The distance between lincoln, ne, and boulder, co, is about 500 miles. the distance between boulder, co, and a third city is 200 miles. assuming the three cities make a triangle on the map, which values represent the possible distance, d, in miles, between lincoln, ne, and the third city?

The sum of the lengths of any two sides of a triangle is greater than the length of the third side (Triangle Inequality Theorem)

Let 

A> Lincoln, NE

B> Boulder, CO

C> third city

we know that

in the triangle ABC

AB=500 miles

BC=200 miles

AC=x

Applying the Triangle Inequality Theorem

1) 500+200 > x> 700 > x> x < 700 miles

2) 200+x > 500> x > 500-200> x > 300 miles

the solution for x is 

300 < x < 700

the interval is> (300,700)

answer: ur mum is gay

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: