The band is selling snacks during lunch. nachos are $2 each and burgers are $4 each. you want to buy at least 5 items. you want to spend no more than $16 total. a. define the variables b. write a system of inequality c. give 2 possible solutions

3 burgers and 2 Nachos or

2 burgers and 4 Nachos.

Step-by-step explanation:

a.)Define variables;

Let n represent Nachos

and b represent burgers

b. System of inequality;

2n+4b ≤ 16

n+b ≥ 5

c. Give 2 possible solutions;

First, using the inequalities above, solve for n;

n ≥ 5-b, then replace n with (5-b) in the second equation;

2(5-b)+4b ≤ 16

10-2b+4b ≤ 16

2b ≤ 16-10

2b ≤ 6

b ≤ 3

Using 3 for b, solve for n;

n+3 ≥ 5

n ≥ 5-3

n ≥ 2

Therefore, one possible solution is ; 3 burgers and 2 Nachos

The second solution can be found this way;

If b=2 use equation 2n+4b ≤ 16 to solve for n;

2n+(2*4) = 16

2n+8= 16

2n=16-8

2n=8

n=4

Therefore second solution is 2 burgers and 4 Nachos.

10x

step-by-step explanation:

the greatest common factor 30 and 20 is 10

5 is a common factor of 30 and 20 but 10 is also a factor and 10 is greater than 5 so 5 will definitely not be apart of our answer

now the most amount of x's you factor our is just 1 factor of 1

so 10x the gcf of the terms in the polynomial

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.