Acyclist traveled 15 kilometers per hour faster than an in-line skater. in the time it took the cyclist to travel 12 kilometers, the skater had gone 6 kilometers. find the speed of the skater.

The speed of the skater is 15 kilometers per hour.

Step-by-step explanation:

Let x be the rate of the skater.

Then the rate of the cyclist is x+15.

Let t represents time, so we get two equations:

(x+15)t = 12 and xt = 6

Now, solving for t;

and

As t is the same for the skater and the cyclist, we will equate both the equations now.

Solving for x;

=>

=>

=>

x = 15

Hence, the speed of the skater is 15 kilometers per hour.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.