A taxi charges a flat rate of $3.00, plus an additional
$0.50 per mile. Carl will only take the taxi home if the
cost is under $10, otherwise he will take a bus. Carl is 15
miles from home. Explain how to write and solve an
inequality to determine if Carl will take the taxi or a bus.

See below.

Step-by-step explanation:

The cost of the taxi is the sum of two costs:

the fixed fee of $3.00 and the $0.50 per mile.

Let x = number of miles.

For x miles, the mile cost is 0.5x

The total cost is $3.00 plus 0.5x

Total cost: 0.5x + 3

We want the total cost to be under $10, so the sum of the two costs must be less than 10.

The inequality is:

0.5x + 3 < 10

Subtract 3 from both sides.

0.5x < 7

Divide both sides by 0.5

x < 14

The cost is under $10 if the distance is under 14 miles.

Since the distance here is 15 miles, the cost of the taxi is over $10, and Carl will take the bus.

y=mx+b

step-by-step explanation:

m is slope, b is y-intercept

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)