On the planet Tott, there are 9 frenks to every 8 vreels. If farmer Yoy has 80 frenks on her rew farm, how many vreels are on the farm?
Round to the nearest tenth if rounding is needed?

71.1 vreels on the farm

Step-by-step explanation:

Create a proportion where x is how many vreels are on the farm:

=

Cross multiply and solve for x:

9x = 640

x = 71.1

So, to the nearest tenth, there are 71.1 vreels on the farm.

there are solutions for all values of k

Step-by-step explanation:

In order for there to be no real solutions, the value of the discriminant must be negative. For this equation, the discriminant is ...

(-(k+2))^2 -4(3)(k-1)

We want to find values of k for which this is negative:

(k^2 +4k +4) -12k +12 < 0

k^2 -8k +16 < 0

(k -4)^2 < 0

A square is never negative, so there are no values of k that result in the equation having no solutions.