3x - 6x + 14 = 2x + 39
-3x + 14 = 2x + 39
-5x = 25
x = -5
Answer: c. 50
Step-by-step explanation:
1. By definition, when you add the exterior angles of a regular polygon, you obtain 360 degrees and the number of sides of that polygon can be calculated by dividing 360 degrees by the measure of the exterior angle of it.
2. As you know, the number of sides cannot be fractions, therefore, if you make the folllowing division:
360°/50°=36/5
You obtain a fraction.
3. Then, an exterior angle of a regular polygon cannot have the measure is 50°.
I think it is a compound event because rolling each die is an independent event.
Answer: 6 cm
Step-by-step explanation:
Given: The ratio of the areas of two similar parallelograms is 4:9.
To find : The height of the bigger one if the smaller is of height 4 cm.
Let h be the height of the bigger one.
Since the areas of similar figures are proportional to the square of their corresponding sides.
Then, 
![\dfrac{16}{h^2}=\dfrac{4}{9}\\\\\Rightarrow\ h^2=\dfrac{9}{4}\times16\\\\\Rightarrow\ h^2=36\\\\\Rightarow\ h= 6\ cm\ \ \ \ \text{[ height cannot be negative.]}](https://tex.z-dn.net/?f=%5Cdfrac%7B16%7D%7Bh%5E2%7D%3D%5Cdfrac%7B4%7D%7B9%7D%5C%5C%5C%5C%5CRightarrow%5C%20h%5E2%3D%5Cdfrac%7B9%7D%7B4%7D%5Ctimes16%5C%5C%5C%5C%5CRightarrow%5C%20h%5E2%3D36%5C%5C%5C%5C%5CRightarow%5C%20h%3D%206%5C%20cm%5C%20%5C%20%5C%20%5C%20%5Ctext%7B%5B%20height%20cannot%20be%20negative.%5D%7D)
Hence, the height of bigger parallelogram = 6 cm
Since
∠CPD = x
and segment PN is the angle bisector of this angle, therefore segment PN
equally divides ∠CPD into two angles. Which means that:
∠CPN = ∠NPD = x / 2
Further,
segment PN is also the perpendicular bisector of AB which further means that
the intersection formed by PN and AB creates a right angle (90°). Therefore:
∠NPD + ∠DPB = 90°
x/2
+ ∠DPB =
90°
∠DPB =
90 – x/2
Therefore:
sin∠<span>DPB = sin(90 – x/2) which is not in the choices</span>
However we know that the
relationship of sin and cos is:
sin(π/2
- θ) = cos θ
Where,
π/2
= 90
θ =
x/2
Therefore:
sin(90 – x/2) = cos(x/2)
Answer:
<span>cos(x/2)</span>
