Answer:
Therefore the slope of the line that passes through the points (-9, -8),(−15,−16) is
![Slope=\dfrac{4}{3}](https://tex.z-dn.net/?f=Slope%3D%5Cdfrac%7B4%7D%7B3%7D)
Step-by-step explanation:
Given:
Let,
point A( x₁ , y₁) ≡ ( -9 ,-8)
point B( x₂ , y₂ )≡ (-15 ,-16)
To Find:
Slope = ?
Solution:
Slope of Line Segment AB is given as
![Slope(AB)=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }](https://tex.z-dn.net/?f=Slope%28AB%29%3D%5Cdfrac%7By_%7B2%7D-y_%7B1%7D%20%7D%7Bx_%7B2%7D-x_%7B1%7D%20%7D)
Substituting the values we get
![Slope(AB)=\dfrac{-16-(-8)}{-15-(-9)}\\\\Slope(AB)=\dfrac{-16+8}{-15+9}\\\\Slope(AB)=\dfrac{-8}{-6}=\dfrac{4}{3}](https://tex.z-dn.net/?f=Slope%28AB%29%3D%5Cdfrac%7B-16-%28-8%29%7D%7B-15-%28-9%29%7D%5C%5C%5C%5CSlope%28AB%29%3D%5Cdfrac%7B-16%2B8%7D%7B-15%2B9%7D%5C%5C%5C%5CSlope%28AB%29%3D%5Cdfrac%7B-8%7D%7B-6%7D%3D%5Cdfrac%7B4%7D%7B3%7D)
Therefore the slope of the line that passes through the points (-9, -8),(−15,−16) is
![Slope(AB)=\dfrac{4}{3}](https://tex.z-dn.net/?f=Slope%28AB%29%3D%5Cdfrac%7B4%7D%7B3%7D)
Answer:
9
Step-by-step explanation:
.9*10=10
it's basically simple multiplication with a decimal
Answer:
14,793
Step-by-step explanation:
![431 \div 9](https://tex.z-dn.net/?f=431%20%5Cdiv%209%20)
=47.8888 when you round it up you can get get about 48 then you estimate to about 50.
Answer:
![B \approx 32.1\°; A \approx 39.0\°](https://tex.z-dn.net/?f=B%20%5Capprox%2032.1%5C%C2%B0%3B%20A%20%5Capprox%2039.0%5C%C2%B0)
Step-by-step explanation:
Sine theorem: in any triangle, the ratio between a side and the sine of the opposite angle is constant
![\frac{sin\ \alpha}a = \frac{sin\ \beta}b =\frac{sin\ \gamma}c](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%5C%20%5Calpha%7Da%20%3D%20%5Cfrac%7Bsin%5C%20%5Cbeta%7Db%20%3D%5Cfrac%7Bsin%5C%20%5Cgamma%7Dc)
In our case, for the left triangle,
![\frac {sin\ 103\°}{11} =\frac{sin\ B} 6 \rightarrow sin\ B = \frac6{11} sin\ 103\°](https://tex.z-dn.net/?f=%5Cfrac%20%7Bsin%5C%20103%5C%C2%B0%7D%7B11%7D%20%3D%5Cfrac%7Bsin%5C%20B%7D%206%20%5Crightarrow%20sin%5C%20B%20%3D%20%5Cfrac6%7B11%7D%20sin%5C%20103%5C%C2%B0)
Time to grab a calculator and crunch numbers. Double check your calculator is in degrees and not in radians (plug in sin 30°, if you're getting 0.5 you're good) and you will get
![sin\ B \approx 0.53 \rightarrow B \approx 32.1\°](https://tex.z-dn.net/?f=sin%5C%20B%20%5Capprox%200.53%20%5Crightarrow%20B%20%5Capprox%2032.1%5C%C2%B0)
Same difference with the right triangle. With the same calculations
![sin\ A = \frac{26}{41} sin 83\° \approx 0.68 \rightarrow A \approx 39.0\°](https://tex.z-dn.net/?f=sin%5C%20A%20%3D%20%5Cfrac%7B26%7D%7B41%7D%20sin%2083%5C%C2%B0%20%5Capprox%200.68%20%5Crightarrow%20A%20%5Capprox%2039.0%5C%C2%B0)