Answer:
146°
Step-by-step explanation:
Blue angle: 34°: 180 (sum of angles in a triangle) - 92 - 54 = 34
x = 180 (flat angle) - 34 = 146°
Please give me Brainliest :)
Given:
second term = 18
fifth term = 144
The nth term of a geometric sequence is:
![\begin{gathered} a_n\text{ = ar}^{n-1} \\ Where\text{ a is the first term} \\ r\text{ is the common ratio} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a_n%5Ctext%7B%20%3D%20ar%7D%5E%7Bn-1%7D%20%5C%5C%20Where%5Ctext%7B%20a%20is%20the%20first%20term%7D%20%5C%5C%20r%5Ctext%7B%20is%20the%20common%20ratio%7D%20%5Cend%7Bgathered%7D)
Hence, we have:
![\begin{gathered} \text{ar}^{2-1}\text{ = 18} \\ ar\text{ = 18} \\ \\ ar^{5-1}=\text{ 144} \\ ar^4\text{ =144} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7Bar%7D%5E%7B2-1%7D%5Ctext%7B%20%3D%2018%7D%20%5C%5C%20ar%5Ctext%7B%20%3D%2018%7D%20%5C%5C%20%20%5C%5C%20ar%5E%7B5-1%7D%3D%5Ctext%7B%20144%7D%20%5C%5C%20ar%5E4%5Ctext%7B%20%3D144%7D%20%5Cend%7Bgathered%7D)
Divide the expression for the fifth term by the expression for the second term:
![\begin{gathered} \frac{ar^4}{ar}\text{ = }\frac{144}{18} \\ r^3\text{ = }\frac{144}{18} \\ r\text{ = 2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7Bar%5E4%7D%7Bar%7D%5Ctext%7B%20%3D%20%7D%5Cfrac%7B144%7D%7B18%7D%20%5C%5C%20r%5E3%5Ctext%7B%20%3D%20%7D%5Cfrac%7B144%7D%7B18%7D%20%5C%5C%20r%5Ctext%7B%20%3D%202%7D%20%5Cend%7Bgathered%7D)
Substituting the value of r into any of the expression:
![\begin{gathered} ar\text{ = 18} \\ a\text{ }\times\text{ 2 = 18} \\ Divide\text{ both sides by 2} \\ \frac{2a}{2}\text{ =}\frac{18}{2} \\ a\text{ = 9} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20ar%5Ctext%7B%20%3D%20%2018%7D%20%5C%5C%20a%5Ctext%7B%20%7D%5Ctimes%5Ctext%7B%202%20%3D%20%2018%7D%20%5C%5C%20Divide%5Ctext%7B%20both%20sides%20by%202%7D%20%5C%5C%20%5Cfrac%7B2a%7D%7B2%7D%5Ctext%7B%20%3D%7D%5Cfrac%7B18%7D%7B2%7D%20%5C%5C%20a%5Ctext%7B%20%3D%209%7D%20%5Cend%7Bgathered%7D)
Hence, the explicit rule for the sequence is:
Answer:
1
Step-by-step explanation:
angles on a straight line are 180 so u do 180 minus 47 gives u 133
Answer:
Therefore 'x' is equal to 65.4°
Step-by-step explanation:
In Right Angle Triangle ABC
∠ B = 90°
AC = Hypotenuse = 12
CB = Adjacent Side = 5
To Find:
∠ C = x
Solution:
In Right Angle Triangle ABC Cosine Identity we have
![\cos C = \frac{\textrm{side adjacent to angle C}}{Hypotenuse}\\](https://tex.z-dn.net/?f=%5Ccos%20C%20%3D%20%5Cfrac%7B%5Ctextrm%7Bside%20adjacent%20to%20angle%20C%7D%7D%7BHypotenuse%7D%5C%5C)
Substituting the values we get
![\cos C = \dfrac{CB}{AC}=\dfrac{5}{12}](https://tex.z-dn.net/?f=%5Ccos%20C%20%3D%20%5Cdfrac%7BCB%7D%7BAC%7D%3D%5Cdfrac%7B5%7D%7B12%7D)
![\angle C = \cos^{-1}(0.4166)=65.37=65.4\°](https://tex.z-dn.net/?f=%5Cangle%20C%20%3D%20%5Ccos%5E%7B-1%7D%280.4166%29%3D65.37%3D65.4%5C%C2%B0)
Therefore 'x' is equal to 65.4°
Acute angle and a right angle makes a obtuse I learned this in 4th