(a) One unique triangle. This is an equilateral triangle since all sides are the same length. Through the SSS property, we can prove that only one triangle is possible here.
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(b) Cannot make a triangle. The triangle inequality theorem says that adding any two sides of a triangle must result in a value larger than the third side. Add up the first two sides (1 and 2) to get 1+2 = 3, which is not larger than the third side (3 units long). I recommend cutting out strips of paper that are 1 inch, 2 inches and 3 inches long, and trying to form a triangle. You'll find that a triangle is not possible. The 1 inch and 2 inch strips will line up to form a straight line that is 3 inches long, and basically you have a flat line (or a triangle with area 0)
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(c) More than one triangle. The angles add up to 180 since 35+60+85, so we can form a triangle. It turns out we can form infinitely many of them. The AA (angle angle) similarity theorem allows us to scale any triangle to make it larger or smaller compared to the original.
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(d) Cannot make a triangle. I'm assuming the 509 should actually be 50°. If so, then a triangle is not possible because the three angles (50, 50, 50) do not add to 180. We have instead 50+50+50 = 150. For any triangle, the three angles must always add to 180 degrees.
Answer:
49.132 m²
Step-by-step explanation:
Area of a triangle=1/2(base×height)
Area=1/2(6×8)
Area=24 m²
Now
Area of semi circle=πr²/2
Area=(3.14)(8÷2)²/2
Area=(3.14)(4)²/2
Area=(3.14)(16)/2
Area=50.265/2
Area=25.132 m²
Now
Total area=area of triangle+semi-circle
Total area=24+25.132
Total area=49.132 m²
G(x) =-16 hope this helps
Answer:
see explanation
Step-by-step explanation:
Using proportion to find the teachers required x, then
= 
( cross- multiply )
221x = 3536 ( divide both sides by 221 )
x = 16
The number of teachers required this year is 16
Answer:
x=3
Step-by-step explanation:
You have to look at the line(axis of symmetry) and determine what number it is it going thought, and whether it is going through the x or y axis.
In this case the axis of symmetry is going through the x axis and 3, therefore the answer is x=3.
Hope this helps!
