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givi [52]
3 years ago
14

What is 7k-7 x 3k-2 ? I came up with 21x/-5.

Mathematics
1 answer:
beks73 [17]3 years ago
6 0

from what I got, it would be −14k −  2

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

6 0
2 years ago
In a random sample of 5 residents of the state of Texas, the mean waste recycled per person per day was 1.9 pounds with a standa
sammy [17]
<h2>Answer with explanation:</h2><h2 />

The confidence interval for population mean is given by :-

\overline{x} \pm\ t_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}

Given : Sample size : n= 5, since n<30 , so the test we use here is t-test.

Sample mean : \overline{x}=1.9\text{ pounds}

Standard deviation: \sigma=0.89\text{ pounds}

Significance level : 1-\alpha:1-0.99=0.01

By using the standard normal distribution table , the critical value corresponds to the given significance level will be :-

t_{n-1,\alpha/2}=t_{5-1,0.01/2}=t_{4,0.005}=4.604

Now, the 99% confidence interval for the mean waste recycled per person per day for the population of Texas will be :-

1.9\pm\ (4.604)\dfrac{0.89}{\sqrt{5}}\\\\\approx1.9\pm1.832\\\\=(1.9-1.832,1.9+1.832)=(0.068,\ 3.732)

Hence, the 99% confidence interval for the mean waste recycled per person per day for the population of Texas  = (0.068, 3.732)

5 0
3 years ago
Brandon answered 48 out of 60 questions correctly on his test. What was Brandon's score as a percent?
Mkey [24]

Answer:

80%

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Which expression is equivalent to 2(3x+4)(x−1)(x−3)?
Vera_Pavlovna [14]

Answer:

A

Step-by-step explanation:

=(2(3x+4)(x−1))(x+−3)

=(2(3x+4)(x−1))(x)+(2(3x+4)(x−1))(−3)

=6x3+2x2−8x−18x2−6x+24

=6x3−16x2−14x+24

6 0
2 years ago
Find the prem of shaded shape
rodikova [14]

Answer: 50m

Step-by-step explanation:

        The perimeter of the shape can be found by adding together all the lengths of the sides. See attached for my work.

5 0
2 years ago
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