Rewrite the function f(x)=3(x-1)^2+9 in the form f(x)=ax^2+bx+c
1 answer:
You might be interested in
The strategy
<span>Model the situation as a right triangle.
Determine the appropriate trigonometric ratio in order to find the missing angle.
Form an equation and solve for the missing angle.
Calculate the final result and round.
</span>
Modeling as a right triangle
This situation can be modeled by the following right triangle. The hypotenuse is 100 meters and the height is 42 meters. <span>We are asked to find the angle of elevation, which is the angle on the left.
</span>Determining the appropriate trigonometric ratio
We are given the side opposite to the missing angle and the hypotenuse <span>The appropriate trigonometric ratio is therefore the SINE.
</span>
<span>Forming an equation and solving
</span>
Denoting the missing angle by θ, we obtain the equation
<span>
</span>Solving the equation, we get
Evaluating this result in the calculator and rounding to the nearest tenth, we get θ =
degrees.
<span>Model the situation as a right triangle.
Determine the appropriate trigonometric ratio in order to find the missing angle.
Form an equation and solve for the missing angle.
Calculate the final result and round.
</span>
Modeling as a right triangle
This situation can be modeled by the following right triangle. The hypotenuse is 100 meters and the height is 42 meters. <span>We are asked to find the angle of elevation, which is the angle on the left.
</span>Determining the appropriate trigonometric ratio
We are given the side opposite to the missing angle and the hypotenuse <span>The appropriate trigonometric ratio is therefore the SINE.
</span>
<span>Forming an equation and solving
</span>
Denoting the missing angle by θ, we obtain the equation
</span>Solving the equation, we get
Evaluating this result in the calculator and rounding to the nearest tenth, we get θ =
<u>Given</u>:
The exterior angle P is 74°
The measure of ∠PRQ is 51°
We need to determine the measure of ∠PQR
<u>Measure of ∠QPR:</u>
From the figure, it is obvious that P is the intersection of the two lines.
The angle 74° and ∠QPR are vertically opposite angles.
Since, vertically opposite angles are always equal, then the measure of ∠QPR is 74°
Thus, the measure of ∠QPR is 74°
<u>Measure of ∠PQR:</u>
The measure of ∠PQR can be determined using the triangle sum property.
Thus, we have;
Substituting the values, we get;
Thus, the measure of ∠PQR is 55°
Hence, Option B is the correct answer.