Identify the matrix transformation of ΔFGH, which has coordinates F(0, −1),G(5, −1), and H(4, 3), for a dilation by a factor of 1/4. Then identify the correct vertices of the image.

Step-by-step explanation:

We are given the position function and need to find the value of t when h<17.

Create an inequality that represents this situation:

The "less than" sign makes this very specifically a conjunction problem as opposed to a disjunction. That's important to the solution. But we'll get there.

The simplest way to solve this is to subtract 81 from both sides:

then divide both sides by -16:

Notice now that the sign is facing the other way since we had to divide by a negative number. Now it's a disjunction. The solution set to this inequality is that t>2 or t<-2. First and foremost, time will never be negative, so we can disregard the -2. Even if that was t<2, the more time that goes by, the greater the time interval is, not the lesser. It's the "<" that doesn't make sense, not only the -2. The solution to this inequality is

t > 2 sec. That means that after 2 seconds, the height of the ball is less than 17 feet.