Answer:
180 degrees
Step-by-step explanation:
Answer:
6(x-3y+6)
Step-by-step explanation:
Answer:
Option C is correct.
The equation
represents the function.
Step-by-step explanation:
Using slope intercept form to find the equation of line :
For any two points
and
the equation of line is given by:
......[1] ;where m is the slope given by:

Consider any two points from table :
let (4, 2) and (0, 4) be any two points.
calculate slope:


Now, substitute in equation [1] we have:

Distributive property i.e, 

Add both sides 2 we get;

Simplify:

Since, y= f(x)

therefore, the equation
represents the function.
Answer: Paul will be 30 years old
Step-by-step explanation:Let the age of her sister be x, then from the given data
=> 4x = 20
=> x = 5 years
The age of her sister is 5 years
In the second case, paul is twice as old as his sister
=> Age of paul = 2(x)
=> Age of paul = 10 years
Paul will be 10 years old when he is twice as old as his sister
Answer:
We want a polynomial of smallest degree with rational coefficients with zeros in
,
and -3. The last root gives us the factor (x+3). Hence, our polynomial is

where
is a polynomial with rational coefficients and roots
and
. The root
gives us a factor
, but in order to obtain rational coefficients we must consider the factor
.
An analogue idea works with
. For convenience write
. This gives the factor
. Hence,

Notice that
. So, in order to satisfy the last condition we divide by 3 the whole polynomial, without altering its roots. Finally, the wanted polynomial is

Step-by-step explanation:
We must have present that any polynomial it's determined by its roots up to a constant factor. But here we have irrational ones, in order to eliminate the irrational coefficients that a factor of the type
will introduce in the expression, we need to multiply by its conjugate
. Hence, we will obtain
that have rational coefficients. Finally, the last condition is given with the intention to fix the constant factor. Usually it is enough to evaluate in the point and obtain the necessary factor.