Answer:
6.69 to the nearest hundredth
Step-by-step explanation:
Use the law of sines
Let x = PQ
x sin 72 = 12 sin 32
x = 6.69 to the nearest hundredth
Triangle R T S is sitting on a horizontal line. Line S R extends through point Q to form exterior angle T R Q. Angle R T S is (2
2 answers:
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Answer:
∠Q = 63.4º, PQ = 2, QO = 4.47
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. There are different types of triangles such as the equilateral triangle, isosceles triangle, scalene triangle, right angled triangle.
Triangle POQ is a right angled triangle because ∠P = 90°. Also, ∠O = 26.6°.
Therefore in ΔPOQ: ∠P + ∠O + ∠Q = 180° (sum of angles in a triangle).
90 + 26.6 + ∠Q = 180
∠Q + 116.6 = 180
∠Q = 180 - 116
∠Q = 63.4°
We can find PQ and QO using sine rule. Sine rule for ΔPOQ is given as:
Answer:
We conclude that the graph y = x² can be transformed into the graph of the given equation y = (x - 12)²+3 by shifting the graph of y = x² right 12 units and then up 3 units.
Hence, option D is true.
Please check the attached graph.
Step-by-step explanation:
Given the parent function
y = x²
Given the transformed function
y = (x - 12)²
Horizontal Translation:
The horizontal translation of y = x² is of the form
f(x-h)
so y = y = (x - 12)² means y = x² is shifted 12 right.
Vertical Translation:
y = x²
Then y = x² + b is a vertical translation of y = x²
if b > 0, then y = x² + b is the graph of y = x² 'b' units up.
if b < 0, then y = x² + b is the graph of y = x² 'b' units down.
Thus, y = x² + 3 means the graph y = x² is vertically shifted up by 2 units.
Please check the attached graph.
- The blue graph is representing the graph of y = x².
- The red graph is representing the graph of y = (x - 12)²+3
Therefore, the graph y = x² can be transformed into the graph of the given equation y = (x - 12)²+3 by shifting the graph of y = x² right 12 units and then up 3 units.
Hence, option D is true.
