It is the second one down
Answer:
a) The possible solutions are:
x=7 and x=-3
b)The extraneous solution
is x=
Step-by-step explanation:
The last step gives us the possible solutions.
![(x + 3)(x - 7) = 0](https://tex.z-dn.net/?f=%28x%20%2B%203%29%28x%20-%207%29%20%3D%200)
By the zero product property,
![x + 3 = 0 \: or \: x - 7 = 0](https://tex.z-dn.net/?f=x%20%2B%203%20%3D%200%20%5C%3A%20or%20%5C%3A%20x%20-%207%20%3D%200)
This implies that:
![x = - 3 \: or \: x = 7](https://tex.z-dn.net/?f=x%20%20%3D%20%20-%203%20%5C%3A%20or%20%5C%3A%20x%20%3D%207)
The original equation is
![\sqrt{30 - 2x} = x - 3](https://tex.z-dn.net/?f=%20%5Csqrt%7B30%20-%202x%7D%20%20%3D%20x%20-%203)
We substitute x=-3 to get;
![\sqrt{30 - 2 \times - 3} = - 3 - 3 \\ \sqrt{30 + 6} = - 6 \\ \sqrt{36} = - 6 \\ 6 = - 6](https://tex.z-dn.net/?f=%5Csqrt%7B30%20-%202%20%5Ctimes%20%20-%203%7D%20%20%3D%20%20-%203%20-%203%20%5C%5C%20%20%5Csqrt%7B30%20%2B%206%7D%20%20%3D%20%20-%206%20%5C%5C%20%20%5Csqrt%7B36%7D%20%3D%20%20-%206%20%5C%5C%20%206%20%3D%20%20-%206%20)
This not true, therefore x=-3 is an extraneous solution.
We substitute x=7
![\sqrt{30 - 2 \times 7} = 7- 3 \\ \sqrt{30 - 14} = 4 \\ \sqrt{16} = 4 \\ 4 = 4](https://tex.z-dn.net/?f=%5Csqrt%7B30%20-%202%20%5Ctimes%207%7D%20%20%3D%207-%203%20%5C%5C%20%20%5Csqrt%7B30%20-%2014%7D%20%20%3D%204%20%5C%5C%20%20%5Csqrt%7B16%7D%20%20%3D%204%20%5C%5C%204%20%3D%204)
Therefore x=7 is the only solution.
Answer:
-25n - 2
Step-by-step explanation:
- 10n - 12 + 10 - 35n
- -25n - 2
Answer:
the hotel charge in the first city is $5250 while the hotel charge in the second city is $3750
Step-by-step explanation:
Let a represent the charge in the first city before tax and b represent the charge in the second city before tax.
Therefore tax in first city = 10% of a = 0.1a
Tax in second city = 8% of b = 0.08b
From the total tax as $825, hence:
0.1a + 0.08b = 825 (1)
The hotel charge before tax in the second city was $1500 lower than in the first. This gives the equation:
b = a - 1500
a - b = 1500 (2)
To find a and b, solve equation 1 and 2 simultaneously. Multiply equation 2 by 0.1 and subtract from equation 1:
0.18b = 675
b = $3750
a = b + 1500 = 3750 + 1500 = 5250
a = $5250
Therefore, the hotel charge in the first city is $5250 while the hotel charge in the second city is $3750