I'm not too sure but I think it's option
1. No, because only one angle of the triangle is congruent.
Answer:
![t_3 = -53\\\\\\t_7 = -17\\t_n= -80 +9n](https://tex.z-dn.net/?f=t_3%20%3D%20-53%5C%5C%5C%5C%5C%5Ct_7%20%3D%20-17%5C%5Ct_n%3D%20-80%20%2B9n)
Step-by-step explanation:
Arithmetic sequence:
![\sf \boxed{t_n=a+(n-1)d}](https://tex.z-dn.net/?f=%5Csf%20%5Cboxed%7Bt_n%3Da%2B%28n-1%29d%7D)
Here a is the first term and d is the common difference.
⇒
------------(I)
⇒ a + 19d = 100 ---------(II)
Subtract equation (I) from (II)
(I1) a + 19d = 100
(II) a + 13d = 46
<u>- - -</u>
6d = 54
d = 54 ÷ 6
![\sf \boxed{d = 9}](https://tex.z-dn.net/?f=%5Csf%20%5Cboxed%7Bd%20%3D%209%7D)
Substitute d = 9 in equation(I) and find 'a',
a + 13*9= 46
a + 117 = 46
a = 46 - 117
a = -71
![\sf t_3 = -71 + 2*9](https://tex.z-dn.net/?f=%5Csf%20t_3%20%3D%20-71%20%2B%202%2A9)
= -71 + 18
= -53
![\sf t_7 = -71 + 6*9](https://tex.z-dn.net/?f=%5Csf%20t_7%20%3D%20-71%20%2B%206%2A9)
= -71 + 54
= -17
![\sf t_n= -71 + (n-1)*9](https://tex.z-dn.net/?f=%5Csf%20t_n%3D%20-71%20%2B%20%28n-1%29%2A9)
= -71 + 9*n - 1 *9
= -71 + 9n - 9
= -71 - 9 + 9n
= - 80 + 9n
Answer:
The answer is the third graph.
Step-by-step explanation:
Since we are looking for a constant balance, we should focus on the line in the graph. In graph 3, we see a line going straight horizontally, without any inclines or declines. Since the word "constant" in Mathematics is a line that has a slope of 0, the answer must be the third graph.
Answer:
Smallest angle: 41°
Second angle: 57°
Third angle: 82°
Step-by-step explanation:
Let's call the smallest angle as ![x](https://tex.z-dn.net/?f=x)
<u>"while a third angle is twice the smallest"</u>: third angle is ![2x](https://tex.z-dn.net/?f=2x)
<u>"One angle of a triangle measures 16∘ more than the smallest":</u> 2nd angle is ![16+x](https://tex.z-dn.net/?f=16%2Bx)
We know sum of 3 angles in a triangle is 180 degrees, so we can set up the equation and solve for x:
![x+(16+x)+(2x)=180\\x+16+x+2x=180\\4x=180-16\\4x=164\\x=\frac{164}{4}=41](https://tex.z-dn.net/?f=x%2B%2816%2Bx%29%2B%282x%29%3D180%5C%5Cx%2B16%2Bx%2B2x%3D180%5C%5C4x%3D180-16%5C%5C4x%3D164%5C%5Cx%3D%5Cfrac%7B164%7D%7B4%7D%3D41)
So smallest angle is 41°
The 2nd angle is 16+41=57°
third angle is 2*41=82°