What is the remainder of (x3 - 6x2 -9x + 3) ÷ (x - 3)
1 answer:
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<u>Answer:</u>
all statements discuss the multiplication of two numbers (we can say they are equivalent based on this context)
first three statements are exactly the same
last three statements are exactly the same
<u>Explanation:</u>
<u>Let's go through the statements one by one:</u>
1) ab > 0 and “a>0, b>0”
We know that when multiplying two positive numbers, the result is always a positive number.
Examples:
2 * 3 = 6
We can note that when the two operands are positive, the result is also positive
2) ab > 0 and “the numbers a and b are of the same sign”
We know that when multiplying two positive numbers or two negative numbers, the result will always be positive
Examples:
2 * 3 = 6
-2 * -3 = 6
We can note that when the two operands have the same sign, the result is positive
3) ab > 0 and “a>0, b>0 or a<0, b<0”
This choice is actually the same as the previous one.
When the two numbers are positive: a > 0 and b > 0
Wen the two numbers are negative: a < 0 and b < 0
Therefore, it is just a paraphrasing of statement 2
4) ab < 0 and “a>0, b<0”
We know that when we multiply numbers of different signs, the result will always be negative
Examples:
2 * -3 = -6
We can note that when the two operands have different signs, the result is negative
5) ab < 0 and “a<0, b>0 or a>0, b<0”
This is the same as statement 4 as it shows that the two operands have different signs (one is greater than zero while the other is less than zero), their product will be a negative number (less than zero)
6) ab < 0 and “the numbers a and b are of different signs”
This is the same as statement 5. It is only a paraphrase of the words.
<u>Based on the above, we can conclude that:</u>
1- all statements discuss the multiplication of two numbers
2- first three statements are exactly the same
3- last three statements are exactly the same
Hope this helps :)
Answers & Step-by-step explanation:
<h2>PEMDAS (Parenthesis, exponents, multiplication, division, addition, subtraction)</h2>Now let's solve your problems!
<h2>___________________________________________________</h2><h2>16.</h2>First, we see if there are any parentheses. Since there are no parentheses, we will evaluate the exponent 3² first.
After this, our problem now looks like this:
<h2>Next, since multiplication (not subtraction) is next on the list, we will evaluate 6 × 3, which equals 18.
After that, we will subtract:
41 - 9 = 32
18 - 26 = -8
We now have 32/-8 or 4/-1 or simply -4.
<h2>The answer is: -4</h2><h2>___________________________________________________</h2><h2>17.</h2>With this, one, note the parentheses. This means that we will do these operations first.
(21 - 4²) = 5
(3 + 1) = 4
The problem now looks like this:
Next, we do the exponents:
8² = 64
After that, we do the multiplication of 5 x 4, which equals 20.
We now have 20/64 - 44, which simplifies to 20/20 or 1/1 or 1.
<h2>The answer is: 1</h2><h2>___________________________________________________</h2><h2>18.</h2>Again, we see parentheses, so that means we need to do these operations first.
(6² - 20) = 16
We now have:
48 ÷ 16 + 5
48/16 = 3 and 3 + 5 = 8
<h2>The answer is: 8</h2><h2>___________________________________________________</h2><h2>19.</h2>Here, we see an exponent 3³, so we'll need to evaluate this first.
3³ = 27
We now have:
4 × 27 ÷ 18 + 14
4 × 27 = 108
108/18 = 6
And finally:
6 + 14 = 20
<h2>The answer is: 20</h2><h2>___________________________________________________</h2><h2>20.</h2>Here we again see the parentheses, which means we need to evaluate the subtraction first.
3 - 8 = -5
We now have:
11 + 2 (-5)
2 × -5 = -10
11 + -10 (same as 11 - 10) = 1
<h2>The answer is: 1</h2><h2>___________________________________________________</h2><h2><em>I AM ALWAYS HAPPY TO HELP :)</em></h2>