Agroup of students is arranging squares into layers to create a project. the first layer has 6 squares. the second layer has 12 squares. which formula represents an arithmetic explicit formula to determine the number of squares in each layer?

a1 = 6; an = 6 + an − 1, n > 0
a1 = 6; an = 6 ⋅ an − 1, n > 0
a1 = 6; an = 6 ⋅ an + 1, n > 0
a1 = 6; an = 6 + an + 1, n > 0

Step-by-step explanation:

In the first layer, there are 6 squares. The second layer has 12 squares.

So, the second term is 6 more than the first term i.e., in general, the number of squares in a layer is 6 greater than the number of squares in its previous layer,

If we generalize this A.P. as arithmetic explicit formula then it becomes

(Answer)

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

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)