Paul creates a CD by mixing together
songs that are either 3 minutes or
4 minutes long. His CD has 22 songs
and is 78 minutes long. How many
three-minute and how many four-minute
songs did he use?

Paul created 10 three minutes songs and 12 four minutes songs.

Step-by-step explanation:

The song he created on his CD is either 3 minutes long or 4 minutes long.

His CD has 22 songs and is 78 minutes. The number of 3 minutes and 4 minutes song can be calculated below.

Let

a = number of 3 minutes song

b = number of 4 minutes song

number of song = 22

a + b = 22(i)

3a + 4b = 78(ii)

Make a subject of the formula in equation (i)

a = 22 - b

Insert the value of a in equation (ii)

3(22 - b) + 4b = 78

66 - 3b + 4b = 78

b = 78 - 66

b = 12

insert the value of b in equation (i)

a + b = 22

a + 12 = 22

a = 22 - 12

a = 10

Paul created 10 three minutes songs and 12 four minutes songs.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.