A string reaches from the top of a 17-foot pole to a point 13 feet from the base of the pole. To the nearest tenth of a foot, how long is the string?

21.4 feets

Step-by-step explanation:

Using Pythagoras rule :

The length of the string:

Hypotenus = sqrt(opposite² + adjacent²)

Length of string = sqrt(17² + 13²)

Length = sqrt(289 + 169)

Length of string = sqrt(458)

Length of string = 21.400

Length = 21.4 feets

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