Answer:
(√6)/2 square units
Step-by-step explanation:
The area of a triangle is half the magnitude of the cross product of the vectors representing adjacent sides.
QR = (4-3, -1-(-4), -4-(-5)) = (1, 3, 1)
QS = (3 -3, -5-(-4), -6-(-5)) = (0, -1, -1)
The cross product is the determinant ...
The magnitude of this is ...
|QR × QS| = √((-2)² +1² +(-1)²) = √6
The area of the triangle is half this value:
Area = (1/2)√6 . . . . square units
Answer:
Step-by-step explanation:
Given
The attached probability distribution of x
Required
Find
To do this, we consider all values of x less than or equal to-3.
So, we have:
From the table:
So, the equation becomes
9514 1404 393
Answer:
x = -1/2, x = 7
Step-by-step explanation:
Written in standard form, the equation is ...
2x² -13x -7 = 0
We observe that factors of (2)(-7) that have a sum of -13 are -14 and +1. Rewriting the middle term using these numbers, we have ...
2x² -14x +x -7 = 0
2x(x -7) +1(x -7) = 0 . . . . . factor pairs of terms
(2x +1)(x -7) = 0 . . . . . . . . factored form
The solutions are the values of x that make these factors zero.
2x +1 = 0 ⇒ x = -1/2
x -7 = 0 ⇒ x = 7
The solutions to the quadratic are x = -1/2 and x = 7.
