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2 years ago

I need some help with these math problems

Mathematics

1 answer:

photoshop1234 [79]2 years ago

3 0

a. Number of more pictures they could take = 43 pictures (approx.)

b. The inequality can be given as 1 ≤ pictures taken ≤ 43

c. The inequality 1 ≤ pictures taken ≤ 43 represents that the pictures taken are equal to or greater than 1 to less than or equal to 43 (The inequality consists of 1 to 43 pictures)

Step-by-step explanation:

a. Given,

The total memory capacity = 65536 KB

The memory for 1 picture = 760 KB

The number of pictures already taken = 43 pictures

The memory used for 43 pictures = 760 * 43 = 32680 KB

The remaining memory space = total memory - used memory

= 65536 - 32680 = 32856 KB

Number of more pictures they could take = remaining space / space per picture

= 32856 KB / 760 KB = 43.231 ≈ 43 pictures.

b. Given,

Number of pictures taken during school = 19 pictures.

Number of pictures taken after school = 24 pictures.

The inequality can be given as 1 ≤ pictures taken ≤ 43

c. Inequality :

"An inequality is a relation that compares a set of values between two numbers and it does not equals to a particular number alone".

Here, the inequality 1 ≤ pictures taken ≤ 43 represents that the pictures taken are equal to or greater than 1 to less than or equal to 43 (The inequality consists of 1 to 43 pictures)

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The coordinates of point A on a grid are (−1, 6). Point A is reflected across the y-axis to obtain point B. The coordinates of p

-Dominant- [34]

Answer:

(1,6)

Step-by-step explanation:

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A number has only 1 factor pair. One of its factors is twice the other factor. What is the number? Explain.

Mrrafil [7]

<h3>Answer: 2</h3>

========================================================

Explanation:

If a number only has one factor pair, then that number must be prime. This is because prime numbers only have factors of 1 and the number itself.

For instance, the value 7 is prime because the only factors of this are 1 and 7.

For something like the number 32, it is composite and not prime because it has the factors {1,2,4,8,16,32} and it leads to these three factor pairs: 1*32, 2*16, 4*8. This is one example showing why the answer isn't composite.

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Let's say that p is the unknown prime we want to find. The factors of this are 1 and p. We're told that "one of the factors is twice the other factor", so that must mean p = 2*1 = 2. We can see that 2 is twice that of 1.

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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.

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2 years ago

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3 years ago