On every 3rd day Ivan goes to the gym to exercise. Every 5th day Gavin goes to the gym to exercise. What is the first day Ivan and Gavin will be at the gym on the same day? During 1 hour of television there are 2 shows on. What is the ratio of hours to shows? If you watch 3 hours of television, what will the ratio be?

15th day

1 / 2 ; 1 / 2

Step-by-step explanation:

Given :

Ivan = Every 3rd

Gavin = Every 5th

To Obtain the first day they'll be at the gym a together;

Lowest common multiple of the days :

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24

Multiples of 5 = 5, 10, 15, 20, 25, 30

Lowest common multiple = 15

2.)

Time in hours = 1

Number of shows = 2

Ratio of hours to shows = 1 / 2

Ratio for 3 hours of watching television :

3 * (1 /2) = 3 / 6 = 1 / 2

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752