Answer: 13.3
Step-by-step explanation:
Since angles in a triangle add to 180 degrees, we know that in triangle UWV,
. Thus, the triangles are similar by AA.
Since corresponding sides of similar triangles are proportional,
![\frac{x}{24}=\frac{20}{36}\\x=(20/36)(24)=\boxed{13.3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B24%7D%3D%5Cfrac%7B20%7D%7B36%7D%5C%5Cx%3D%2820%2F36%29%2824%29%3D%5Cboxed%7B13.3%7D)
![\sf\implies \: - 15 - ( - 4) + 17](https://tex.z-dn.net/?f=%20%20%5Csf%5Cimplies%20%5C%3A%20%20-%2015%20-%20%28%20-%204%29%20%2B%2017)
![\sf \implies \: - 15 + 4 + 17](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20%5C%3A%20%20-%2015%20%2B%204%20%2B%2017)
![\sf \implies \: - 15 + 21](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20%5C%3A%20%20-%2015%20%2B%2021)
![\boxed{ \tt \: ans \dashrightarrow 6}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Ctt%20%5C%3A%20ans%20%5Cdashrightarrow%206%7D)
<h3>Remember these laws of integers:</h3>
- (+)(-)=(-)
- (-)(+)=(-)
- (-)(-)=(+)
- (+)(+)=(+)
Answer:
-18
Step-by-step explanation:
![-4(-2)+\frac{(-12)}{+3}-20+(+4)+(-6)=8-\frac{12}{3}-20+4-6=8-4-20+4-6=-18](https://tex.z-dn.net/?f=-4%28-2%29%2B%5Cfrac%7B%28-12%29%7D%7B%2B3%7D-20%2B%28%2B4%29%2B%28-6%29%3D8-%5Cfrac%7B12%7D%7B3%7D-20%2B4-6%3D8-4-20%2B4-6%3D-18)
Answer:
Obtuse isosceles
Step-by-step explanation:
Two sides are the same length, so we know this is an isosceles triangle.
To determine if it's acute, right, or obtuse, we can compare it to a right triangle using Pythagorean Theorem:
c² = a² + b²
c² = 3² + 3²
c² = 18
c = √18
So if this were a right triangle, c would be √18, which is somewhere between 4 and 5.
Since the long side is greater than √18, we know this must be an obtuse triangle.
So this is an obtuse isosceles.
The sum of the first 14 terms of the finite geometric series 0.5+ (-1) +2+... is -2730.5
<h3>How to determine the sum of the series?</h3>
The series is given as:
0.5+ (-1) +2+...
The above series is a geometric series, with the following parameters:
- First term, a = 0.5
- Common ratio, r = -2
- Number of terms, n = 14
The sum of the first 14 terms is calculated using:
![S_n= a *(1 - r^n) \div (1 - r)](https://tex.z-dn.net/?f=S_n%3D%20a%20%2A%281%20-%20r%5En%29%20%5Cdiv%20%281%20-%20r%29)
So, we have:
![S_{14}= 0.5 *(1 - (-2)^{14}) \div (1 + 2)](https://tex.z-dn.net/?f=S_%7B14%7D%3D%200.5%20%2A%281%20-%20%28-2%29%5E%7B14%7D%29%20%5Cdiv%20%281%20%2B%202%29)
Evaluate
![S_{14}= -2730.5](https://tex.z-dn.net/?f=S_%7B14%7D%3D%20-2730.5)
Hence, the sum of the series is -2730.5
Read more about series at:
brainly.com/question/6561461
#SPJ1