the length for each remaining side is 69 inches
<span>Triangle PQR is a right triangle. First we have to find the length of each side of the triangle. This can be done using the points provided, along with the Pythagorean theorem, which is a^2+b^2=c^2.
PR^2 = (7- -2)^2+(3-5)^2 = 85 => PR = sqrt(85)
QR^2 = (7- -1)^2+(3-1)^2 = 68 => QR = sqrt(68)
QP^2 = (1-5)^2+(-1 - -2)^2 =17 => QP = sqrt(17)
Now that we have the sides of the triangle, we can put them into the Pythagorean theorem again to see that it works out:
(Sqrt(17))^2 + (sqrt(68))^2 = (sqrt(85))^2
17 + 68 = 85
85 = 85
Since the Pythagorean theorem works for right triangles, the triangle is indeed a right triangle.</span>
Answer:
x = -2 ±sqrt(7)
Step-by-step explanation:
3x^2 +12 x = 9
Divide each side by 3
3x^2 /3 +12x/3 = 9/3
x^2 +4x = 3
Take the coefficient of x
4
Divide by 2
4/2 =2
Square it
2^2 =4
Add it to each side
x^2 +4x+4 = 3+4
x^2 +4x+4 = 7
(x+2)^2 = 7
Take the square root of each side
x+2 = ±sqrt(7)
Subtract 2 from each side
x+2-2 = -2 ±sqrt(7)
x = -2 ±sqrt(7)
Answer:
hi
Step-by-step explanation:
hi
