Let f(x)=x^2−9 and g(x)=x^2−7x+12 . what is (f/g)(x) ?

The answer is:

To solve the problem,  we need to factorize the quadratic functions in order to be able to simplify the expression.

We can factorize quadratic functions in the following way:

Also, we can factorize/simplify quadratic expressions in the following way, if we have the following quadratic expression:

We can factorize it by finding two numbers which its products give as result "c" (j) and its algebraic sum gives as result "b" (k), and then, rewrite the expression in the following way:

Where,

x, is the variable.

j, is the first obtained value.

k, is the second obtained value.

We are given the functions:

Then, factoring we have:

First expression,

Second expression,

We need to find two number which product gives as result 12 and their algebraic sum gives as result -7. Those numbers are -4 and -3.

Now, rewriting the expression we have:

So, solving we have:

Have a nice day!

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.