Micah found the least common multiple of 8 and 12. his work is shown below. multiples of 8: 8, 12, 16, 20, 24, 28, . . multiples of 12: 12, 24, 36, 48, 60, . . the least common multiple is 12. what is micah’s error?

a. micah listed some values that were not multiples.

b. micah listed factors of each number instead of multiples.

c. micah should have multiplied 8 and 12 to find the least common multiple.

d. micah selected a multiple that is not the least of the common multiples.

Option (A) is correct.

Micah listed some values that were not multiples.

Step-by-step explanation:

Least common multiple is the smallest number that is multiple of all given numbers.

Since, Micah found the least common multiple of 8 and 12.

Multiples of 8 are 8, 16, 24, 32 , 40, 48, 56,

Multiples of 12 are 12, 24, 36, 48, 60,

Thus, least common multiple of 8 and 12 as per the definition stated above is 24.

So, Micah’s error is that Micah listed some values that were not multiples as he stated multiples of 8 as  8, 12, 16, 20, 24, 28, . .  which is wrong.

Thus, option (A) is correct.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be