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3 years ago

The first term of a geometric sequence is –2 and the common ratio is -1/4.

Mathematics

2 answers:

Simora [160]3 years ago

8 0

Just took the test, the right answer is B

hram777 [196]3 years ago

4 0

-2*-1/4=1/2
1/2*-1/4=-1/8
-1/8*-1/4=1/32

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A box of cereal contains 18 cups. Ben eats 2 1/4 cups every serving. How many servings can he eat?

g100num [7]

Ben can have 8 servings total!

Hope this helps! :)

4 0

3 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

The equation of the line f is y =4/9x+3/2.Line g is perpendicular to f. What is the slope of line g?

tangare [24]

Answer:

-9/4

Step-by-step explanation:

A perpendicular slope is on that is the negative reciprocal. current slope=4/9 and the negative recipocal is -9/4.

7 0

2 years ago

If 14x = ^13√14, what value of x makes this equation true?

Andrews [41]

The value of x is 1/13 (4th choice)

Step-by-step explanation:

${a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} }$

If 14^x = ¹³√14, what value of x makes this equation true?

$\sqrt[13]{14} = {14}^{x} \\ \sqrt[13]{14} = {14}^{ \frac{1}{13} }$

So, the value of x is 1/13 (4th choice)

Hope it helpful and useful :)

6 0

3 years ago

Supposed you have been given the task of engineering this product knowing that in your state the cost of electricity is 18 cents

Usimov [2.4K]

You would have about 3472 Hours

.18\8=1.44 for 8 hour

5000/1.44=3472

Hope this helps :)

5 0

2 years ago