Find the sale of the item. Round to two decimal places if necessary.
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<u>Given</u>:
The given figure shows the intersection of the two lines.
The angles formed by the intersection of the two lines are (3x - 8)° and (2x + 12)°
We need to determine the equation to solve for x and to find the value of x.
<u>Equation to solve for x:</u>
Since, the two angles (3x - 8)° and (2x + 12)° are vertically opposite angles and the vertical angles are always equal.
Hence, we have;
Thus, the equation to solve for x is
<u>Value of x:</u>
The value of x can be determined by solving the equation
Thus, we have;
Thus, the value of x is 20.
Considering the definition of axis of symmetry, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.
<h3>Axis of symmetry</h3>An axis of symmetry is an imaginary reference line that, when dividing any shape into two parts, its opposite points are equidistant from each other, that is, they are symmetrical.
In other words, the axis of symmetry is a vertical line that divides the parabola into two congruent halves.
The axis of symmetry is the line perpendicular to the "x" axis that contains the vertex of the function, that is, it always passes through the vertex of the parabola. So the x-coordinate of the vertex is the equation of the axis of symmetry.
That is, in a quadratic function that has the form:
f(x)= ax² + bx + c
the axis of symmetry is a vertical line and it is defined as .
In this case, you know:
- a= 3
- b=12
- c=9
Replacing in the definition of axis of symmetry:
Solving:
<u><em>x= -2</em></u>
Finally, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.
Learn more about axis of symmetry:
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