Answer:
x = 6
Step-by-step explanation:
According to Exterior Angle Property of a triangle , measure of an exterior angle is the sum of its opposite interior angles.
Using the exterior angle property ,
![17x - 23 = 3x + 17 + 8x - 4](https://tex.z-dn.net/?f=17x%20-%2023%20%3D%203x%20%2B%2017%20%2B%208x%20-%204)
![= > 17x - 23 = 11x + 13](https://tex.z-dn.net/?f=%20%3D%20%20%3E%2017x%20-%2023%20%3D%2011x%20%2B%2013)
![= > 17x - 13x = 23 + 13](https://tex.z-dn.net/?f=%20%3D%20%20%3E%2017x%20-%2013x%20%3D%2023%20%2B%2013)
![= > 6x = 36](https://tex.z-dn.net/?f=%20%20%3D%20%20%3E%206x%20%3D%2036)
![= > x = \frac{36}{6} = 6](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20x%20%3D%20%20%5Cfrac%7B36%7D%7B6%7D%20%20%3D%206)
Answer:
–12 < m < 4
Step-by-step explanation:
I did it on ed 2020
Answer:
![a=36.87\ units](https://tex.z-dn.net/?f=a%3D36.87%5C%20units)
![B=57.47^o](https://tex.z-dn.net/?f=B%3D57.47%5Eo)
![C=71.53^o](https://tex.z-dn.net/?f=C%3D71.53%5Eo)
Step-by-step explanation:
step 1
Find the length side a
Applying the law of cosines
![a^2=b^2+c^2-2(b)(c)cos(A)](https://tex.z-dn.net/?f=a%5E2%3Db%5E2%2Bc%5E2-2%28b%29%28c%29cos%28A%29)
substitute the given values
![a^2=40^2+45^2-2(40)(45)cos(51^o)](https://tex.z-dn.net/?f=a%5E2%3D40%5E2%2B45%5E2-2%2840%29%2845%29cos%2851%5Eo%29)
![a^2=1,359.4466](https://tex.z-dn.net/?f=a%5E2%3D1%2C359.4466)
![a=36.87\ units](https://tex.z-dn.net/?f=a%3D36.87%5C%20units)
step 2
Find the measure of angle B
Applying the law of sines
![\frac{a}{sin(A)} =\frac{b}{sin(B)}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%28A%29%7D%20%3D%5Cfrac%7Bb%7D%7Bsin%28B%29%7D)
substitute the given values
![\frac{36.87}{sin(51^o)} =\frac{40}{sin(B)}](https://tex.z-dn.net/?f=%5Cfrac%7B36.87%7D%7Bsin%2851%5Eo%29%7D%20%3D%5Cfrac%7B40%7D%7Bsin%28B%29%7D)
![sin(B)=\frac{sin(51^o)}{36.87}{40}](https://tex.z-dn.net/?f=sin%28B%29%3D%5Cfrac%7Bsin%2851%5Eo%29%7D%7B36.87%7D%7B40%7D)
![B=sin^{-1}(\frac{sin(51^o)}{36.87}{40})=57.47^o](https://tex.z-dn.net/?f=B%3Dsin%5E%7B-1%7D%28%5Cfrac%7Bsin%2851%5Eo%29%7D%7B36.87%7D%7B40%7D%29%3D57.47%5Eo)
step 3
Find the measure of angle C
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
![A+B+C=180^o](https://tex.z-dn.net/?f=A%2BB%2BC%3D180%5Eo)
substitute the given values
![51^o+57.47^o+C=180^o](https://tex.z-dn.net/?f=51%5Eo%2B57.47%5Eo%2BC%3D180%5Eo)
![108.47^o+C=180^o](https://tex.z-dn.net/?f=108.47%5Eo%2BC%3D180%5Eo)
![C=180^o-108.47^o=71.53^o](https://tex.z-dn.net/?f=C%3D180%5Eo-108.47%5Eo%3D71.53%5Eo)
Answer:
Yes, it makes it true
Step-by-step explanation:
Plug in 3 and 10 as x and y into the inequality:
y > 2x + 2
10 > 2(3) + 2
10 > 6 + 2
10 > 8
Since 10 is bigger than 8, this inequality is true.
So, (3, 10) makes the inequality true.
Answer:
<u><em>3 cm</em></u>
Step-by-step explanation:
<em>Volume of a cube = (edge)³</em>
<em>27 = (edge)³</em>
<em>edge = ∛27</em>
<em>edge = 3 cm</em>