<h3>
Answer: D) 3/150</h3>
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Explanation:
With the use of a calculator, we see that,
- 11/19 = 0.57894736842106...., the decimals eventually repeat; but unfortunately my calculator ran out of room to show the repeating portion
- 4/7 = 0.5714285714285714..., the block "571428" repeats forever
- 1/3 = 0.333333.... the 3s go on forever
- 3/150 = 0.02
So 3/150 converts to the terminating decimal 0.02
The word "terminate" means "stop". In the other decimal values, the decimal digits go on forever repeating the patterns mentioned.
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A non-calculator approach will have us simplify 3/150 into 1/50 after dividing both parts by the GCF 3. Then notice how 50 has the prime factorization of 2*5*5. The fact that the denominator 50 can be factored in terms of only 2's and 5's is enough evidence to conclude that the fraction converts to a terminating decimal.
If the denominator factors into some other primes, other than 2s and 5s, then we don't have a terminating decimal. So that's why 11/19, 4/7 and 1/3 convert to non-terminating decimals.
Answer:
Step-by-step explanation:
we are given
we can simplify left side and make it equal to right side
we can use trig identity
now, we can plug values
now, we can simplify
now, we can factor it
![\frac{(sin(a)+cos(a))[3-4(sin^2(a)+cos^2(a)-sin(a)cos(a)]}{sin(a)+cos(a)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28sin%28a%29%2Bcos%28a%29%29%5B3-4%28sin%5E2%28a%29%2Bcos%5E2%28a%29-sin%28a%29cos%28a%29%5D%7D%7Bsin%28a%29%2Bcos%28a%29%7D%20)
we can use trig identity
![\frac{(sin(a)+cos(a))[3-4(1-sin(a)cos(a)]}{sin(a)+cos(a)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28sin%28a%29%2Bcos%28a%29%29%5B3-4%281-sin%28a%29cos%28a%29%5D%7D%7Bsin%28a%29%2Bcos%28a%29%7D%20)
we can cancel terms
now, we can simplify it further
now, we can use trig identity
we can replace it
so,
Answer:
Length of the garden = 10 ft
Step-by-step explanation:
Perimeter of a garden = 2(length + width)
Perimeter of the garden = 32 ft
Width of the garden = 6 ft
Length of the garden = x ft
Perimeter of a garden = 2(length + width)
32 = 2 ( x + 6 )
Open parenthesis
32 = 2x + 12
Subtract 12 from both sides
32 - 12 = 2x + 12 - 12
20 = 2x
Divide both sides by 2
20 / 2 = 2x / 2
10 = x
x = 10 ft
Therefore, length of the garden = x = 10 ft
