<span>To write this sum as a single fraction we need to put both of them over a common denominator. Our common denominator will be the simplest thing that has both 3 and 5 as a factor, which is 15 (x-2)/3 + (x+3)/5 = 5(x-2)/15 + 3(x+3)/15 Now we can put both numerators over the same denominator to get (5(x-2) + 3(x+3))/15 Next we should multiply out and simplify the numerator (5(x-2) + 3(x+3))/15 = (5x -10 +3x +9)/15 = (8x-1)/15
hope this helps but dont know if its right</span>
Answer:
θ = 36.9°, 90°, 216.9°, or 270°
Step-by-step explanation:
4 sin 2θ − 3 cos 2θ = 3
Use double angle formulas:
4 (2 sin θ cos θ) − 3 (cos²θ − sin²θ) = 3
8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3
Use Pythagorean identity:
8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3 (sin²θ + cos²θ)
8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3 sin²θ + 3 cos²θ
8 sin θ cos θ − 6 cos²θ = 0
2 cos θ (4 sin θ − 3 cos θ) = 0
2 cos θ = 0
θ = 90° or 270°
4 sin θ − 3 cos θ = 0
4 sin θ = 3 cos θ
tan θ = 3/4
θ = 36.9° or 216.9°
<u>Answer:
</u>
Two required integers are 5 and 10.
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Solution:
</u>
Given that a positive integer is twice another. The sum of the reciprocals of the positive integers is
We have to find the two integers.
Let assume that one integer = x
Since another integer is twice of first one, so second integer = 2x
Reciprocal of first integer =
Reciprocal of first integer =
Given that sum of reciprocal =
On solving above equation for x,
2x=10
x=5
First integer = x = 5
Second integer = 2x = 10
Hence two required integers are 5 and 10.
Answer:
3/2
Step-by-step explanation:
A couple of different methods are used for dividing fractions.
1. "Invert and multiply". Dividing by a number is the same as multiplying by its reciprocal:
(3/4) / (1/2) = (3/4) × (2/1)
= (3·2)/(4·1) = 6/4 = 3/2
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2. Make the denominators the same and use the ratio of numerators.
(3/4) / (1/2) = (3/4) / (2/4) = 3/2
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For these fractions, you can recognize that 3/4 is 1/4 more than 1/2, and that 1/4 is half of 1/2. That means 3/4 is half-again as much as 1/2, so is 1 1/2 = 3/2 times 1/2. This tells you the ratio (3/4) : (1/2) = 3/2.
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Along the lines of the above, you can write the ratio as ...
(3/4) : (1/2)
and multiply by 4 to get
= (3/4)×4 : (1/2)×4 = 3 : 2
Answer:
Step-by-step explanation:
Let the volume of full bottle is y milliliter.
According to the question,
Thus, the volume of full bottle =
⇒ Option A is correct.