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3 years ago

What is a constant interval and how does it appear on a graph?

2 answers:

8 0

Pre-Calculus - Identify where a function is increasing decreasing or constant from the graph

Example: The graph shown above is decreasing from the point (3,4) to the point (5,-5), described as decreasing when 3 < x < 5. Using interval notation, it is described as decreasing on the interval (3,5). Constant: A function is constant, if as x increases (reading from left to right), y stays the same.

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8090 [49]3 years ago

3 0

A function whose value does not vary, regardless of the input.

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Polynomial expressions with matching

yuradex [85]

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]:

$\displaystyle 3x - 2y = \sqrt[3]{27x^3 - 8y^3} \\ 3x - 4y = \sqrt[3]{27x^3 - 64y^3}$

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]:

$\displaystyle 3x + 2y = \sqrt[3]{27x^3 + 8y^3} \\ 3x + 4y = \sqrt[3]{27x^3 + 64y^3}$

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 Difference\Sum of Cubes, SOAP can vary depending on how an expression is given to you. They resemble each other though.

6 0

2 years ago

Find the value of x. 8:5 = 1/x:1

tatiyna

Answer:x=61

Step-by-step explanation

856−5x3{131}=2

8(x−9)+5(5−18)+1(15−6x)=2

8x−72−65+15−6x=2

2x=122

x=61

sorry if i'm wrong

5 0

1 year ago

How many l sounds are in the word snake

Alex

s n a ke =4 they are only 4 sound in snake when you sound it out

8 0

2 years ago

Read 2 more answers

Which of these problem situations could best be modeled by the equation below? 52(18) + x = 1200 Debbie sold 52 boxes of fruit f

kirill [66]

Answer:

a) Debbie sold 52 boxes of fruit for $18 each plus a bonus x, for selling the boxes quickly. Find x, the bonus if Debbie sold the fruit quickly and earned $1200.

Step-by-step explanation:

The model equation is given as:

52(18) + x = 1200

a) Debbie sold 52 boxes of fruit for $18 each plus a bonus x, for selling the boxes quickly. Find x, the bonus if Debbie sold the fruit quickly and earned $1200.

52($18) + x = $1200

52(18) + x = $1200

Option a is correct

b) Katrina earned $18 plus a weekly bonus x, for managing her money wisely each week for 52 weeks. Find x, if Katrina earned $1200.

x = weekly bonus, hence, we have the equation:

$18 + (x)52 = $1200

Option b is wrong

c) Marissa has $52 in her savings account. She earns $18 for each lawn she mows. Find x, the number of weeks she needs to mow lawns in order to have a total of $1200.

This is represented as:

$52 + $18(x) = $1200

Option c is wrong

d) Edward had a balance of $52 in the bank. He added x dollars to his account last month. This week he deposited another $18. Find x, the amount Edward deposited in the bank last month if his total savings is now $1200.

This is represented as :

$52+ $x + $18 = $1200

Option d is wrong.

Therefore, the correct statement that modelled the equation is option a

5 0

2 years ago

Scarlett is practicing math fluency. She has 100 math operation flashcards with 42 addition problem cards, 56 subtraction cards,

vichka [17]

Answer:

Step-by-step explanation:

Bro don’t trust me

4 0

2 years ago