What’s the least common multiple (lcm) for each group of numbers? a. 6 and 15 b. 4 and 11 c. 6, 9, and 12 d. 8, 10, and 20 what’s the least common denominator (lcd) for each group of fractions? a. 1⁄6 and 7⁄8 b. 3⁄4 and 7⁄10 c. 7⁄12, 3⁄8 and 11⁄36 d. 8⁄15, 11⁄30 and 3⁄5

LCM is least common multiple.

a. 6 and 15

6 = 2 x 3

15 = 3 x 5

LCM = 3 x 5 x 2 = 30

b. 4 and 11

4 = 2 x 2

11 = 1 x 11

LCM = 2 x 2 x 11 = 44

c. 6, 9, and 12

6 = 2 x 3

9 = 3 x 3

12 = 2 x 2 x 3

LCM = 2 x 2 x 3 x 3 = 36

d. 8, 10, and 20

8 = 2 x 2 x 2

10 = 2 x 5

20 = 2 x 2 x 5

LCM = 2 x 2 x 2 x 5 = 40

LCD is the least common denominator. Means we will find the LCM of denominators.

a. 1⁄6 and 7⁄8

6 = 2 x 3

8 = 2 x 2 x 2

LCD = 2 x 2 x 2 x 3 = 24

b. 3⁄4 and 7⁄10

4 = 2 x 2

10 = 2 x 5

LCD = 2 x 2 x 5 = 20

c. 7⁄12, 3⁄8 and 11⁄36

12 = 2 x 2 x 3

8 = 2 x 2 x 2

36 = 2 x 2 x 3 x 3

LCD = 2 x 2 x 2 x 3 x 3 = 72

d. 8⁄15, 11⁄30 and 3⁄5

15 = 3 x 5

30 = 2 x 3 x 5

5 = 1 x 5

LCD = 2 x 3 x 5 = 30

you would have to sell 24 bracelets.

step-by-step explanation:

84/3.5 = 24

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!