The vertex form of quadratic equation is expressed as:
y = a (x - h)² + k
We manipulate the given equation to be the same as the vertex form. First we transpose the constants to the left-hand side.
y - 14 = 5x² + 20x
Then, we factor out in right hand side the coefficient of the x² term.
y- 14 = 5 (x² + 4x)
We divide the coefficient of the x term with 2 and take its square. We add this value to both sides of the equation but we should remember that in the left-hand side we should multiply this value with five to keep it balanced.
y - 14 + 20 = 5 (x² + 4x +4)
We simplify the right-hand side as:
y + 6 = 5 (x + 2)²
We can now manipulate further the equation above in the vertex form. Thus,
y= 5 [ x- (-2)]² - 6
Answer: b) they loaded 112356 lbs of cargo
Step-by-step explanation:
When a boat or an object floats in water, the volume of water that it displaces is equivalent to its weight.
When moving into the port, the cargo boat displaced 2200 ft³ of water. Since the density of water is 62.42 lb/ft³ and mass = density × volume, then the mass of the cargo boat on entering the port is
2200 × 62.42 = 137324 lbs
On leaving the port, it displaces 4000 ft³ of water. The mass of the cargo boat on leaving the port is
4000 × 62.42 = 249680 lbs
The difference in both masses is
249680 - 137324 = 112356 lbs
Therefore, they loaded 112356 lbs of cargo
Answer:
the answer to 5x-7(2-4x)= =33x−14
the answer to 8 - 3(6 - 6x) ==18x−10
the answer to 9a - 4(2a + 5) ==a−20
Step-by-step explanation:
Answer:x
Step-by-step explanation:
After Greg makes the pudding 1 time, it takes him
hours to make it.
After Greg makes the pudding 2 times, it takes him
hours to make it
After Greg makes the pudding 2 times, it takes him
hours to make it
so The function is
Answer: f of x equals 2 multiplied by 0.8 to the power of x
