We have that
y = −14x² − 2x − 2
First, we need to transform the equation into its vertex form
(x - h)²=4p(y - k)
<span>Group
terms that contain the same variable
</span>y = (−14x² − 2x )− 2
<span>Factor the
leading coefficient
</span>y = -14*(x² + (2/14)x )− 2
<span>Complete
the square Remember to balance the equation
</span>y = -14*(x² + (2/14)x +(2/28)²-(2/28)²)− 2
y = -14*(x² + (2/14)x +(2/28)²)− 2+14*(2/28)²
y = -14*(x² + (2/14)x +(2/28)²)− 2+56/784
Rewrite as perfect squares
y = -14*(x+(2/28))²− 1512/784------>(x+1/14)²=(-1/14)*(y+1512/784)
4p=-1/14------> p=-1/56
This is a vertical parabola and its focus <span>(h, k + p)</span>
<span>h=-1/14</span>
<span>k+p=(-1512/784)+(-1/56)----> (-1512-14)/784)----> -1526/784</span>
<span>
</span>
<span>the focus is</span>
<span>(-1/14,-1526/784)</span>
The sign would be NEGATIVE
It is very simple, <span>|2x + 4| > 14, we have 2x+4>14 or -(2x+4) >14 (absolute value definition) so 2x> 14-4, x>10/2=5 or -2x>14+4, -x>18/2=9, implies x< - 9
the solution is x>5, or x< -9, so the answer is </span>number line with open circles on _9 and 5, shading going in the opposite directions.
Answer:
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Step-by-step explanation:
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Answer: The correct option is (A). 464 square units.
Step-by-step explanation: We are given a rectangle inside a regular hexagon in the figure.
We know that each side of a regular hexagon has same measure, so the measure of each side is
a = 18 units.
Therefore, the area of the regular hexagon is given by
Since the rectangle has length and breadth of 21 units and 18 units respectively, so the area of the rectangle is
Thus, the area of the shaded region in the figure will be
Hence, option (A) is correct.
