In baseball, the lengths of the paths between consecutive bases are 90 feet, and the paths form right angles. The player on first base tries to steal second base. How far does the ball need to travel from home plate to second base to get the player out? Round your answer to the nearest tenth. The ball needs to travel about feet.

AC = 127,26 f    distance from home plate to second base

Step-by-step explanation:

Let call  A , B , C  Home plate,  first base and second base respectively

These three point form a right triangle with legs ( AB  = BC = 90 feet)

we have an isosceles triangle with a right angle and two angles of 45⁰

So we need to compute distance AC (hypotenuse)

AC²  =  AB² + BC²    ⇒  AC²  = 2AB²   ⇒ AC = AB √2

AC = 90 * 1,414

AC = 127,26 f

the first one, all those points on the line just make a strait line.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)