span><span>1300</span>÷<span>13600</span>=<span>1300</span>(3600)=12</span></span>
