The correct graph is D.
We can tell this for two reasons. Firstly, you would need a dotted line. Since the equation includes a greater than sign, and not a greater than or equal to sign, it must be dotted.
Then we need to figure out whether to shade above or below the line. The best way to find this is by checking whether the point (0,0) should be shaded.
y + 2 > -3x - 3
0 + 2 > -3(0) - 3
2 > -3 (TRUE)
Since this is a true statement, the side with (0,0) needs to be shaded. Graph D is the only one that has a dotted line and (0,0) shaded.
Answer:
20
Step-by-step explanation:
Givens
Let child one = x
Let child two = y
Let child three = z
Equations
x^2 + y^2 + z^2 = 100
xy + xz + yz = 150
Solution
There's a trick here. The square of their weights added together is equal (with some modification) to the given conditions. Start by squaring (x+y+z).
(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2xz + 2yz
Take out 2 as a common factor from the last three terms.
(x + y + z)^2 = (x^2 + y^2 + z^2+ 2(xy + xz + yz) )
Substitute the given conditions into the equation. (x^2 + y^2 + z^2) = 100 and 2*(xy + xz + yz) = 2 * 150
(x + y + z)^2 = 100 + 2*150
(x + y + z)^2 = 100 + 300
(x + y + z)^2 = 400
Take the square root of both sides.
sqrt(x+y+z)^2 = sqrt(400)
x + y + z = 20
Note
This answer tells you nothing about the values of x y and z. On the other hand it does not ask for the values of x y and z.
