Answer: 1/12.
Step-by-step explanation: If the fair die has 12 faces that means the numbers on the die are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Among these, the only multiple of 12 is 12 itself. 12*1 = 12, so 12 is a multiple of 12. Thus, the probability that the number of dots on the top face of the die is a multiple of 12 is 1 out of 12.
5. c = 13
6. b=6
7. b=8
8. a=30
9. a=2√3
Step-by-step explanation:
We will use Pythagorean theorem in each to find the length of missing side.
![a^2+b^2=c^2](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E2)
5. a=12, b=5
Putting in formula
![(12)^2+(5)^2=c^2\\144+25=c^2\\169=c^2\\c^2=169](https://tex.z-dn.net/?f=%2812%29%5E2%2B%285%29%5E2%3Dc%5E2%5C%5C144%2B25%3Dc%5E2%5C%5C169%3Dc%5E2%5C%5Cc%5E2%3D169)
Taking square root on both sides
![\sqrt{c^2}=\sqrt{169}\\c=13](https://tex.z-dn.net/?f=%5Csqrt%7Bc%5E2%7D%3D%5Csqrt%7B169%7D%5C%5Cc%3D13)
Therefore,
c = 13
6. a=8 , c=10
Putting in formula
![(8)^2+b^2=(10)^2\\64+b^2=100\\b^2=100-64\\b^2=36\\](https://tex.z-dn.net/?f=%288%29%5E2%2Bb%5E2%3D%2810%29%5E2%5C%5C64%2Bb%5E2%3D100%5C%5Cb%5E2%3D100-64%5C%5Cb%5E2%3D36%5C%5C)
Taking square root on both sides
![\sqrt{b^2}=\sqrt{36}\\b=6](https://tex.z-dn.net/?f=%5Csqrt%7Bb%5E2%7D%3D%5Csqrt%7B36%7D%5C%5Cb%3D6)
b=6
7. a=15, c=17
Putting in formula
![(15)^2+b^2=(17)^2\\225+b^2=289\\b^2=289-225\\b^2=64](https://tex.z-dn.net/?f=%2815%29%5E2%2Bb%5E2%3D%2817%29%5E2%5C%5C225%2Bb%5E2%3D289%5C%5Cb%5E2%3D289-225%5C%5Cb%5E2%3D64)
Taking square root on both sides
![\sqrt{b^2}=\sqrt{64}\\b=8](https://tex.z-dn.net/?f=%5Csqrt%7Bb%5E2%7D%3D%5Csqrt%7B64%7D%5C%5Cb%3D8)
b=8
8. b=40, c=50
Putting in formula
![a^2+(40)^2=(50)^2\\a^2+1600=2500\\a^2=2500-1600\\a^2=900](https://tex.z-dn.net/?f=a%5E2%2B%2840%29%5E2%3D%2850%29%5E2%5C%5Ca%5E2%2B1600%3D2500%5C%5Ca%5E2%3D2500-1600%5C%5Ca%5E2%3D900)
Taking square root on both sides
![\sqrt{a^2}=\sqrt{900}\\a=30](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5E2%7D%3D%5Csqrt%7B900%7D%5C%5Ca%3D30)
a=30
9. b=2 , c=4
Putting in formula
![a^2+(2)^2=(4)^2\\a^2+4=16\\a^2=16-4\\a^2=12](https://tex.z-dn.net/?f=a%5E2%2B%282%29%5E2%3D%284%29%5E2%5C%5Ca%5E2%2B4%3D16%5C%5Ca%5E2%3D16-4%5C%5Ca%5E2%3D12)
Taking square root on both sides
![\sqrt{a^2}=\sqrt{12}\\\sqrt{a^2}=\sqrt{2*2*3}\\a=2\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5E2%7D%3D%5Csqrt%7B12%7D%5C%5C%5Csqrt%7Ba%5E2%7D%3D%5Csqrt%7B2%2A2%2A3%7D%5C%5Ca%3D2%5Csqrt%7B3%7D)
a=2√3
Keywords: square root, pythagorean theorem
Learn more about square root at:
#LearnwithBrainly
-2 -9 so that means the minimum of j is 9
Good luck.
Answer:
y=-2x+4
Step-by-step explanation:
Hello there!
Using y=mx+b, -2 is the slope and 4 is the y-intercept.
;)