If the measures of two sides of a triangle are 3.1 feet and 4.6 feet, which is the least possible measure to the nearest tenth for the third side?
a. 1.6 feet
b. 4.6 feet
c. 8 feet
d. 7.5 feet

  a. 1.6 feet

Step-by-step explanation:

The triangle inequality requires the sum of the shortest two sides exceed the longest side. If x represents the shortest side, that means ...

  x + 3.1 > 4.6

  x > 1.5 . . . . . . . subtract 3.1

The smallest answer choice meeting this requirement is 1.6 feet.

Comment on this answer

A measure of 1.5001 feet will satisfy the triangle inequality. That value would round to 1.5 when rounded to the nearest tenth.

The correct answer is 2. for some reason its not listed in choices

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.