21/2 as a improper fraction

11 answers

The improper fraction form of 21/2 is 10 1/2.
The conjecture "if n is a whole number, then 3n+1 is a prime number" is disproved by which statement?
3×2+1=7
3×6+1=19
3×4+1=13
3×8+1=25
The conjecture is disproved by the statement "3×8+1=25" because 25 is not a prime number.
Simplify (5x+7y)(6x+7y)
To simplify the expression (5x+7y)(6x+7y), you can use the distributive property.

First, distribute 5x to both terms inside the second parentheses:
(5x)(6x) + (5x)(7y)

This simplifies to:
30x^2 + 35xy

Next, distribute 7y to both terms inside the second parentheses:
(7y)(6x) + (7y)(7y)

This simplifies to:
42xy + 49y^2

Now, combine the simplified terms to get the final answer:
30x^2 + 35xy + 42xy + 49y^2

The simplified expression is:
30x^2 + 77xy + 49y^2
Evaluate log¹²144
To evaluate log₁²₁₄₄, we are looking for the exponent to which we must raise 12 to get 144.

Let's break down 144 into factors:
144 = 12 × 12 = 12²

Since 12 raised to the power of 2 equals 144, we can say that log₁²₁₄₄ = 2.

Therefore, log₁²₁₄₄ equals 2.
Estimate 19 8/9- 10 1/8
To estimate the value of 19 8/9 - 10 1/8, we can round the fractional parts to get a rough estimate.

19 8/9 ≈ 20

10 1/8 ≈ 10

Now we can subtract these estimates:

20 - 10 = 10

So, the estimated value of 19 8/9 - 10 1/8 is 10.
Simplify (3-2i)(1-6i)
To simplify (3-2i)(1-6i), we can use the distributive property.

First, distribute 3 to both terms inside the second parentheses:
3(1) + 3(-6i)

This simplifies to:
3 - 18i

Next, distribute -2i to both terms inside the second parentheses:
-2i(1) -2i(-6i)

This simplifies to:
-2i + 12i^2

Remember that i^2 is equal to -1.

Substituting -1 for i^2, we get:
-2i + 12(-1)

Simplifying further:
-2i - 12

Finally, combine the simplified terms to get the final answer:
-12 - 2i

The simplified expression is -12 - 2i.