The sum of a number and its reciprocal is 65/8. find the numbers.

8 and

Step-by-step explanation:

x + =

need to eliminate the denominator:

x(8x) + (8x) = (8x)

8x² + 8 = 65x

8x² - 65x + 8 = 0

(8x -1)(x - 8) = 0

(8x -1) = 0           (x - 8) = 0

x =                      x = 8

there will be 35 boys in each team. : )

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form