Ethan needs to save at least $500 to purchase a new dirt bike. so far, he had saved $175. if he hopes to use two-fifths of his next paycheck to cover the amount, how much money must he make in his paycheck?

he must make $812.5 or more in his paycheck

Step-by-step explanation:

Let x represent the amount if money that Ethan must make on his next paycheck.

Ethan needs to save at least $500 to purchase a new dirt bike. So far, he had saved $175. If he hopes to use two-fifths of his next paycheck to cover the amount, then the equation becomes

175 + 2x/5 ≥ 500

2x/5 ≥ 500 - 175

2x/5 ≥ 325

2x ≥ 325 × 5

2x ≥ 1625

x ≥ 1625/2

x ≥ 812.5

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

congruent segments

step-by-step explanation: