Rewrite in standard form of a circle
x^2-6x+y^2-4y-12=0

+ =

Step-by-step explanation:

The standard form of equation of a circle is written in the form:

+ =

where a and b are the coordinates of the center and r is the radius.

All we need to do is to covert the given equation into this form, how do we do that?

We will achieve this by using the completing method of solving quadratic equation.

Firstly re - write the equation , that is

- 6x + -4y = 12

The next thing is to Complete the square for each of  x and y

How do we do this ?

i. multiply the coefficient of x and y by 1/2

ii. square the results

iii. Add the result to both sides of the equation , that is

- 6x + - 4y + = 12 ++

The next thing is to write the Left hand side of the equation as a perfect square binomial and simplify the Right hand side. That is

+ = 25 , that is

+ =

Which is now in standard form of the equation of a circle.

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation:

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!