Justine swims freestyle at a pace of 150 laps per hour. Justine swims breaststroke 20 laps per hour slower than she swims butterfly. If Justin freestyles speed is three times faster than her butterfly speed in laps per hour and r represents Justin's breaststroke speed in laps per hour.

her breaststroke speed is 30 laps per hour.

Step-by-step explanation:

Let b represent Justine’s butterfly speed.

Let r represent Justine’s breaststroke speed.

Justine swims freestyle at a pace of 150 laps per hour. If Justine’s freestyle speed is three times faster than her butterfly speed, it means that

3b = 150

b = 150/3

b = 50 laps per hour

Justine swims breaststroke 20 laps per hour slower than she swims butterfly. This means that

r = b - 20

r = 50 - 20

r = 30 laps per hour

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15