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3 years ago

3x+y=15 3x-y=15 (using elimination method)

Mathematics

2 answers:

morpeh [17]3 years ago

5 0

Answer:

x = 5

y = 0

Step-by-step explanation:

3x + y = 15

3x -y = 15

Add the two equations;

6x = 30

Inverse operations;

6x = 30

/6 /6

x = 5

Back substitute;

3(5) + y = 15

15 + y = 15

y = 0

Yanka [14]3 years ago

4 0

Answer:

Step-by-step explanation:

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Ella grew 3 over 4 of an inch last year. Ben grew 2 over 3 of an inch last year. How much more did Ella grow than Ben last year?

IrinaK [193]

Answer:

Ella grew $\frac{1}{12}$ of an inch more

Step-by-step explanation:

For this problem, you want to subtract Ben's growth from Ella's.

This expression would be $\frac{3}{4}$ - $\frac{2}{3}$ .

To work these out, they must have the same denominator (which should be the lowest common multiple or LCM).

In this case, the LCM is 12, so you want to multiply each side so the denominator is 12. This means the first fraction should be multiplied by $\frac{3}{3}$ and the second by $\frac{4}{4}$ .

This makes the expression $\frac{9}{12}$ - $\frac{8}{12}$ , which equals $\frac{1}{12}$ .

**This content involves adding and subtracting fractions, which you may want to revise. I'm always happy to help!

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3 years ago

16,80, 400,... Find the 6th term.

jekas [21]

Answer:

Step-by-step explanation:

50,000

I think

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2 years ago

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

According tot he rational root theorem, which statement about f(x)=12x^3-5x^2+6x+9 is true?

vampirchik [111]

Answer:

If there are any rational roots, it would be a factor of your constant term (9) divided by a factor of the high-order coefficient (12).

3 0

3 years ago

Frozen motts sticks cost $.022 each. If there are 6 sticks in on order, what is the portion cost for an order of motts sticks?

solong [7]

Answer:

$ 1.32

Step-by-step explanation:

Given :-

Cost of each Mott's Stick = $0.22 .

Now there are 6 sticks in an order . So the cost of six sticks will be ,

→ Cost = $ 0.22 × 6

→ Cost = $ 1.32

<h3>Hence the cost of an order of sticks is $ 1.32 </h3>

8 0

2 years ago