Use the Pythagorean Theorem to find the distance between (-3, 4) and (6, 1). Show all calculations.

3√10 units

Step-by-step explanation:

From point (-3,4) make a horizontal line to the same x-coordinate as (6,1).  That would be (6,4).  The distance from (-3,4) to (6,4) is 9 units.  Then, make a vertical line from (6,1) to meet at also (6,4) . The distance between (6,1) and (6,4) is 3.  You could graph this and see that these lines are perpendicular.  Then, draw a line from (-3,4) to (6,1), which would be the hypotenuse of the triangle you just created.  Now, the Pythagorean Theorem is a^2+b^2=c^2.  You already know a and b, which is 9 and 3.  Therefore, 81+9=c^2 . c^2=90.  C=√90=3√10.  The distance between (-3,4) and (6,1) is 3√10

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3