The choir sold boxes of candy and teddy bears near valentine’s day to raise money. they sold 57 items altogether. bears sold for $8.00 each and each box of candy sold for $6.00. they collected $380. how much of each item did they sell

19 bears, 38 boxes of candy.

Step-by-step explanation:

We can use a system of equations (b = # of bears, c = # of candy boxes):

b + c = 57, 8b + 6c = 380.

We can use substitution by isolating b in the first eq.: b = 57 - c, then substitution b with 57 - c in the second eq.: 8(57 - c) + 6c = 380.

Then, we solve: 456 - 8c + 6c = 380, 76 = 2c, c = 38 candy boxes.

Finally we plug in 38 for c in the first eq.: b + 38 = 57, b = 19 bears.

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

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl