For her exercise today, keiko plans to both run and swim. let r be the number of laps she runs and let s be the number of laps she swims. each lap she runs takes her 5 minutes, and each lap she swims takes her 3 minutes. she wants to exercise for at least 30 minutes today. using the values and variables given, write an inequality describing this.

5r + 3s ≥ 30

Step-by-step explanation:

We know Keiko wants to do exercise at least 30 minutes a day, and she wants ideally to mix up the activities, by combining running and swimming into her schedule.

Since each lap she runs takes 5 minutes and each lap she swims takes 3 minutes, these will be the left side of the inequality:

5r + 3s

She wants to exercise at least 30 minutes a day, so...

5r + 3s ≥ 30

she could do 3 laps of running and 5 laps of swimming for example.

3 x ( 2 x 3 + x 2 − 4 )

Step-by-step explanation:

Factor  3 x  out of  3 x 3 . 3 x ( x 2 ) − 12 x + 6 x 4

Factor  3 x  out of  − 12 x . 3 x ( x 2 ) + 3 x ( − 4 ) + 6 x 4

Factor  3 x  out of  6 x 4 . 3 x ( x 2 ) + 3 x ( − 4 ) + 3 x ( 2 x 3 )

Factor  3 x  out of  3 x ( x 2 ) + 3 x ( − 4 ) . 3 x ( x 2 − 4 ) + 3 x ( 2 x 3 )

Factor  3 x  out of  3 x ( x 2 − 4 ) + 3 x ( 2 x 3 ) . 3 x ( x 2 − 4 + 2 x 3 )

Reorder terms. 3 x ( 2 x 3 + x 2 − 4 )

so the Greatest common factor of 3x^3 - 12x + 6x4 is 3 x ( 2 x 3 + x 2 − 4 )