Answer:
Step-by-step explanation:
Well 8 hundredths is also know as 0.08 if we put in in the decimal form.
I hope this helps :D
Answer:
![\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190](https://tex.z-dn.net/?f=%20%5Ctheta%20%3D%20cos%5E%7B-1%7D%20%28%5Cfrac%7B10%7D%7B%5Csqrt%7B9%7D%20%5Csqrt%7B25%7D%7D%29%3Dcos%5E%7B-1%7D%20%28%5Cfrac%7B10%7D%7B15%7D%29%20%3D%20cos%5E%7B-1%7D%20%28%5Cfrac%7B2%7D%7B3%7D%29%20%3D%2048.190)
Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel
And the anfle is approximately ![\theta \approx 48](https://tex.z-dn.net/?f=%20%5Ctheta%20%5Capprox%2048)
Step-by-step explanation:
For this case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.
a=[1,2,-2], b=[4,0,-3,]
The dot product on this case is:
![a b= (1)*(4) + (2)*(0)+ (-2)*(-3)=10](https://tex.z-dn.net/?f=%20a%20b%3D%20%281%29%2A%284%29%20%2B%20%282%29%2A%280%29%2B%20%28-2%29%2A%28-3%29%3D10)
Since the dot product is not equal to zero then the two vectors are not orthogonal.
Now we can calculate the magnitude of each vector like this:
![|a|= \sqrt{(1)^2 +(2)^2 +(-2)^2}=\sqrt{9} =3](https://tex.z-dn.net/?f=%20%7Ca%7C%3D%20%5Csqrt%7B%281%29%5E2%20%2B%282%29%5E2%20%2B%28-2%29%5E2%7D%3D%5Csqrt%7B9%7D%20%3D3)
![|b| =\sqrt{(4)^2 +(0)^2 +(-3)^2}=\sqrt{25}= 5](https://tex.z-dn.net/?f=%20%7Cb%7C%20%3D%5Csqrt%7B%284%29%5E2%20%2B%280%29%5E2%20%2B%28-3%29%5E2%7D%3D%5Csqrt%7B25%7D%3D%205)
And finally we can calculate the angle between the vectors like this:
![cos \theta = \frac{ab}{|a| |b|}](https://tex.z-dn.net/?f=%20cos%20%5Ctheta%20%3D%20%5Cfrac%7Bab%7D%7B%7Ca%7C%20%7Cb%7C%7D)
And the angle is given by:
![\theta = cos^{-1} (\frac{ab}{|a| |b|})](https://tex.z-dn.net/?f=%20%5Ctheta%20%3D%20cos%5E%7B-1%7D%20%28%5Cfrac%7Bab%7D%7B%7Ca%7C%20%7Cb%7C%7D%29)
If we replace we got:
![\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190](https://tex.z-dn.net/?f=%20%5Ctheta%20%3D%20cos%5E%7B-1%7D%20%28%5Cfrac%7B10%7D%7B%5Csqrt%7B9%7D%20%5Csqrt%7B25%7D%7D%29%3Dcos%5E%7B-1%7D%20%28%5Cfrac%7B10%7D%7B15%7D%29%20%3D%20cos%5E%7B-1%7D%20%28%5Cfrac%7B2%7D%7B3%7D%29%20%3D%2048.190)
Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel
And the anfle is approximately ![\theta \approx 48](https://tex.z-dn.net/?f=%20%5Ctheta%20%5Capprox%2048)
Answer:
![y = \frac{-x}{3} + 5](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B-x%7D%7B3%7D%20%2B%205)
Step-by-step explanation:
Given A (x₁, y₁) = ( -6, 7) and B (x₂, y₂) = (-3, 6)
Slope of line passing through points ( -6, 7) and (-3, 6) is:
m = ![\frac{y_{2} -y_{1}}{x_{2} -x_{1}} =\frac{6 - 7}{-3 + 6} =\frac{-1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D%20-y_%7B1%7D%7D%7Bx_%7B2%7D%20-x_%7B1%7D%7D%20%3D%5Cfrac%7B6%20-%207%7D%7B-3%20%2B%206%7D%20%3D%5Cfrac%7B-1%7D%7B3%7D)
Now, the equation of line in point-slope form:
(y - y₁) = m (x - x₁)
Substituting the value of m and (x₁, y₁) = ( -6, 7) in above equation,
![(y - 7) = \frac{-1}{3}(x - (-6))](https://tex.z-dn.net/?f=%28y%20-%207%29%20%3D%20%5Cfrac%7B-1%7D%7B3%7D%28x%20-%20%28-6%29%29)
![(y - 7) = \frac{-1}{3}(x + 6)](https://tex.z-dn.net/?f=%28y%20-%207%29%20%3D%20%5Cfrac%7B-1%7D%7B3%7D%28x%20%2B%206%29)
![3y - 21 = -x - 6](https://tex.z-dn.net/?f=3y%20-%2021%20%3D%20-x%20-%206)
![3y = -x - 6 + 21](https://tex.z-dn.net/?f=3y%20%3D%20-x%20-%206%20%2B%2021)
![3y = -x + 15](https://tex.z-dn.net/?f=3y%20%3D%20-x%20%2B%2015)
![y = \frac{-x + 15}{3}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B-x%20%2B%2015%7D%7B3%7D)
![y = \frac{-x}{3} + 5](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B-x%7D%7B3%7D%20%2B%205)
Option B is the correct answer.
Answer:
The 4th option, 10g + 24 = t
Step-by-step explanation:
It costs 24 dollars per month no matter what.
$10 * the amount of GB you want
Add those two values to get the total cost per month.
In this case you want 5 GB, so substitute the g in the equation for 5. You will get:
10 * 5 +24 = t
50 + 24 = t
74 = t
So it costs 74 dollars per month to get 5 GB.
Im confused what the question is...