The sides of ADEF are d, e, and f. If the lengths of d = 12 and e = 19, what are the possible lengths of f?

The possible range of values for F are from 8 to 30

Step-by-step explanation:

Here, we have a triangle DEF and we want to get the possible lengths of the third side

To evaluate the possible lengths of the third side , we need to follow a rule

The rule is that, for the third side, the sum of the two other sides must be greater than it

This means that the length should be less than d + e

Mathematically;

f < d + e

f < 12 + 19

f < 31

So it could be 30

It could also range from 30 to 8

This is because if it is less than 8, then the addition to 12 will be less than or equal to 19

the equation for this situation is y=122+45. to solve the equation you would add 45 and 122 to get a total of 167lbs. in conclusion, grace's weight eight weeks ago was 167lbs.  

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.