Answer:
![\frac{\sqrt3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt3%7D%7B2%7D)
Step-by-step explanation:
![sin(A)=\frac{1}{2}](https://tex.z-dn.net/?f=sin%28A%29%3D%5Cfrac%7B1%7D%7B2%7D)
//this is retrieved from looking at the unit circle
![cos(A) = cos(\frac{\pi}{6}) = \frac{\sqrt3}{2}](https://tex.z-dn.net/?f=cos%28A%29%20%3D%20cos%28%5Cfrac%7B%5Cpi%7D%7B6%7D%29%20%3D%20%5Cfrac%7B%5Csqrt3%7D%7B2%7D)
Point (4,8) reflected across the y-axis is (-4,8).
Step-by-step explanation:
Point (4,8) reflected across the y-axis is (-4,8).
When reflecting a pair of numbers across the y-axis, the x-axis changes to its opposite.
Thus, in this case, 4 would change to -4.
I hope this helped!!
Answer: the answer is 35.1
Step-by-step explanation:
The answer should be 85,000
Answer:
Option (C)
Step-by-step explanation:
In this question we will use the property " similarity of the triangles".
If DE and AC are parallel two triangles BED and BCA will be similar, corresponding sides of the triangles will be proportional.
![\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BBA%7D%7D%7B%5Ctext%7BBD%7D%7D%3D%5Cfrac%7B%5Ctext%7BBC%7D%7D%7B%5Ctext%7BBE%7D%7D)
Option (A).
![\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BBA%7D%7D%7B%5Ctext%7BBD%7D%7D%3D%5Cfrac%7B%5Ctext%7BBC%7D%7D%7B%5Ctext%7BBE%7D%7D)
![\frac{22+12}{12}=\frac{14+26}{14}](https://tex.z-dn.net/?f=%5Cfrac%7B22%2B12%7D%7B12%7D%3D%5Cfrac%7B14%2B26%7D%7B14%7D)
![\frac{34}{12}=\frac{40}{14}](https://tex.z-dn.net/?f=%5Cfrac%7B34%7D%7B12%7D%3D%5Cfrac%7B40%7D%7B14%7D)
![\frac{17}{6}=\frac{20}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B17%7D%7B6%7D%3D%5Cfrac%7B20%7D%7B7%7D)
But ![\frac{17}{6}\neq \frac{20}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B17%7D%7B6%7D%5Cneq%20%5Cfrac%7B20%7D%7B7%7D)
Therefore, given triangles are not similar.
AC and DE are not parallel.
Option (B).
![\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BBA%7D%7D%7B%5Ctext%7BBD%7D%7D%3D%5Cfrac%7B%5Ctext%7BBC%7D%7D%7B%5Ctext%7BBE%7D%7D)
![\frac{25}{25-7}=\frac{21+9}{21}](https://tex.z-dn.net/?f=%5Cfrac%7B25%7D%7B25-7%7D%3D%5Cfrac%7B21%2B9%7D%7B21%7D)
![\frac{25}{18}=\frac{30}{21}](https://tex.z-dn.net/?f=%5Cfrac%7B25%7D%7B18%7D%3D%5Cfrac%7B30%7D%7B21%7D)
![\frac{25}{18}=\frac{10}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B25%7D%7B18%7D%3D%5Cfrac%7B10%7D%7B7%7D)
But ![\frac{25}{18}\neq \frac{10}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B25%7D%7B18%7D%5Cneq%20%5Cfrac%7B10%7D%7B7%7D)
Therefore, AC and DE are not parallel.
Option (C).
![\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BBA%7D%7D%7B%5Ctext%7BBD%7D%7D%3D%5Cfrac%7B%5Ctext%7BBC%7D%7D%7B%5Ctext%7BBE%7D%7D)
![\frac{22.5+15}{15}=\frac{40}{40-24}](https://tex.z-dn.net/?f=%5Cfrac%7B22.5%2B15%7D%7B15%7D%3D%5Cfrac%7B40%7D%7B40-24%7D)
![\frac{37.5}{15}=\frac{40}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B37.5%7D%7B15%7D%3D%5Cfrac%7B40%7D%7B16%7D)
2.5 = 2.5
Therefore, AC║DE.
Option (D).
![\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BBA%7D%7D%7B%5Ctext%7BBD%7D%7D%3D%5Cfrac%7B%5Ctext%7BBC%7D%7D%7B%5Ctext%7BBE%7D%7D)
![\frac{17.5+5}{17.5}=\frac{20.4+6}{20.4}](https://tex.z-dn.net/?f=%5Cfrac%7B17.5%2B5%7D%7B17.5%7D%3D%5Cfrac%7B20.4%2B6%7D%7B20.4%7D)
![\frac{22.5}{17.5}=\frac{26.4}{20.4}](https://tex.z-dn.net/?f=%5Cfrac%7B22.5%7D%7B17.5%7D%3D%5Cfrac%7B26.4%7D%7B20.4%7D)
![\frac{9}{7}=\frac{22}{17}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B7%7D%3D%5Cfrac%7B22%7D%7B17%7D)
But ![\frac{9}{7}\neq \frac{22}{17}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B7%7D%5Cneq%20%5Cfrac%7B22%7D%7B17%7D)
Therefore, AC and DE are not parallel.
Option (C) will be the answer.