Is this a trick question, i assume you just add all the number getting 2.4 miles or he is 0 miles away from his house when he completes his jog
Answer:
x < 22
Step-by-step explanation:
X - 8 < 14
Add x to each side
X - 8+8 < 14+8
x < 22
Step-by-step explanation:
Answer: c=5.4
The two roots are 3/5 and 9/5
Step-by-step explanation:
assume 5x2−12x c=0 is supposed to be 5x^2 - 12x + c = 0
p = (12 + sqrt(144-20c))/10
q = (12 - sqrt(144-20c))/10
p-3q=0,
1.2 + 0.1sqrt(144-20c) +
-3.6 + 0.3sqrt(144-20c) = 0
-2.4 + 0.4sqrt(144-20c) +2.4 = 2.4
sqrt(144-20c) = 2.4/0.4 = 6
144-20c=36
144-36=20c
c = 108/20 = 5.4
5x^2-12x+5.4=0
x = 3/5 or x = 9/5
Answer: ![\frac{\sqrt[4]{10xy^3}}{2y}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B4%5D%7B10xy%5E3%7D%7D%7B2y%7D)
where y is positive.
The 2y in the denominator is not inside the fourth root
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Work Shown:
![\sqrt[4]{\frac{5x}{8y}}\\\\\\\sqrt[4]{\frac{5x*2y^3}{8y*2y^3}}\ \ \text{.... multiply top and bottom by } 2y^3\\\\\\\sqrt[4]{\frac{10xy^3}{16y^4}}\\\\\\\frac{\sqrt[4]{10xy^3}}{\sqrt[4]{16y^4}} \ \ \text{ ... break up the fourth root}\\\\\\\frac{\sqrt[4]{10xy^3}}{\sqrt[4]{(2y)^4}} \ \ \text{ ... rewrite } 16y^4 \text{ as } (2y)^4\\\\\\\frac{\sqrt[4]{10xy^3}}{2y} \ \ \text{... where y is positive}\\\\\\](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cfrac%7B5x%7D%7B8y%7D%7D%5C%5C%5C%5C%5C%5C%5Csqrt%5B4%5D%7B%5Cfrac%7B5x%2A2y%5E3%7D%7B8y%2A2y%5E3%7D%7D%5C%20%5C%20%5Ctext%7B....%20multiply%20top%20and%20bottom%20by%20%7D%202y%5E3%5C%5C%5C%5C%5C%5C%5Csqrt%5B4%5D%7B%5Cfrac%7B10xy%5E3%7D%7B16y%5E4%7D%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%5B4%5D%7B10xy%5E3%7D%7D%7B%5Csqrt%5B4%5D%7B16y%5E4%7D%7D%20%5C%20%5C%20%5Ctext%7B%20...%20break%20up%20the%20fourth%20root%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%5B4%5D%7B10xy%5E3%7D%7D%7B%5Csqrt%5B4%5D%7B%282y%29%5E4%7D%7D%20%5C%20%5C%20%5Ctext%7B%20...%20rewrite%20%7D%2016y%5E4%20%5Ctext%7B%20as%20%7D%20%282y%29%5E4%5C%5C%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%5B4%5D%7B10xy%5E3%7D%7D%7B2y%7D%20%5C%20%5C%20%5Ctext%7B...%20where%20y%20is%20positive%7D%5C%5C%5C%5C%5C%5C)
The idea is to get something of the form 
in the denominator. In this case, 
To be able to reach the 
, your teacher gave the hint to multiply top and bottom by 
For more examples, search out "rationalizing the denominator".
Keep in mind that ![\sqrt[4]{(2y)^4} = 2y](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%282y%29%5E4%7D%20%3D%202y)
only works if y isn't negative.
If y could be negative, then we'd have to say ![\sqrt[4]{(2y)^4} = |2y|](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%282y%29%5E4%7D%20%3D%20%7C2y%7C)
. The absolute value bars ensure the result is never negative.
Furthermore, to avoid dividing by zero, we can't have y = 0. So all of this works as long as y > 0.
