You would shift this to the right 8 places. This is because in vertex form, the x value is the opposite of the number in the parenthesis with the x.
Answer:
(x + 3)^2 is left 3 because it becames 0 at -3
(x - 3)^2 is right 3 because it becames 0 at 3
x^2 +3 is up 3 because your just adding 3 units up
x^2 - 3 is down 3 because your just subtracting 3 units down
Step-by-step explanation:
Answer:
a = length of the base = 2.172 m
b = width of the base = 1.357 m
c = height = 4.072 m
Step-by-step explanation:
Suppose we want to build a rectangular storage container with open top whose volume is 12 cubic meters. Assume that the cost of materials for the base is 12 dollars per square meter, and the cost of materials for the sides is 8 dollars per square meter. The height of the box is three times the width of the base. What’s the least amount of money we can spend to build such a container?
lets call a = length of the base
b = width of the base
c = height
V = a.b.c = 12
Area without the top:
Area = ab + 2bc + 2ac
Cost = 12ab + 8.2bc + 8.2ac
Cost = 12ab + 16bc + 16ac
height = 3.width
c = 3b
Cost = 12ab + 16b.3b + 16a.3b = 12ab + 48b² + 48ab = 48b² + 60ab
abc = 12 → ab.3b = 12 → 3ab² = 12 → ab² = 4 → a = 4/b²
Cost = 48b² + 60ab = 48b² + 60b.4/b² = 48b² + 240/b
C(b) = 48b² + 240/b
C'(b) = 96b - 240/b²
Minimum cost: C'(b) = 0
96b - 240/b² = 0
(96b³ - 240)/b² = 0
96b³ - 240 = 0
96b³ = 240
b³ = 240/96
b³ = 2.5
b = 1.357m
c = 3b = 3*1.357 = 4.072m
a = 4/b² = 2.172m
Answer:
√185 or 13.60 units to the nearest hundredth.
Step-by-step explanation:
For the points (x1,y1) and (x2,y2) the length between the points is given by:
L = √ [ (x2-x1)^2 + (y2-y1)^]
So here we have:
Length of AB √ [ (7- - 4)^2 + (-2 - 6)^2]
= √ (121 + 64)
= √185.
112 cm² * 6 triangles = 672 cm²
