For this case we have that by definition, the slope of a line is given by:
![m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%20%7By_%20%7B2%7D%20-y_%20%7B1%7D%7D%20%7Bx_%20%7B2%7D%20-x_%20%7B1%7D%7D)
Where:
and
are two points through which the line passes.
Question 1:
According to the image, we have the following points:
![(x_ {1}, y_ {1}) :( 2, -6)\\(x_ {2}, y_ {2}): (- 6,5)](https://tex.z-dn.net/?f=%28x_%20%7B1%7D%2C%20y_%20%7B1%7D%29%20%3A%28%202%2C%20-6%29%5C%5C%28x_%20%7B2%7D%2C%20y_%20%7B2%7D%29%3A%20%28-%206%2C5%29)
Substituting we have:
![m = \frac {5 - (- 6)} {- 6-2} = \frac {5 + 6} {- 8} = \frac {11} {- 8} = - \frac {11} {8}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%20%7B5%20-%20%28-%206%29%7D%20%7B-%206-2%7D%20%3D%20%5Cfrac%20%7B5%20%2B%206%7D%20%7B-%208%7D%20%3D%20%5Cfrac%20%7B11%7D%20%7B-%208%7D%20%3D%20-%20%5Cfrac%20%7B11%7D%20%7B8%7D)
Thus, the slope is: ![- \frac {11} {8}](https://tex.z-dn.net/?f=-%20%5Cfrac%20%7B11%7D%20%7B8%7D)
Question 2:
According to the image, the line goes through the following points:
![(x_ {1}, y_ {1}): (- 1,2)\\(x_ {2}, y_ {2}) :( 2, -2)](https://tex.z-dn.net/?f=%28x_%20%7B1%7D%2C%20y_%20%7B1%7D%29%3A%20%28-%201%2C2%29%5C%5C%28x_%20%7B2%7D%2C%20y_%20%7B2%7D%29%20%3A%28%202%2C%20-2%29)
Substituting we have:
![m = \frac {-2-2} {2 - (- 1)} = \frac {-4} {2 + 1} = \frac {-4} {3} = - \frac {4} {3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%20%7B-2-2%7D%20%7B2%20-%20%28-%201%29%7D%20%3D%20%5Cfrac%20%7B-4%7D%20%7B2%20%2B%201%7D%20%3D%20%5Cfrac%20%7B-4%7D%20%7B3%7D%20%3D%20-%20%5Cfrac%20%7B4%7D%20%7B3%7D)
Thus, the slope is: ![- \frac {4} {3}](https://tex.z-dn.net/?f=-%20%5Cfrac%20%7B4%7D%20%7B3%7D)
Answer:
Slope 1: ![- \frac {11} {8}](https://tex.z-dn.net/?f=-%20%5Cfrac%20%7B11%7D%20%7B8%7D)
Slope 2:![- \frac {4} {3}](https://tex.z-dn.net/?f=-%20%5Cfrac%20%7B4%7D%20%7B3%7D)
Answer:
Step-by-step explanation:
symmmmmmmmmmm
∑ ( from n = 1 to n =5 ) 3 · ( -2 ) ^( n -1 )
a 1 = 3 · ( -2 ) ^0 = 3
a 2 = 3 · ( - 2 ) = - 6
a 3 = 3 · 4 = 12
a 4 = 3 · ( - 8 ) = - 24
a 5 = 3 · 16 = 48
3 - 6 + 12 - 24 + 48 = 33
Answer: C ) 33
Step-by-step explanation:
<h3>
Need to FinD :</h3>
- We have to find the measures of other two angles of triangle.
![\red{\frak{Given}} \begin{cases} & \sf{The\ measure\ of\ one\ angle\ of\ traingle\ is\ {\pmb{\sf{10^{\circ}}}}.} \\ & \sf{The\ other\ two\ angles\ are\ in\ the\ ratio\ of\ {\pmb{\sf{3\ :\ 14}}}.} \end{cases}](https://tex.z-dn.net/?f=%20%5Cred%7B%5Cfrak%7BGiven%7D%7D%20%5Cbegin%7Bcases%7D%20%26%20%5Csf%7BThe%5C%20measure%5C%20of%5C%20one%5C%20angle%5C%20of%5C%20traingle%5C%20is%5C%20%7B%5Cpmb%7B%5Csf%7B10%5E%7B%5Ccirc%7D%7D%7D%7D.%7D%20%5C%5C%20%26%20%5Csf%7BThe%5C%20other%5C%20two%5C%20angles%5C%20are%5C%20in%5C%20the%5C%20ratio%5C%20of%5C%20%7B%5Cpmb%7B%5Csf%7B3%5C%20%3A%5C%2014%7D%7D%7D.%7D%20%5Cend%7Bcases%7D)
We know that,
- The other two angles of triangle are in the ratio of 3 : 14. So, let us consider the other two angles of the triangle be 3x and 14x.
Angle sum property,
- The angle sum property of triangle states that the sum of interior angles of triangle is 180°. By using this property, we'll find the other two angles of the triangle.
![\rule{200}{3}](https://tex.z-dn.net/?f=%5Crule%7B200%7D%7B3%7D)
![\sf \dashrightarrow {10^{\circ}\ +\ 3x\ +\ 14x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {10^{\circ}\ +\ 17x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 180^{\circ}\ -\ 10^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 170^{\circ}} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{170^{\circ}}}{\cancel{17}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 10^{\circ}.}}}}_{\sf \blue {\tiny{Value\ of\ x}}}}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cdashrightarrow%20%7B10%5E%7B%5Ccirc%7D%5C%20%2B%5C%203x%5C%20%2B%5C%2014x%5C%20%3D%5C%20180%5E%7B%5Ccirc%7D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Csf%20%5Cdashrightarrow%20%7B10%5E%7B%5Ccirc%7D%5C%20%2B%5C%2017x%5C%20%3D%5C%20180%5E%7B%5Ccirc%7D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Csf%20%5Cdashrightarrow%20%7B17x%5C%20%3D%5C%20180%5E%7B%5Ccirc%7D%5C%20-%5C%2010%5E%7B%5Ccirc%7D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Csf%20%5Cdashrightarrow%20%7B17x%5C%20%3D%5C%20170%5E%7B%5Ccirc%7D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Csf%20%5Cdashrightarrow%20%7Bx%5C%20%3D%5C%20%5Cdfrac%7B%5Ccancel%7B170%5E%7B%5Ccirc%7D%7D%7D%7B%5Ccancel%7B17%7D%7D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cdashrightarrow%20%7B%5Cunderbrace%7B%5Cboxed%7B%5Cpink%7B%5Cfrak%7Bx%5C%20%3D%5C%2010%5E%7B%5Ccirc%7D.%7D%7D%7D%7D_%7B%5Csf%20%5Cblue%20%7B%5Ctiny%7BValue%5C%20of%5C%20x%7D%7D%7D%7D%20)
∴ Hence, the value of x is 10°. Now, let us find out the other two angles of the triangle.
![\rule{200}{3}](https://tex.z-dn.net/?f=%5Crule%7B200%7D%7B3%7D)
Second AnglE :
∴ Hence, the measure of the second angle of triangle is 30°. Now, let us find out the third angle of triangle.
![\rule{200}{3}](https://tex.z-dn.net/?f=%5Crule%7B200%7D%7B3%7D)
Third AnglE :
∴ Hence, the measure of the third angle of the triangle is 140°.
Answer:
37
Step-by-step explanation:
35^2+12^2=1369
√1369=37