Determine which set of numbers can be the measures of the sides of a triangle.
question 6 options:
a)
13, 10, 16
b)
1, 2, 3
c)
5.2, 11, 4.9
d)
208, 9, 219

  a)  13, 10, 16

Step-by-step explanation:

The usual form of the triangle inequality requires the sum of the two shortest sides exceed the longest side (a+b>c). The only choice for which this is true is ...

  10 + 13 > 16 . . . . choice A

Comment on the triangle inequality

Some authors also allow the sum to equal the longest side (a+b≥c). In that case, choice B (1+2=3) is also an answer. This "triangle" would look like a line segment of length 3. It has zero area.

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.

14

step-by-step explanation:

14 x 3 = 42