Natasha spent 1\dfrac121 2 1 1, start fraction, 1, divided by, 2, end fraction hours on the beach. she fell asleep for \dfrac34 4 3 start fraction, 3, divided by, 4, end fraction of the time she was on the beach and then woke up with a terrible sunburn. how many hours was natasha asleep on the beach?

1 and 1/8 hours or

Step-by-step explanation:

Natasha spent one and a half hours on the beach, which can be rewritten as 3/2 hours. Out of that time, she spent 3/4 sleeping. The total time she spent sleeping on the beach is determined by the product of the amount of time she spent on the beach by the fraction of that time she spent asleep:

Natasha was asleep on the beach for 1 and 1/8 hours or 1 hour 7 minutes and 30 seconds.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1