Devin is training for a competitive race by swimming and running. He covers a total distance of 9 km by swimming for 45 minutes and running for 20 minutes. The following day he swims for 30 minutes and runs for 40 minutes, covering a total of 14 km. Which system of linear equations can be used to find Devin's swimming rate (x) and his running rate (y) in kilometers per hour? A) 3 4 x + 1 3 r = 9 1 2 x + 2 3 y = 14 B) 3 4 x + 1 3 y = 14 1 2 x + 2 3 y = 9 C) 3 4 x + 1 3 y = 9 1 2 x − 2 3 y = 14 D) 3 4 x + 1 3 y = 23 1 2 x + 2 3 y = 23

The system is:

Explanation:

You must translate the two verbal statements into algebraic expressions, under the assumption that the swimming rate and the running rate are constant.

The names of the variables are given:

1. First verbal statement

He covers a total distance of 9 km by swimming for 45 minutes and running for 20 minutes.

The distance covered is equal to the rate multiplied by the time.

Since the rates are in km/h, you mus change the times from minutes to hours:

Total distance = 9km

2. Second verbal statement

The following day he swims for 30 minutes and runs for 40 minutes, covering a total of 14 km.

Total distance = 14km

Hence, the system is:

0.02

step-by-step explanation:

time of 9 192 631 770 periods of the radiation corresponding to the transition between the 2 hyperfine levels of the ground state of the caesium 133 atom at 0 k (but other seconds are sometimes used in astronomy)

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4