The number of grocery items on two grocery lists differs by 7. the total number of items is 33. how many items are on each list?

There are 20 items on one grocery list and 13 items on second grocery list.

Step-by-step explanation:

We are given that there are two grocery list and one of the grocery list have seven things less than the other grocery list.

Let x be the number of items on one grocery list.

Then, by the given information, there are x -7 items on the second grocery list.

The total number of items on both the list are 33.

Then, according to the question,

Thus, there are 20 items on one grocery list and (20 -7) = 13 items on second grocery list.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.