Lynn plans to sell lemonade to raise at least $40 for the science fair. she sells each cup of lemonade for $0.70 and spends $0.23 per cup for supplies. set up and solve an inequality to find out the minimum number of cups she must sell to reach her goal.

The minimum number of cups she must sell to reach her goal=43 cups

Step-by-step explanation:

Total earnings=Total Lemonade sales-Supplies expenditure

where;

Total earnings=$40

Total Lemonade sales=Price per cup×Number of cups sold(n)=(0.7×n)=0.7n

Supplies Expenditure=0.23 per cup=(0.23×n)=0.23n

Replacing;

40=0.7n+0.23n

Inequality; 0.7n+0.23n=40

Solving;

0.93n=40

n=40/0.93)=43 cups

The minimum number of cups she must sell to reach her goal=n=43 cups

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)

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2