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
The final amount of yards the team has is 8 yards.
Because you're trying to make them congruent, equal the two expressions to each other.
So, for #10 you would equal them so it would look like this.
2x+2=5x-19
Then you would just go ahead and simplify
2x+2=5x-19
-2x -2x
---------------
2= 3x -19
+19 +19
---------------
21=3x
--- ----
3 3
x=7
This means that x should be 7. You can check this just by plugging it in
2x+2
2(7)+2 = 16
5x-19
5(7)-19= 16
Same with #11.
x+8=3x-14
-x -x
--------------
8=2x-14
+14 +14
--------------
22=2x
--- ----
2 2
x=11
Check.
x+8
11+8= 19
3x-14
3(11) - 14 = 19
Answer:
C
Step-by-step explanation:
5ax²-20x³+2a-8x
=5 x²(a-4x)+2(a-4x)
=(a-4x)(5x²+2)
