Select the answer which is equivalent to the given expression using your calculator. (-5)/(-20+sqrt5) (20-sqrt5)/(79) (20+sqrt5)/(79) (60+3sqrt5)/(79) (60-3sqrt5)/(79)

Question

Select the answer which is equivalent to the given expression using your calculator.  (-5)/(-20+sqrt5)  (20-sqrt5)/(79)  (20+sqrt5)/(79)  (60+3sqrt5)/(79)  (60-3sqrt5)/(79)

Bytelearn · Accepted Answer

Calculate Denominator: Calculate the denominator of the given expression using a calculator. (-20 + sqrt(5)) is calculated as follows: First, find the square root of 5, which is approximately 2.236. Then, add this value to -20. -20 + 2.236 = -17.764Calculate Expression Value: Calculate the value of the entire expression using the calculated denominator. The expression is (-5)/(-17.764). Now, divide -5 by -17.764 to get the value of the expression. -5 / -17.764 ≈ 0.281Compare with Options: Compare the calculated value with the given options. We have approximately 0.281 for the expression (-5)/(-20+sqrt5). Now, we need to check which of the given options is equivalent to this value.Calculate Option A: Calculate the value of each option using a calculator and compare it with the calculated value of the original expression. Option A: (20-sqrt5)/(79) 20 - sqrt(5) ≈ 20 - 2.236 = 17.764 17.764 / 79 ≈ 0.225 This does not match our calculated value of 0.281.Calculate Option B: Calculate the value of option B. Option B: (20+sqrt5)/(79) 20 + sqrt(5) ≈ 20 + 2.236 = 22.236 22.236 / 79 ≈ 0.281 This matches our calculated value of 0.281.Verify Remaining Options: Verify that the remaining options do not match the calculated value. Option C: (60+3sqrt5)/(79) 60 + 3*sqrt(5) ≈ 60 + 3*2.236 = 60 + 6.708 = 66.708 66.708 / 79 ≈ 0.844 This does not match our calculated value of 0.281.  Option D: (60-3sqrt5)/(79) 60 - 3*sqrt(5) ≈ 60 - 3*2.236 = 60 - 6.708 = 53.292 53.292 / 79 ≈ 0.675 This does not match our calculated value of 0.281.

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\frac{-5}{-20+\sqrt{5}}$ $\newline$ $\frac{20-\sqrt{5}}{79}$ $\newline$ $\frac{20+\sqrt{5}}{79}$ $\newline$ $\frac{60+3 \sqrt{5}}{79}$ $\newline$ $\frac{60-3 \sqrt{5}}{79}$

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