0.11111...=1/9
4*(0.11111...)=4*(1/9)=4/9
Therefore, 0.44444...=4/9
Answer:
The ladder will go approximately 35.71 ft up the building.
Step-by-step explanation:
The 50 ft ladder is leaning against a building and the base of the ladder is 35 feet from the base of the building.
It means the ladder will form a right triangle with the building with the following dimensions:
Using the Pythagorean Theorem to determine the height,
![a^2+b^2=c^2](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E2)
Here,
Substitute the given values into the equation to determine the height:
![a^2+b^2=c^2](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E2)
![a^2+\left(35\right)^2=\left(50\right)^2](https://tex.z-dn.net/?f=a%5E2%2B%5Cleft%2835%5Cright%29%5E2%3D%5Cleft%2850%5Cright%29%5E2)
![a^2+1225=2500](https://tex.z-dn.net/?f=a%5E2%2B1225%3D2500)
![a^2=1275](https://tex.z-dn.net/?f=a%5E2%3D1275)
![\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7Dx%5E2%3Df%5Cleft%28a%5Cright%29%5Cmathrm%7B%5C%3Athe%5C%3Asolutions%5C%3Aare%5C%3A%7Dx%3D%5Csqrt%7Bf%5Cleft%28a%5Cright%29%7D%2C%5C%3A%5C%3A-%5Csqrt%7Bf%5Cleft%28a%5Cright%29%7D)
![a=\sqrt{1275},\:a=-\sqrt{1275}](https://tex.z-dn.net/?f=a%3D%5Csqrt%7B1275%7D%2C%5C%3Aa%3D-%5Csqrt%7B1275%7D)
![a\:=\:35.71,\:\:\:a\:=\:-35.71](https://tex.z-dn.net/?f=a%5C%3A%3D%5C%3A35.71%2C%5C%3A%5C%3A%5C%3Aa%5C%3A%3D%5C%3A-35.71)
We know that height can not be negative. Thus,
ft
Therefore, the ladder will go approximately 35.71 ft up the building.
Observe that the difference of the sequence is 30. The first term is 12.
Let's use the arithmetic sequence formula
![a_n=a_1+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d)
Replacing the given information, we have.
![\begin{gathered} a_n=12+(n-1)\cdot30 \\ a_n=12+30n-30 \\ a_n=30n-18 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a_n%3D12%2B%28n-1%29%5Ccdot30%20%5C%5C%20a_n%3D12%2B30n-30%20%5C%5C%20a_n%3D30n-18%20%5Cend%7Bgathered%7D)
<h2>Hence, the right answer is C because it relates correctly the first term and the difference.</h2>
Answer:
A = 60
B = 55
C = 65
Step-by-step explanation:
The sum of the angles of a triangle is 180
A + B+C = 180
x+ x-5 + 65 = 180
Combine like terms
2x+60 =180
Subtract 60 from each side
2x= 180-60
2x= 120
Divide by 2
2x/2 = 120/2
x= 60
A = 60
B = 60-5= 55
C = 65