We can use two data points to find the linear function that relates the two quantities. For example, a linear function relating calories (C) consumed over days(d) can be generated from the following data: -After 3 days 4,100 calories have been consumed. -After 8 days 10,600 calories have been consumed. The slope of this function is and indicates the number of calories consumed each day. The y-intercept of this function is and indicates the calories consumed at day . This function can be modeled by C=

Step-by-step explanation:

Let the number of days be x because x is the independent variable

Any y is the number of calories consumed the dependent variable.

Now slope = y2 - y2/ x2 - x2

= 10600-4100/8-3

= 6500/5 = 1300

From our analysis we know it consumes 1300 per day so ideally on day 3 we expect him to consume 1300x3= 3900

But the given value is 4100

This means it's inherent energy is 4100-3900= 200

This is the y- intercept and it occurs when x= 0

from the above explanation we know that

C = 200. and it's the y- intercept.

Look at the general equation of a line

y = mx + C; when x= 0, y = C; note we define C as the value of y when x = 0

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)