The difference between two numbers is 14. If two
times the smaller is added to one-half the larger, the
result is 52. Find the numbers.

x = 18

y=32

Step-by-step explanation: Let the two No.s be x and y respectively

x = Smaller no.

y = Larger no.

Given = y-x = 14

∴ y = 14+x

∴x=x

2(x) + y/2 = 52

2(x) + (14+x)/2 = 52

∴4x/2 + 14+x/2 = 52

(4x+14+x)/2 = 52

5x+14 = 52×2=104

∴5x+14= 104

5x=104-14=90

5x=90

∴x=90/5= 18

∴y=14+x

y=14+18=32

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.

1696 hundred thousand

step-by-step explanation: