Answer:
Distance is 
units
Step-by-step explanation:
Use the distance formula which is 
where 
is the distance between points 
and 
We are given that is 
and is 
, therefore the distance between the two points is:
Therefore, the distance between and is units.
Answer:
w = 8
Step-by-step explanation:
Based on the altitude theorem of a right triangle, we have:
w + 4 = √(24*6)
w + 4 = √144
w + 4 = 12
w + 4 - 4 = 12 - 4
w = 8
Start by doing a subtraction of 6 to both sides so that the equation becomes -2x^2 + 7x + 1 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [ -7 ± √((7)^2 - 4(-2)(1)) ] / ( 2(-2) )
x = [-7 ± √(49 - (-8) ) ] / ( -4 )
x = [-7 ± √(57) ] / ( -4)
x = [-7 ± sqrt(57) ] / ( -4 )
x = 7/4 ± -sqrt(57)/4
The answers are 7/4 + sqrt(57)/4 and 7/4 - sqrt(57)/4.
