Answer:
Amount they ate is 6/8 or 3/4 of the pizza
Amount left over is 2/8 or 1/4 of the pizza.
Step-by-step explanation:
your family at 6 out of 8 pieces and simplified thats 3/4 if you divide both by 2
so the pieces left over would be 2 pieces or 2 out of the 8 pieces are left over.
making your fraction 2/8
Now you simplify and you can divided both 2 and 8 by 2
Making your other fraction 1/4
Answer:
Step-by-step explanation:
The equation to solve is:
To get rid of the "square", we need to take square root of both sides:
Then we use algebra to find the value(s) of x. Remember, when we take square root, we have to add up a "+-" (on the right side). Shown below:
So these are 2 answers for x.
Answer:
- sin(2x) = -4/5
- cos(2x) = 3/5
- tan(2x) = -4/3
Step-by-step explanation:
It may be easiest to start with tan(2x).
tan(2x) = 2tan(x)/(1 -tan(x)²)
tan(2x) = 2(-1/2)/(1 -(-1/2)²) = -1/(3/4)
tan(2x) = -4/3 . . . . . still a 4th-quadrant angle
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Then cosine can be found from ...
cos(2x) = 1/√(tan(2x)² +1) = 1/√((-4/3)²+1) = √(9/25)
cos(2x) = 3/5
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Sine can be found from these two:
sin(2x) = cos(2x)tan(2x) = (3/5)(-4/3)
sin(2x) = -4/5
Answer: 15.59 or 9√3
Step-by-step explanation:
We can use the Pythagorean Theorem to calculate the third side.
c² = a² + b² In a 30 60 90 Triangle, the hypotenuse is twice the length of the short leg of the right angle.
c is the hypotenuse. a is the short leg
18² = 9² + b²
324 = 81 + b² Subtract 81 from both sides.
324 - 81 = b² becomes b² = 243 Take the square root of both sides
b = 15.5884 . This can be rounded to 15.59 or 15.6 depending on significant digits or amount of precision required.
The proportions of the sides of the 30 60 90 triangle can also be used:
2² = 1² + b²
4 = 1 + b²
3 = b²
√3 = b
You can always multiply the length of the short leg by √3 to get the length of the side opposite the 60° angle
