The standard form of a quadratic equation is
,
where 
, 
, and 
are coefficients. You want to get the given equation into this form. You can accomplish this by putting all the non-zero values on the left side on the equation.
In this case, the given equation is
Since 
is on the right side of the equation, we subtract that from both sides. The resulting equation is
Looking at the standard form equation , we can see that
Answer:
c = -6
d = 2
Step-by-step explanation:
After reflection about the x-axis:
A --> A'
(2,3) --> (2,-3)
(4,3) --> (4,-3)
(2,6) --> (2,-6)
After translation:
(2 + c, -6 + d) --> (-4, -4)
2+c = -4
c = -6
-6+d = -4
d = 2
Answer: a) The figure can be reasonably divided into two geometries:
• a rectangular prism
• a hemisphere.
b) The volume of the rectangular prism is given by
V = lwh
V = (10 cm)(5 cm)(4 cm) = 200 cm³
The volume of the hemisphere is given by
V = (2π/3)r³
V = (2π/3)(3 cm)³ = 18π cm³
c) The total volume of the figure is
total volume = (prism volume) + (hemisphere volume)
V = 200 cm³ + 18π cm³
V ≈ 256.549 cm³
Step-by-step explanation:
Answer: 2
Step-by-step explanation:
try each value in the equation
2(0) + 1 = 3
0 + 1 = 3
1 ≠ 3
so 0 doesn’t work
2(1) + 1 = 3
2 + 1 = 3
3 = 3
this works, so the answer is 1
h(t) = -46t² + 40t + 3
We can think this graph by t being the x-axis and h being y-axis
So we want the maximum value to y.
We know by math that the vertex of a parabola is (-b/2a, -Δ/4a)
So the y value of the vertex is -Δ/4a
Let's calculate:
Δ = b² - 4.a.c
Δ = 40² - 4.(-46).3
Δ = 2152
Yvertex = -2152/4.(-46)
Yvertex = 2152/184
Yvertex = 269/23
Now we have the value of y we need to equal it to the equation
269/23 = -46t² + 40t + 3
-46t² + 40t + 3 - 269/23 = 0
-46t² + 40t - 200/23 = 0
Δ = b² - 4.a.c
Δ = 40² - 4 . -46 . (-200/23)
Δ = 1600 - 4. -46 . (-200/23)
Δ = 0
There's 1 real root.
In this case, x' = x'':
x = (-b +- √Δ)/2a
x' = (-40 + √0)/2.-46
x'' = (-40 - √0)/2.-46
x' = -40 / -92
x'' = -40 / -92
x' = 0,43478260869565216
x'' = 0,43478260869565216
So, after approximately 0,4348 seconds the balloon will reach the highest point.
B) height after 2 seconds
h(2) = -46.2² + 40.2 + 3
h(2) = -46.4 + 80 + 3
h(2) = -184 + 83
h(2) = -101
Not sure how it's possible but it would be -101.
