A multivitamin tablet contains 18.5 mg of calcium. How much

If f(x)=logx, explain the transformation that occurs when f(0.25(x-5))+3

nevsk [136]

Answer:

First, let's explain the transformations in a general way:

Vertical shift.

If we have a function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

This will move the graph of f(x) up or down a distance of N units.

if N is positive, then the shift is upwards

if N is negative, then the shift is downwards.

Horizontal shift.

If we have a function f(x), a horizontal shift of N units is written as:

g(x) = f(x + N)

This will move the graph of f(x) to the right or left a distance of N units.

if N is positive, then the shift is to the left

if N is negative, then the shift is to the right.

Horizontal dilation/contraction.

For a function f(x), an horizontal contraction dilation is written as:

g(x) = f(k*x)

where:

k is called the "scale factor"

If k < 1, then the graph "dilates" horizontally.

if k > 1, then the graph "contracts" horizontally.

Now, in this problem we have:

f(x) = log(x)

And the transformed function is:

g(x) = f(0.25*(x - 5)) + 3

Then, the transformations that take place here are, in order:

Vertical shift of 3 units up:

g(x) = f(x) + 3.

Horizontal shift of 5 units to the right:

g(x) = f(x - 5) + 3

Horizontal dilation of scale factor 0.25

g(x) = f( 0.25*(x - 5)) + 3

replacing f(x) by log(x) we have

g(x) = log(0.25*(x - 5)) + 3.

6 0

3 years ago

Johnny and his father go fishing at 5:00 AM. After motoring 6 km upstream, Johnny writes a letter to his friend, puts the letter

Alik [6]

Answer:9/2 km per hour

Step-by-step explanation:

equation,

6/9-x + 6/x=8/3

8 0

3 years ago

Read 2 more answers

A pole that is 3m tall casts a shadow that is 1.22m long. At the same time, a nearby building casts a shadow that is 38.5m long.

vichka [17]

Refer to the diagram shown below.

The height of the pole is CD (3 m), and its shadow is AB (1.22 m).
The height of the building is h m, and its shadow is AD (38.5 m).

The two triangles ΔABC and ΔADE are similar because of AAA.
Therefore
$\frac{DE}{BC} = \frac{AD}{AB} \\\\ \frac{h}{3} = \frac{38.5}{1.22}$

Cross multiply.
1.22 h = 3*38.5 = 115.5
h = 115.5/1.22 = 140.91 m

Answer: 141 m (nearest meter)