Step-by-step explanation:
AB · BE = CB · BD Given
CB/BE = AB/BD Division Property of Equality
<ABC = <DBE Vertical angles are equal
ΔABC ≅ ΔDBE SAS Similarity Theorem
Hope it helps
Answer:
2.14 X 10(power4)
Step-by-step explanation:
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
Answer:
239 ft².
Step-by-step explanation:
Let P represent the price for tiling.
Let S represent the size of the room.
From the question,
Price (P) varies directly as the size (S) i.e
P & S
P = KS
Where K is the constant of proportionality.
Next, we shall determine the value of K as follow
Price (P) = $ 4224
Size (S) = 264 ft²
Constant of proportionality (K) =?
P = KS
4224 = K × 264
Divide both side by 264
K = 4224/264
K = 16
Finally, we shall determine the size of the kitchen that will cost $ 3824 for tiling.
This is illustrated below:
Price (P) = $ 3824
Constant of proportionality (K) = 16
Size (S) =?
P = KS
3824 = 16 × S
Divide both side by 16
S = 3824/16
S = 239 ft²
Therefore, the size of the kitchen is 239 ft².
Answer:
x > 1/9
Step-by-step explanation:
Given that:
3x-1>-6x
Adding 6x + 1 on both sides we get
3x-1 + 6x + 1>-6x + 6x +1
3x + 6x > 1
Adding both variables
9x > 1
Dividing both sides b 9 we get
9x/9 > 1/9
x > 1/9
I hope it will help you!
