In what direction and by how many units is the graph of f(x) = 5 cos(4x − π) − 1 vertically and horizontally shifted?

graph shifted horizontally right by π unit and Vertically down by 1 unit.

Step-by-step explanation:

Given  :  f(x) = 5 cos(4x − π) − 1 .

To find : In what direction and by how many units is the graph shifted .

Solution : We have given that f(x) = 5 cos(4x − π) − 1 .

By the transformation  rule : f(x) →→→f(x-h) graph is shifted to right by h unit

f(x) →→→f(x) -k mean graph shifted vertically down .

Then , graph of  f(x) = 5 cos(4x − π) − 1  shifted horizontally right by π unit and Vertically down by 1 unit,

Therefore, graph shifted horizontally right by π unit and Vertically down by 1 unit.

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.