In your own words, define “rate of change.” Give an example.This is Advanced Functions, not sure how to explain the term out on paper but ik what it means, any help?
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PLEASE HELP!! Please solve question I need help!
The prefix kilo in the metric system means ____ units
** If you your answer contains an irrational number (a never ending decimal number) leave the number under the square root symbol.
Bryan started to evaluate a decimal expression. 2.5(42 ÷ 3.2 – 10(0.2) + 3)– 5.2 2.5(16 ÷ 3.2 – 10(0.2) + 3) – 5.2 What should Bryan's next step look like?
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Answer: 12ab^3
Step-by-step explanation:
The length of the rectangle will be gotten by dividing the area by the width. This will be:
Length = 72 a^3b^4 / 6a^2 b
= 72 × a × a × a × b × b × b × b / 6 × a × a × b
= 12 × a × b × b × b
= 12ab^3
2. Simplify the expression.
(8+i)(2+7i)
3. Find the conjugate of the complex number 8+12i
A. 96
B. 8-`1i
C. -96i
D. 20
4. Use the complex conjugate to find the absolute value of 8+12i
A. 12
B. square root of 208
C. square root of 84
D. 8
Answers
The correct answers are:
(1) 4+5i
(2) 9+58i
(3) 8 - 12i (Option B; The question's options have a typo)
(4) Square root of 208 (Option B).
Explanations:
(1) Given: (6+6i)-(2+i)
We need to simplify the given expression. For that, add real parts with each other, and add imaginary parts of the complex numbers with each other. Remember that the numbers with the symbol "i" are the imaginary parts of the complex number. Therefore,
(6-2) + (6i - i) = 4 + 5i (ans)
(2) Given: (8+i)(2+7i)
Now in this case we will multiply two complex numbers with each other; here in this case, we have to remember that . Now let us find out the multiplication of two complex numbers:
(8+i)(2+7i)
8(2+7i) + i(2+7i)
16 + 58i + 7(-1)
= 9 + 58i
Hence the correct answer is 9+58i.
(3) Given: 8+12i
In simple terms, in order to find the conjugate of the complex number, we take the real number of the complex number as is, but we change the sign of the imaginary part of the complex number. In the given expression, 8 is the real number; hence, we will take it as is, whereas, +12i is the imaginary part of 8+12i. So to find the conjugate, we will change +12i to -12i.
Therefore, the conjugate of the complex number will become 8 - 12i (Option B; The question's options have a typo).
(4) Given: 8+12i
First, we need to find the complex conjugate of the given complex number. Please see the explanation given in Part (3) above to find the complex conjugate. The complex conjugate of 8+12i is 8-12i
Now, to find the absolute value of the complex conjugate 8-12i, follow these steps:
|8-12i|
We will add the square of the real number (8) with the square of the imaginary number (-12) and take the square-root at the end to find the absolute value:
Hence the correct answer is square root of 208 (Option B).
2. 9 - 58i
3. tbh idek
4. /sqrt{208}
what is the fraction ten twelfths in it's simplest form ?
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The correct answer is:
5/6.
Explanation:
To simplify this fraction, we divide the numerator and denominator by the greatest common factor.
The factors of 10 are: 1, 2, 5 and 10.
The factors of 12 are: 1, 2, 3, 4, 6, and 12.
The greatest common factor of the two is 2.
Simplifying this, we have:
10/12 = (10÷2)/(12÷2) = 5/6.
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= -4.8y + 20.1 - 12.7y - 9.3 =
= -17.5y + 10.8
-x + 6y = 26
Elimination
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5x+6y=50
-1(-x+6y=26) =x-6y=-26
Cancel out the 6y's add the rest
6x=24
X=4
Substitute x back into the original
-(4)+6y=26
-4+6y=26
6y=30
Y=5
Get the point (4,5)
-x+6y=26
Make the second problem and multiply everything by -1
5x+6y=50
-1(-x+6y=26)
X-6y=-26
Eliminate the y and combine evrything
6x=24
Divide 6 both sides
X=4
Then substitute the x
-(4)+6y=50
-4+6y=50
Add 4 both sides
6y=54
Divide 6 and y=9 x=4