Given:
Anna’s cell phone plan charges her $30 per month plus a $150 one-time activation fee.
Evelyn’s cell phone plan charges her $20 per month, plus a $450 one-time activation fee.
To find:
The number of months after which the costs for the girls’ cell phone plans the same.
Solution:
Let x be the number of months.
Total cost = Fixed cost + Variable cost
According to the question, cost equation for Anna’s cell phone is
...(i)
Cost equation for Evelyn's cell phone is
...(ii)
Equate (i) and (ii) to find the time after which the costs for the girls’ cell phone plans the same.
![150+30x=450+20x](https://tex.z-dn.net/?f=150%2B30x%3D450%2B20x)
![30x-20x=450-150](https://tex.z-dn.net/?f=30x-20x%3D450-150)
![10x=300](https://tex.z-dn.net/?f=10x%3D300)
Divide both sides by 10.
![x=\dfrac{300}{10}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B300%7D%7B10%7D)
![x=30](https://tex.z-dn.net/?f=x%3D30)
Therefore, the costs for the girls’ cell phone plans the same after 10 months.
For this case we must find the value of "x" of the following equation:
![x ^ 2-9 = 0](https://tex.z-dn.net/?f=x%20%5E%202-9%20%3D%200)
So:
We add 9 to both sides of the equation:
![x ^ 2-9 + 9 = 9\\x ^ 2 = 9](https://tex.z-dn.net/?f=x%20%5E%202-9%20%2B%209%20%3D%209%5C%5Cx%20%5E%202%20%3D%209)
We apply square root on both sides of the equation to eliminate the exponent on the left side:
![x = \pm \sqrt {9}](https://tex.z-dn.net/?f=x%20%3D%20%5Cpm%20%5Csqrt%20%7B9%7D)
Thus, the solutions are:
![x_ {1} = + 3\\x_ {2} = - 3](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20%2B%203%5C%5Cx_%20%7B2%7D%20%3D%20-%203)
ANswer:
![x_ {1} = + 3\\x_ {2} = - 3](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20%2B%203%5C%5Cx_%20%7B2%7D%20%3D%20-%203)
Opcion C
Answer:
Step-by-step explanation:
There is a difference in the two questions, but the result is found the same way
line is in the form y = mx + b
where m is the slope and b is the y intercept.
Perpendicular lines have negative reciprocal slopes
The desired line from the picture has a slope of 5
Now we plug in the included point
2 = 5(1) + b
b = -3
y = 5x - 3
The desired line from the write up has a slope of 1
Now we plug in the included point
2 = (1) + b
b = 1
y = x + 1
Answer:
1017/100
Step-by-step explanation:
68
%
=
17
25
Explanation:
68
% = 68/100
=68/100÷4
=17/25
And finally we have:
1.050 as a fraction equals 105/100
105÷17=6.17
100÷25=4
6.17+4=10.17
And finally we have:
10.17 as a fraction equals 1017/100
15. The formula is a^2+b^2=c^2. So you just plug in the 9 and 12 in the a and b. You get 225. You then take the square root of that and get 15.