<u>Answer:</u>
- <em>3.25</em>
<u>Step-by-step explanation:</u>
<em>Rule: An absolute value will always be positive. </em>
<em>=> Referring to the rule, the absolute value of |–3.25| is 3.25.</em>
Hoped this helped.
Write the coordinates of the vertices after a reflection over the line x = 3. F,G,H
1 answer:
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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: There is 162 ml of first brand and 108 ml of second brand.
Step-by-step explanation:
Since we have given that
Percentage of vinegar that the first brand contains = 7%
Percentage of vinegar that the second brand contains = 12%
Percentage of vinegar in mixture = 9%
Total amount of dressing = 270 ml
We will use "Mixture and Allegation":
First brand Second brand
7% 12%
9%
--------------------------------------------------------
12%-9% : 9%-7%
3% : 2%
So, ratio of first brand to second brand in a mixture is 3:2.
So, Amount of first brand she should use is given by
Amount of second brand she should use is given by
Hence, there is 162 ml of first brand and 108 ml of second brand.