Answer:
Step-by-step explanation:
1. The slope is -5/2
2. There is no slope for the second one it's just y=3
3. The slope is 3
4. These are perpendicular lines
5. These lines are parallel.
6. These lines are neither perpendicular nor parallel.
7. These lines are perpendicular
8. y = 4/3x - 2
9. y = -1/2x + 5
10. x = -1
Hope this helps!
<span>the answer would be 0.27777777777</span>
Applying the limit concept, it is found that the limit is 2 for 3 positive values of b.
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The function given is:
![f(x) = 0.1x^4 - 0.5x^3 - 3.3x^2 + 7.7x - 1.99](https://tex.z-dn.net/?f=f%28x%29%20%3D%200.1x%5E4%20-%200.5x%5E3%20-%203.3x%5E2%20%2B%207.7x%20-%201.99)
The limit of the function as x tends to b is:
![\lim_{x \rightarrow b} f(x) = 0.1b^4 - 0.5b^3 - 3.3b^2 + 7.7b - 1.99](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Crightarrow%20b%7D%20f%28x%29%20%3D%200.1b%5E4%20-%200.5b%5E3%20-%203.3b%5E2%20%2B%207.7b%20-%201.99)
To find when the result of the limit is 2:
![0.1b^4 - 0.5b^3 - 3.3b^2 + 7.7b - 1.99 = 2](https://tex.z-dn.net/?f=0.1b%5E4%20-%200.5b%5E3%20-%203.3b%5E2%20%2B%207.7b%20-%201.99%20%3D%202)
Placing into standard polynomial format:
![0.1b^4 - 0.5b^3 - 3.3b^2 + 7.7b - 3.99 = 0](https://tex.z-dn.net/?f=0.1b%5E4%20-%200.5b%5E3%20-%203.3b%5E2%20%2B%207.7b%20-%203.99%20%3D%200)
Using a calculator, the solutions are: ![b_1 = -4.9978613719838, b_2 = 0.84536762603715, b_3 = 1.1540644992178, b_4 = 7.9984292467288](https://tex.z-dn.net/?f=b_1%20%3D%20-4.9978613719838%2C%20b_2%20%3D%200.84536762603715%2C%20b_3%20%3D%201.1540644992178%2C%20b_4%20%3D%207.9984292467288)
Of those, 3 are positive, thus the limit is 2 for 3 positive values of b.
A similar problem is given at brainly.com/question/23625870
Answer:
The length of DF must be between 21 and 53.
Step-by-step explanation:
In a triangle, the length of two sides added together must exceed the length of the 3rd side. So, since EF is the shortest of the two givens, we know that EF + DF must be greater than DE. So we can plug in these numbers to find the minimum.
EF + DF > DE
16 + DF > 37
DF > 21
Now, for the upper maximum, we know that the two given lengths must be greater than the length of DF. So again, we can solve for the maximum using the amounts.
DE + EF > DF
37 + 16 > DF
53 > DF
With these two in mind, we know that DF must be between 21 and 53