How many multiples of $8$ are between $100$ and $500$?

There are 50 multiples of 8 between 100 and 500

Step-by-step explanation:

1. We need to find out the multiple of 8 closest and higher than 100.

80, 88, 96, 104, 112, 120 It's 104

2. We need to find out the multiple of 8 closest and lower than 500.

480, 488, 496, 504, 512, 520It's 496

3. Now, we use 104 and 496, this way:

(496 - 104)/8 + 1 =

392/8 + 1 =

49 + 1 = 50

There are 50 multiples of 8 between 100 and 500

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.