The amount that a consultant charges for her work can be modeled using a linear function for 4 hours of work the consulatant charges $400 for 5 hours she charges $450 write the function f(h) that represents the amount the consultant charges for h hours of work

Let the amount of consultant charges be y

and let the hours of work be x.

From the given condition, we have

(4, 400) and (5, 450)

Use Slope intercept form for two points and

i,e    ......[1]

, where m is the slope which is given by:

.

For the given points (4, 400) and (5, 450);

First calculate the slope:

.

Now, put this value of m in equation [1] ;

Use distributive property on RHS ( i.e, )

Now, add 400 to both sides of an equation:

Simplify:

y = 50x+200.

or

f(x) = 50x+200, where x be the hours of work.

Therefore, the function that represents the amount the consultant charges for h hours of works ;

f(h) = 50h+200

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.