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Darya [45]
3 years ago
7

What is the answer?! Please help!

Mathematics
1 answer:
Step2247 [10]3 years ago
8 0
The notation "sqrt" is shorthand for "square root"

sqrt(-x+10)-x = 2
sqrt(-x+10) = x+2 ... add x to both sides
-x+10 = (x+2)^2 ... square both sides
-x+10 = x^2+4x+4 ... use FOIL
x^2+5x-6 = 0 ... get everything to one side; combine like terms
(x-1)(x+6) = 0 ... factor
x-1=0 or x+6 = 0 ... zero product property
x = 1 or x = -6  .... solve each sub-equation for x

The possible solutions are x = 1 or x = -6. We need to check each of those solutions

Let's check x = 1
sqrt(-x+10)-x = 2
sqrt(-1+10)-1 = 2
sqrt(9)-1 = 2
3-1 = 2
2 = 2
So x = 1 has been confirmed

Let's check x = -6
sqrt(-x+10)-x = 2
sqrt(-(-6)+10)-(-6) = 2
sqrt(6+10)+6 = 2
sqrt(16)+6 = 2
4+6 = 2
10 = 2
The last equation is false, so x = -6 is extraneous. It's not a true solution

----------------------------------

In summary, the value x = 1 is the only solution

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Time taken by Chris to clean a stadium  = 3 hours

Rate of work done by Chris =\dfrac{1}{3}

Let t be the time taken by both of them to clean the stadium together.

According to the question , we have

Rate of work done together = Rate of work done by Kelvin+Rate of work done by Chris

\dfrac{1}{t}=\dfrac{1}{5}+\dfrac{1}{3}\\\\ \Rightarrow\ \dfrac{1}{t}=\dfrac{3+5}{15}\\\\ \Rightarrow\ \dfrac{1}{t}=\dfrac{8}{15}\\\\\Rightarrow\ t=\dfrac{15}{8} =1.875

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