AB = 6 cm, AC = 12 cm, CD = ?
In triangle ABC, ∠CBA = 90°, therefore in triangle BCD ∠CBD = 90° also.
Since ∠BDC = 55°, ∠CBD = 90°, and there are 180 degrees in a triangle, we know ∠DCB = 180 - 55 - 90 = 35°
In order to find ∠BCA, use the law of sines:
sin(∠BCA)/BA = sin(∠CBA)/CA
sin(∠BCA)/6 cm = sin(90)/12 cm
sin(∠BCA) = 6*(1)/12 = 0.5
∠BCA = arcsin(0.5) = 30° or 150°
We know the sum of all angles in a triangle must be 180°, so we choose the value 30° for ∠BCA
Now add ∠BCA (30°) to ∠DCB = 35° to find ∠DCA.
∠DCA = 30 + 35 = 65°
Since triangle DCA has 180°, we know ∠CAD = 180 - ∠DCA - ∠ADC = 180 - 65 - 55 = 60°
In triangle DCA we now have all three angles and one side, so we can use the law of sines to find the length of DC.
12cm/sin(∠ADC) = DC/sin(∠DCA)
12cm/sin(55°) = DC/sin(60°)
DC = 12cm*sin(60°)/sin(55°)
DC = 12.686 cm
We have to find LCM of 12,14,16
Refer to the attachment
LCM=2×2×2×2×3×7=16×21=336years
Answer:
and 
.
Step-by-step explanation:
Equation:
Solution:
Set factors equal to zero,that is:
Solving for equation 1:
Solving for equation 2:
Hence,the solutions to the quadratic equation in factored form is and .
Good luck on your assignment!
Answer:
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = £600
r = 3.2% = 3.2/100 = 0.32
n = 1 because it was compounded once in a year.
t = 6 years
Therefore,.
A = 600(1 + 0.032/1)^1 × 6
A = 600(1.032)^6
A = £724.82
Answer:
19
Step-by-step explanation:
f(-7) = 4(-7) + 9
-28 + 9
= 19
