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Answer:
Choice A, 20(3n-m)
Step-by-step explanation:
First, lets combine like terms for the question 54n - 20m + 6n,
60n - 20m.
Next, lets rule out the choices that are visibly wrong. This includes Choice B, because it wouldn't equal what is above and Choice C, as it ignores unlike terms.
Now, it is down to Choices A and D. Let's use the distributive property to simplify these options.
Choice A:
20(3n-m)
60n-20m
Choice D:
20(m-3n)
20m-60m
With this, it can be concluded that the correct answer is Choice A since it equals 60n-20m, which is equal to the original question when like terms are combined.
For multiplying radical expressions, we are first to list down the given.
f(x) = (x + 3/x)^(1/2), and
g(x) = (x + 3/2x)^(1/2)
We take a look at first the values of the radicands, these are the numbers inside the radical signs. Since, both of the radicands are raised to exponent 1/2, it is easy to say that we just have to multiply them and raise the product to the exponent 1/2 as well. That is,
(f·g)(x) = ((x + 3/x)(x + 3/2x))^(1/2)
Simplifying,
(f·g)(x) = ((x² + 3/2 + 3 + 9/2x²)^(1/2))
Further simplification will lead us to the final answer of,
<em>(f·g)(x) = (x² + 9/2 + 9/2x²)^(1/2)</em>
Answer:
2.69≤x≤17.31
Step-by-step explanation:
Lety the amount in the other Piggy bank be x.
The difference in the amount of money between the two banks is no more than $10 is expressed as;
|x-7.31| ≤ 10
The value in the modulus sign can be positive or negative
If positive;
x-7.31 ≤ 10
x ≤ 10+7.31
x≤17.31
If negative
-(x-7.31) ≤ 10
-x+7.31 ≤ 10
-x ≤ 10-7.31
-x ≤ 2.69
Multiply both sides by -1
x ≥ -2.69
The compound inequality representing the amount of money in the other bank is -2.69≤x≤17.31