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vovangra [49]
3 years ago
15

The factorization of 8x3 -125 is (2x-5)(jx2 +kx+25)

Mathematics
1 answer:
lbvjy [14]3 years ago
3 0

\bf ~\hspace{10em}\textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) ~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 8x^3-125~~ \begin{cases} 8=2\cdot 2\cdot 2\\ \qquad 2^3\\ 125=5\cdot 5\cdot 5\\ \qquad 5^3 \end{cases}\implies 2^3x^3-5^3\implies (2x)^3-5^3 \\[2em] [2x-5][(2x)^2+(2x)(5)+5^2]\implies (2x-5)(\stackrel{\stackrel{j}{\downarrow }}{4}x^2+\stackrel{\stackrel{k}{\downarrow }}{10}x+25)

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How many solutions does the system of equations below have?
galben [10]

Answer:

C

Step-by-step explanation:

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3 years ago
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put the following values in ascending order 4 2/7, 31/7, 3 5/7, 29/7, 27/7, the above are fractions you will get brainliest
Pavlova-9 [17]

Answer:

2/7 , 5/7 , 3 , 27/7 , 4 , 29/7 , 31/7

Step-by-step explanation:

2/7= 0.3

5/7= 0.7

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27/7= 3.9

4

29/7= 4.1

31/7= 4.4

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3 years ago
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I need help for these fraction questions! I will give brainleist! Please!!
Zina [86]
So it seems as if the first problem is asking this:

2 \frac{1}{6} - \frac{11}{15}x. 

If x=0.15, then 11/15*(0.15) is 0.11 or 11/100. 

The second problem is asking:

\frac{x}{4} + \frac{1}{2} = \frac{x}{3} + \frac{1}{6}

To solve algebraically, you want to get rid of the denominators under the x's. To do so, you want to multiply by the Least Common Multiple (LCM) of the denominators. For 3 and 4, the LCM is 12. Multiply everything by 12 to get:

3x+6=4x+2

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3 years ago
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Which of the following is not a true bi-conditional statement?
mrs_skeptik [129]
<h3>Answer: Choice B) </h3>

Jane goes to the beach if and only if it is a sunny day.

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

Reason:

A regular conditional statement is in the form "If P, then Q" where P and Q are placeholders for other statements.

For example, we can replace "P" with "it rains" and replace "Q" with "the grass gets wet". This means "If P, then Q" becomes "If it rains, then the grass gets wet".

It's hopefully clear that the example above is a one way street. It points in only one direction. The act of raining leads directly to the grass being wet. However, we cannot go in reverse. If we see the grass is wet, it doesn't mean it rained. Perhaps someone turned on a hose or sprinkler system. P leads to Q, but Q does not lead to P.

In short, all of what is mentioned so far is considered a regular conditional statement. So far we haven't addressed bi-conditional statements.

----------------

Bi-conditional statements are conditionals that work in reverse.

An example would be "If a figure is a square, then it has 4 congruent sides and 4 right angles". That conditional statement works in reverse. Therefore "If a figure has 4 congruent sides and 4 right angles, then the figure is a square" is also true simply by what it means to be a square.

So the format "If P, then Q" can be reversed to "If Q, then P" to have an equivalently true statement. The common practice is to use "if and only if" to help shorten things.

We would have the template "P if and only if  Q" which is the same as "Q if and only if P". The order doesn't matter since we can reverse things just fine.

Often you'll find bi-conditional statements when it comes to definitions. The term "weekend" literally means the day is either Saturday or Sunday, which is why choice C is another bi-conditional. A very similar situation applies to choice D as well.

--------------------

We've found that choices A, C and D are bi-conditional statements. They can be ruled out. We're left with choice B.

This is not a bi-conditional. Why not? It's assumed that Jane would go to the beach on a sunny day, but perhaps she enjoys the beach just fine on cloudy days. There's also the fact she could be doing other things on sunny days. The presence of the sun doesn't automatically mean the beach. If you said "It gets warm if and only if it's a sunny day", then I think this is more in line with a bi-conditional.

This is why <u>choice B</u> is the final answer.

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