Step-by-step explanation:
The angle relationship is vertically opposite angles.
so
x = 77°
Answer:
A factor that is a prime number. In other words: any of the prime numbers that can be multiplied to give the original number. Example: The prime factors of 15 are 3 and 5 (because 3×5=15, and 3 and 5 are prime numbers). See: Prime Number. Prime Factorization.
Answer:
b. 768
Explanation:
From the given sequence, we can note that we multiply each term by 4 to get the next one.
This is elaborated as follows:
3 * 4 = 12
12 * 4 = 48
48 * 4 = 192
192 * 4 = 768
This means that the next term in the sequence would be 768
Hope this helps :)
Answer:
The answer is the option A
![\frac{1}{2}(\sqrt{[(y2)^{2}+(x2)^{2}]*[(y1)^{2}+(x1)^{2}]})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28%5Csqrt%7B%5B%28y2%29%5E%7B2%7D%2B%28x2%29%5E%7B2%7D%5D%2A%5B%28y1%29%5E%7B2%7D%2B%28x1%29%5E%7B2%7D%5D%7D%29)
Step-by-step explanation:
see the attached figure with letters to better understand the problem
we know that
The area of the triangle is equal to
![A=\frac{1}{2}bh](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7Dbh)
where
b is the base
h is the height
In this problem
![b=AB, h=AC](https://tex.z-dn.net/?f=b%3DAB%2C%20h%3DAC)
the formula to calculate the distance between two points is equal to
Find the distance AB
![A(0,0), B(x2,y2)](https://tex.z-dn.net/?f=A%280%2C0%29%2C%20B%28x2%2Cy2%29)
substitute
Find the distance AC
![A(0,0), C(x1,y1)](https://tex.z-dn.net/?f=A%280%2C0%29%2C%20C%28x1%2Cy1%29)
substitute
Find the area of the triangle
we have
![b=\sqrt{(y2)^{2}+(x2)^{2}}, h=\sqrt{(y1)^{2}+(x1)^{2}}](https://tex.z-dn.net/?f=b%3D%5Csqrt%7B%28y2%29%5E%7B2%7D%2B%28x2%29%5E%7B2%7D%7D%2C%20h%3D%5Csqrt%7B%28y1%29%5E%7B2%7D%2B%28x1%29%5E%7B2%7D%7D)
substitute
![A=\frac{1}{2}(\sqrt{[(y2)^{2}+(x2)^{2}]*[(y1)^{2}+(x1)^{2}]})](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%28%5Csqrt%7B%5B%28y2%29%5E%7B2%7D%2B%28x2%29%5E%7B2%7D%5D%2A%5B%28y1%29%5E%7B2%7D%2B%28x1%29%5E%7B2%7D%5D%7D%29)
The coordinates of the point that partitions PT is (5, 11).
Solution:
Given P(2, 2) and T(7, 17).
Line segment PT is divided the coordinates of the point in the ratio 3 : 2.
Let R be the divided point the line segment PT.
<u>Section Formula:</u>
The point (x, y) which divides the line segment of the points
and
in the ratio m : n is
![$\left(\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n}\right)](https://tex.z-dn.net/?f=%24%5Cleft%28%5Cfrac%7Bm%20x_%7B2%7D%20%2B%20n%20x_%7B1%7D%7D%7Bm%20%2B%20n%7D%2C%20%5Cfrac%7Bm%20y_%7B2%7D%20%2B%20n%20y_%7B1%7D%7D%7Bm%20%2B%20n%7D%5Cright%29)
Here
and m = 3, n = 2
Substitute these in the given formula.
![$R(x)=\left(\frac{3\times 7 + 2\times2}{3+2}, \frac{3\times17 + 2\times2}{3+2}\right)](https://tex.z-dn.net/?f=%24R%28x%29%3D%5Cleft%28%5Cfrac%7B3%5Ctimes%207%20%2B%202%5Ctimes2%7D%7B3%2B2%7D%2C%20%5Cfrac%7B3%5Ctimes17%20%2B%202%5Ctimes2%7D%7B3%2B2%7D%5Cright%29)
![$R(x)=\left(\frac{21 + 4}{5}, \frac{51 + 4}{5}\right)](https://tex.z-dn.net/?f=%24R%28x%29%3D%5Cleft%28%5Cfrac%7B21%20%2B%204%7D%7B5%7D%2C%20%5Cfrac%7B51%20%2B%204%7D%7B5%7D%5Cright%29)
![$R(x)=\left(\frac{25}{5}, \frac{55}{5}\right)](https://tex.z-dn.net/?f=%24R%28x%29%3D%5Cleft%28%5Cfrac%7B25%7D%7B5%7D%2C%20%5Cfrac%7B55%7D%7B5%7D%5Cright%29)
![$R(x)=(5, 11)](https://tex.z-dn.net/?f=%24R%28x%29%3D%285%2C%2011%29)
Hence the coordinates of the point that partitions PT is (5, 11).