NOT NECESSARILY would a triangle be equilateral if one of its angles is 60 degrees. To be an equilateral triangle (a triangle in which all 3 sides have the same length), all 3 angles of the triangle would have to be 60°-angles; however, the triangle could be a 30°-60°-90° right triangle in which the side opposite the 30 degree angle is one-half as long as the hypotenuse, and the length of the side opposite the 60 degree angle is √3/2 as long as the hypotenuse. Another of possibly many examples would be a triangle with angles of 60°, 40°, and 80° which has opposite sides of lengths 2, 1.4845 (rounded to 4 decimal places), and 2.2743 (rounded to 4 decimal places), respectively, the last two of which were determined by using the Law of Sines: "In any triangle ABC, having sides of length a, b, and c, the following relationships are true: a/sin A = b/sin B = c/sin C."¹
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We have that
N 11)
a) graph the equation y=x²-3x-10
using a graph tool
see the attached figure
b) Determine the roots of the equations
the roots of the equations are the values for y=0
x²-3x-10=0
x²-3x-10=(x+2)*(x-5)=0
the roots are
x1=-2
x2=5
see the attached figure problem 11
N 12) what is the value of x in the equation?
3x²=7x
3x²=7x-------> 3x²-7x=0--------> x*(3x-7)=0
x1=0
3x-7=0------> 3x=7------> x=7/3
the values of x are
x1=0
x2=7/3---> 2.33
see the attached figure problem 12
N 13) what is the value of x in the equation?
x²-5x=6----------> x²-5x-6=0
x²-5x-6=0-------> (x+1)*(x-6)=0
the values of x are
x1=-1
x2=6
N 14) what is the value of x in the equation?
2x²-5x=12--------> 2x²-5x-12=0
using a graph tool
see the attached figure problem N 14
2x²-5x-12=0----------> (x+3/2)*(x-4)=0
the values of x are
x1=-3/2
x2=4
Answer:
Almost...
The correct answer would be
To find the area of the base, multiply 15 times 16 then divide by 2
Then multiply by 19 to find the volume of the shape
Step-by-step explanation:
The base is a triangle
The area of a triangle = base length times height divided by 2
The triangle has a base length of 16 and a height of 15
So to find the area of the base we multiply 15 times 16 and divide that by 2
The volume of a prism is equal to the area of the base times the length of the prism
The length of the prism is 19 so we would then multiply by 19
Answer:
60 ft.
Step-by-step explanation:
We can solve this problem with a simple proportion:
24 / 10 = h / 25
10h = 24 * 25
600 = 10h
60 ft. = h