How much grape juice would you need to mix with 15/4 quarts of sparkling water. (a recipe for sparkling grape juice calls for 1 1/2 quarts of sparkling water and 3/4 quart of grape juice)

15/8 quarts

Step-by-step explanation:

The recipe calls for 1 1/2 quarts of sparkling water.  This can be written as the improper fraction 3/2 (this is because 1 whole = 2/2; 2/2 + 1/2 = 3/2).

Using 15/4 quarts sparkling water means we used 5/2 times as much as the recipe calls for.  This means we would use 5/2 times the amount of grape juice as well; 5/2(3/4) = 15/8.

22 and 22

step-by-step explanation:

10 plus 12 equals 22.

12 plus 10 also equals 22 because regardless of what order they're in, they're gonna equal the same thing.

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