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
Explanation:
f(x) = (x-4)(x+2)
1) For x-intercept, y will be 0
<u />
<u>x-intercept</u>: (4, 0), (-2, 0)
2) For vertex: x = -b/2a where ax² + bx + c
<u>Quadratic function</u>:
<u>vertex</u>:
y: (x-4)(x+2) = (1-4)(1+2) = -9
ordered pair of vertex: (1, -9)
3) For y-intercept, x will be 0
<u>y-intercept</u>: (0, -8)
Answer:
1, 2
2, 5
3, 8
4, 11
5, 14
Step-by-step explanation:
you just plug each n value into the <em>n</em>
Answer:
Length of side AB = 5
Step-by-step explanation:
A regular polygon is one in which all angles are equal and all the sides have the same length.
Now, it means that;
AB = BC = CD = DE = AE
We are told that BC is represented by 3x - 4 while DE is represented by the expression 4x - 9.
Thus, from equal length of sides of a regular polygon, we have;
3x - 4 = 4x - 9
4x - 3x = 9 - 4
x = 5
Thus, length of BC = 3(5) - 4 = 15 - 4 = 11
Therefore, Length of AB = 5
Answer:
Step-by-step explanation:
The sum of 83 and a number would be as an expression, where 
is "said number".
