If AD = 21, BF = 8, and DF = 8, what is the value of AB?

AB would be 21

Step-by-step explanation:

Sides BF and DF equal 8, because triangles BFC and DFC are both right triangles and they have two equal sides (hypotenuses are equal and both triangles share side FC), triangles BFC and DFC are congruent triangles, which means side DC is equal to BC. Since right triangles ADC and ABC share side AC and BC = DC, they are congruent triangles, meaning AB will equal AD, which is 21.

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)

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c