Determine if the statement is always, sometimes, or never true:
an equilateral triangle is an acute triangle.
a. always
b. sometimes
c. never
a scalene triangle is a right triangle.
a. always
b. sometimes
c. never

1. a. Always.

2. Sometimes.

Step-by-step explanation:

We have been given two sentences. We are asked to choose the correct option for the given statements.

1. An equilateral triangle is an acute triangle.

We know that the measure of each angle of an equilateral triangle is equal that is 60 degrees.

Since each angle of an equilateral triangle is less than 90 degrees, therefore, an equilateral triangle is "always" an acute triangle.

2. A scalene triangle is a right triangle.

We know that a scalene triangle has all sides with different measure. A scalene triangle will be a right triangle, if its sides are Pythagorean triplets.

Therefore, a scalene triangle is "sometimes" a right triangle.

b

step-by-step explanation:

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.