Answer:
- 5.8206 cm
- 10.528 cm
- 23.056 cm^2
Step-by-step explanation:
(a) The Law of Sines can be used to find BD.
BD/sin(48°) = BD/sin(50°)
BD = (6 cm)(sin(48°)/sin(60°)) ≈ 5.82064 cm
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(b) We can use the Law of Cosines to find AD.
AD^2 = AB^2 +BD^2 -2·AB·BD·cos(98°) . . . . . angle ABD = 48°+50°
AD^2 ≈ 110.841
AD ≈ √110.841 ≈ 10.5281 . . . cm
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(c) The area of ∆ABD can be found using the formula ...
A = ab·sin(θ)/2 . . . . . where a=AB, b=BD, θ = 98°
A = (8 cm)(5.82064 cm)sin(98°)/2 ≈ 23.0560 cm^2
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Angle ABD is the external angle of ∆BCD that is the sum of the remote interior angles BCD and BDC. Hence ∠ABD = 48° +50° = 98°.
Given:
Polynomial 
To find:
The values of x.
Solution:
Quadratic equation formula:
Here 
.
Substitute the values in the formula, we get
Option E and option F are the roots of the polynomial.
The values of x are 
.
B) Parallelogram JKLM is translated and then dilated
as well as c
C) Parallelogram JKLM is dilated and translated
C is the best answer because is size is changing. In all the others nothing is changing except the position which remains congruent and similar but C does not . The sizes changes which makes them not congruent but still similar.
In an isosceles triangle, the base angles are congruent. The third angle is called the vertex angle.
Here, the vertex angle is <A.
Therefore, m<C = m<B.
m<A = 3m<B + 20
m<A + m<B + m<C = 180
3m<B + 20 + m<B + m<B = 180
5m<B + 20 = 180
5m<B = 160
m<B = 32
m<C = m<B = 32
Answer: m<C = 32 deg
