Set up the given triangle on x-y coordinates with right angle at (0,0). So the two vertices are at (5,0) and (0,2
![sqrt{x} n]{3}](https://tex.z-dn.net/?f=sqrt%7Bx%7D%20n%5D%7B3%7D%20)
)
let (a,0) and (0,b) be two vertices of the<span> equilateral triangle. So the third vertex must be at </span>
for a pt (x,y) on line sx+ty=1, the minimum of
equals to
smallest value happens at
so area is
hence m=75, n=67, p=3
m+n+p = 75+67+3 = 145
X² <span>+ 11x + 7
because 7 is a prime number, this doesn't factor prettily. you'll want to use the quadratic formula; if you aren't familiar with it, i'd either research it or look it up in your textbook, because it's clunky and not easily understood in this format:
(-b </span>± √((b)² - 4ac))/(2a)
in your equation x² + 11x + 7 ... a = 1, b = 11, and c = 7. what you do is you take the coefficients of every term, then plug it into your equation:
(-11 ± √((11)² - 4(1)(7))/(2(1))
not pretty, i know. but, regardless, you can simplify it:
(-11 ± √((11)² - 4(1)(7))/(2(1))
(-11 ± √(121 - 28))/2
(-11 ± √93)/2
and you can't simplify it further. -11 isn't divisible by 2, and 93 doesn't have a perfect square that you can take out from beneath the radical. the ± plus/minus symbol indicates that you have 2 answers, so you can write them out separately:
(x - (-11 - √93)/2) and (x + (-11 - √93)/2)
they look confusing, but those are your two factors. they can be simplified just slightly by changing the signs in the middle due to the -11:
(x + (11 + √93)/2) (x - (11 - √93)/2)
and how these would read, just in case the formatting is too confusing for you: x plus the fraction 11 + root 93 divided by 2. the 11s and root 93s are your numerator, 2s are your denominator.
Answer:
DE = 24
Step-by-step explanation:
The midsegment DE is half the length of the third side AC , that is
DE = 
AC = × 48 = 24
Answer: 36 degrees
Step-by-step explanation:
subtract 5 from 30=25
add 11 to 25
25+11=36
The slope is always change in y value over change in x value so if you pick any 2 points on the line you’ll see that the slope is 30/40 and that simplified is 3/4 so the slop is 3/4
