Which set of transformations is needed to graph  f(x) = –0.1cos(x) – 4 from the parent cosine function? areflection across the  y-axis, vertical compression by a factor of 0.1, vertical translation 4 units upbreflection across the  x-axis, vertical compression by a factor of 0.1, vertical translation 4 units downcvertical stretching by a factor of 0.1, vertical translation 4 units down, reflection across the  y-axisdvertical stretching by a factor of 0.1, vertical translation 4 units up, reflection across the  x-axis

the parent function for this case is:

f (x) = cos (x)

we apply the following transformations:

reflections:

to graph y = -f (x), reflect the graph of y = f (x) on the x-axis.

we have then:

f (x) = -cos (x)

expansions:

to graph y = a * f (x)

if 0 < a < 1, the graph of y = f (x) is compressed vertically by a factor a

we have then:

f (x) = -0.1cos (x)

vertical translations :

suppose that k> 0

to graph y = f (x) -k, move the graph of k units down.

we have then:

f (x) = -0.1cos (x) -4

answer:

b

reflection across the x-axis, vertical compression by a factor of 0.1, vertical translation 4 units down

$53.50

step-by-step explanation:

you have to subtract the amount of money chuck earned ($72.50) by the cost of the gas for the mower ($11.25) and the new string for the trimmer he bought ($7.75).

72.50-11.25=61.25

and then subtract $61.25 by the second thing he bought (the new string for the trimmer)

61.25-7.75=53.5

so in total it's $53.50 (53 dollars and 50 cents)

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).