The function f(x) = -x² + 8x-7 is translated five units down. Write the new equation in vertex form and state the vertex.

Solve the problem by making up an equation. a child is 12 years old, and his father is 32 years older. in how many years will the age of the father be 3 times the age of the child?

A. what is the area of the base? use complete sentences to explain your reasoning. b. what is the volume of the prism? use complete sentences to explain your reasoning.

Which scenarios are most effectively explored by conducting an experiment? there is more than one correct answer. select all that apply. researchers want to study the effectiveness of a particular drug for treating migraines. they want to know which dosage of the drug yields the best results with the least side effects. to ensure fair results, the researchers want to ensure that participants and dosage administrators do not know which dosage participants receive. a teacher wants to plan a class fieldtrip and quickly determine where students prefer to go for the class fieldtrip. a car mechanic wants to know which of two engine brands makes better-performing engines. he wants to test the engines in identical situations and rate their performance in a way that can be fairly measured. a chemist studies the properties of a metal compound. she wants to know how the sample size of the metal affects its ability to conduct electricity. she wants to conduct the research in a controlled environment to minimize bias. a realty company wants to know the average income of its clients. the company wants to gather data income from current clients.