You can find any ordered pair in which the y coordinate is 4 times the x coordinate.
For example, an ordered pair could be (2,8) or (5,20)
Answer:
The larger acute angle is equal to 50.8 degrees.
Step-by-step explanation:
Let's solve for both of the acute angles for the purpose of checking our work at the end with angle A being the top angle and angle B being the one on the base of the triangle (that's not the 90 degrees one). Determining whether to use sin/cos/tan comes from SOH-CAH-TOA.
A = cos^-1 (2√6/2√15)
However, you need to move the radical out of the denominator by multiplying √15 to the numerator and denominator. You should come up with (2√90)/30. So,
A = cos^-1 (2√90/30) = 50.768 degrees.
B = sin^-1 (2√90/30) = 39.231 degrees.
Now, we can check the work by adding the 2 angles to 90 and, if it comes to 180, it's right.
cos^-1 (2√90/30) + sin^-1 (2√90/30) + 90 = 180.
If you have any questions on where I got a formula or any step, feel free to ask in the comments!
Answer:
Step-by-step explanation:
Keep these rules in mind:
- (a + b)² = a² + 2ab + b²
- (a - b)² = a² - 2ab + b²
- (a + b)(a - b) = a² - b²
Firstly, solve the exponent and multiplication:
![4x^2-20x+25-0.5x](https://tex.z-dn.net/?f=4x%5E2-20x%2B25-0.5x%3C4x%5E2-1-15)
Next, combine like terms:
![4x^2-20.5x+25](https://tex.z-dn.net/?f=4x%5E2-20.5x%2B25%3C4x%5E2-16)
Next, subtract 4x² on both sides:
![-20.5x+25](https://tex.z-dn.net/?f=-20.5x%2B25%3C-16)
Next, subtract 25 on both sides:
![-20.5x](https://tex.z-dn.net/?f=-20.5x%3C-41)
Lastly, divide both sides by -20.5. And since you are dividing by a <u>negative</u>, flip the inequality sign:
![x>2](https://tex.z-dn.net/?f=x%3E2)
<u>Your answer is x > 2.</u>
Answer:
And we can find this probability using the normal standard distribution or excel and we got:
And if we convert this into % we got 84% so then the best solution would be:
84%
Step-by-step explanation:
Let X the random variable that represent the size of gasoline tanks of a population, and for this case we know the distribution for X is given by:
Where
and
We are interested on this probability
And we can use the z score formula given by:
Using the last formula we got:
And we can find this probability using the normal standard distribution or excel and we got:
And if we convert this into % we got 84% so then the best solution would be:
84%