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3 years ago

If f(x)=x^2-5 And g(x)=x-3, what is the composition of f(g(x))

Mathematics

1 answer:

Novosadov [1.4K]3 years ago

4 0

Answer:

f(g(x))=((x-3)^2)-5

Step-by-step explanation:

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Samantha deposited $100 in a bank account that has earned 5% interest during th his year. Audrey deposited $50 more than Samanth

Nina [5.8K]

Samantha has $100*1.05=$105, and Audrey has $150*1.04=$156. The difference is $156-$105=$51.

5 0

3 years ago

Use the identity tan(theta) = sin(theta) / cos(theta) to show that tan(???? + ????) = tan(????)+tan(????) / 1−tan(????) tan(????

VMariaS [17]

Answer:

See the proof below.

Step-by-step explanation:

For this case we need to proof the following indentity:

$tan(x+y) = \frac{tan (x) + tan(y)}{1- tan(x) tan(y)}$

So we need to begin with the definition of tangent, we know that $tan (x) =\frac{sin(x)}{cos(x)}$ and we can do this:

$tan (x+y) = \frac{sin (x+y)}{cos(x+y)}$ (1)

We also have the following identities:

$sin (a+b) = sin (a) cos(b) + sin (b) cos(a)$

$cos(a+b)= cos(a) cos(b) - sin(a) sin(b)$

Now we can apply those identities into equation (1) like this:

$tan (x+y) =\frac{sin (x) cos(y) + sin (y) cos(x)}{cos(x) cos(y) - sin(x) sin(y)}$ (2)

We can divide numerator and denominator from expression (2) by $\frac{1}{cos(x) cos(y)}$ we got this:

$tan (x+y) = \frac{\frac{sin (x) cos(y)}{cos (x) cos(y)} + \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{cos(x) cos(y)}{cos(x) cos(y)} -\frac{sin(x)sin(y)}{cos(x) cos(y)}}$

And simplifying we got:

$tan (x+y) = \frac{tan(x) + tan(y)}{1-tan(x) tan(y)}$

And that complete the proof.

8 0

3 years ago

John bought three thermos flask at a total of st 1080 he later sold at 400 each what was his percentage

trasher [3.6K]

Answer:

$\boxed{ \bold{ \boxed{ \sf {11.11\%}}}}$

Step-by-step explanation:

Given,

Cost price of three thermos flask = 1080

Selling price of each thermos flask = 400

Finding the selling price of three thermos flask

Since, the cost of 3 thermos flask is more than that of 1 thermos flask. So, the cost of 1 thermos flask is multiplied by 3 ( i.e 400 × 3 = 1200 )

Here, the selling price is greater than cost price.

So, there is profit.

And we know that,

$\sf{profit = sp \: - \: cp}$