Dante Michael's charge account statement showed a previous balance of $277.45 a finance charge of $3.22 new purchases of $299.33
1 answer:
You might be interested in
Answer:
The difference of 27x³ and 8y³ → [3x - 2y][9x² + 6xy + 4y²]
The difference of 27x³ and 64y³ → [3x - 4y][9x² + 12xy + 16y²]
The sum of 27x³ and 64y³ → [3x + 4y][9x² - 12xy + 16y²]
The sum of 27x³ and 8y³ → [3x + 2y][9x² - 6xy + 4y²]
Step-by-step explanation:
For the first two, we use the Difference of Cubes [(a³ - b³)(a² + 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:
Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign in your given expression, which will be a plus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:
Given: 27x³ - 64y³
[3x - 4y][9x² + 12xy + 16y²]
↑ ↑ ↑
same as opposite ALWAYS POSITIVE
given of given
Given: 27x³ - 8y³
[3x - 2y][9x² + 6xy + 4y²]
↑ ↑ ↘
same as opposite ALWAYS POSITIVE
given of given
Now, for the last two, we use the Sum of Cubes [(a³ + b³)(a² - 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:
Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign is in your given expression, which will be a minus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:
Given: 27x³ + 64y³
[3x + 4y][9x² - 12xy + 16y²]
↑ ↑ ↘
same as opposite ALWAYS POSITIVE
given of given
Given: 27x³ + 8y³
[3x + 2y][9x² - 6xy + 4y²]
↑ ↑ ↘
same as opposite ALWAYS POSITIVE
given of given
I am delighted to assist you anytime!
* As you can see, when using the <em>Difference\Sum of Cubes</em>, SOAP can vary depending on how an expression is given to you. They resemble each other though.
Answer: 
Note: to write the domain in interval notation, you'd write [-4,5]
if you need the domain in set-builder notation, then you'd write
------------------------------------------------------------------------------
Explanation:
The domain is the set of possible x input values. Look at the left most point (-4,-1). The x coordinate here is x = -4. This is the smallest x value allowed. The largest x value allowed is x = 5 for similar reasons, but on the other side of the graph.
So that's how I got (x is between -4 and 5; inclusive of both endpoints)
Writing [-4,5] for interval notation tells us that we have an interval from -4 to 5 and we include both endpoints. The square brackets mean "include endpoint"
Writing is the set-builder notation way of expressing the domain. The 
portion means "x is a real number"
Note: to write the domain in interval notation, you'd write [-4,5]
if you need the domain in set-builder notation, then you'd write
------------------------------------------------------------------------------
Explanation:
The domain is the set of possible x input values. Look at the left most point (-4,-1). The x coordinate here is x = -4. This is the smallest x value allowed. The largest x value allowed is x = 5 for similar reasons, but on the other side of the graph.
So that's how I got
Writing [-4,5] for interval notation tells us that we have an interval from -4 to 5 and we include both endpoints. The square brackets mean "include endpoint"
Writing