If you are solving to find n, divide 1/3 by 3/4, which is 4/9
Answer:
The 3rd:
f(x) = (x - 1)(x - 1)(x – 6)
Step-by-step explanation:
Its roots are the x-values for which f(x)=0, that are:
x1=1
x2=1
x3=6
We use the fact that if x+y+z = 0, then x³+y³+ z³ = 3 x y z.<span>
(x</span>²-y²) + (y²-z²) + (z²-x²) = 0<span>
also: (x-y) + (y-z)+ (z-x) = 0
we assume that: x </span>≠y ≠ z.
<span>
hence,
(x²-y²)³ + (y²-z²)³ + (z²-x²)³ ÷ (x-y)³ + (y-z)³ + (z-x)³
= 3 (x</span>²-y²) (y²-z²) (z²-x²) ÷ [3 (x-y) (y-z) (z-x)]
<span>= (x+y) (y+z) (z+x)</span>
Answer:
Jaden added instead of subtracting 23 and 5
Step-by-step explanation:
Answer:
4) 16√3 in²
5) 63 cm²
Step-by-step explanation:
The formula to use in these cases is ...
A = (1/2)ab·sin(θ)
where a, b are the side lengths and θ is the angle between them.
It helps to know the trig functions of the "special" angles used here.
sin(120°) = sin(60°) = (√3)/2
cos(60°) = 1/2
sin(135°) = cos(45°) = (√2)/2
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4) The external angle at the base is the supplement of 120°, so is 60°. Then the length of the missing segment between the end of the base and the right angle at h is ...
x = (8 in)cos(60°) = (8 in)(1/2) = 4 in
So, the bottom edge of the triangle is 12 in - 4 in = 8 in.
The area is ...
A = (1/2)(8 in)(8 in)sin(120°) = (1/2)64(√3)/2 in² = 16√3 in²
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5) As in the previous problem, the difference between the given horizontal dimension and the base of the triangle is ...
x = (18 cm)cos(180°-135°) = 18(√2)/2 cm = 9√2 cm
Then the base of the triangle is ...
16√2 cm -9√2 cm = 7√2 cm
The area is then ...
A = (1/2)(18 cm)(7√2 cm)(√2)/2 = 63 cm²