First, find the value of x. Note that the angles x, 0.5x and 3x sum up to 4.5x, and that this sum has the value 180 degrees. Solving this equation for x, we get x = 40 degrees.
Now, 0.5x and 0.5y are vertical angles, and thus x = y. So, with x being 40 degrees, y = 40 degrees.
Answer: or
Step-by-step explanation:
We can convert from mixed numbers to decimal numbers:
Since they cleaned up 8.2 kilograms of trash in one neighborhood and 11.5 kilograms in another neighborhood, the total trash they cleaned up was:
We know that they sent 1.25 kilograms to be recycled. Then, in order to calculate how many kilograms of trash they threw away, we must subtract the total kilograms of trash they cleaned up and the kilograms they sent to be recycled.
Then:
or
<h3>Answer:</h3>
Area of DEFG = (1/2)a²
<h3>Explanation:</h3>
See the attached diagram.
Line FB ║ EG and line GA ║DF. ∆GFA ≅ ∆FGX, and ∆EXF ≅ ∆BAG. Then the area of ∆BFG is equal to the area of ∆EGF and, by symmetry, the area of ∆FDE.
This means the area of DEFG is the same as the area of ∆DFB.
The problem statement tells us ∠FDG = 45°. By symmetry, ∠EGD = 45° and by corresponding angles related to parallel lines ∠FBD = 45°. Then ∠DFB = 90° and the area of ∆DFB = (1/2)(DF)(FB) = (1/2)a².
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<em>Alternate approach</em>
Recognize that ∠EGD = ∠FDG = 45°, so ∠DXG = 90°. This means all the triangles internal to DEFG are right triangles. Designate the distance XF with the variable <em>b</em>. Then DX = (a-b) and the area of the trapezoid is ...
... Area(DEFG) = Area(DXG) + Area(DXE) + Area(GXF) + Area(FXE)
... = (1/2)(a-b)² +(1/2)(a-b)(b) +(1/2)(a-b)(b) +(1/2)b²
... = (1/2)(a² -2ab +b² +ab -b² +ab -b² +b²)
... = (1/2)(a² +ab(-2+1+1) +b²(1-1-1+1))
... Area(DEFG) = (1/2)a²
Answer:
yup
Step-by-step explanation:
yup
Answer:
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Step-by-step explanation:
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