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2 years ago

Which is the solution to the inequality? y minus 27 greater-than-or-equal-to negative 13

Mathematics

2 answers:

Over [174]2 years ago

7 0

Answer:

y ≥ 14

Step-by-step explanation:

y - 27 ≥ -13

you manipulate this inequality like it is an equation. Only take care that the inequality swaps if you multiply by a negative. In this case, that is not needed.

y - 27 +27 ≥ -13+27

y ≥ 14

Y_Kistochka [10]2 years ago

6 0

Answer:

y is greater than or equal to 14

Step-by-step explanation:

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The polynomial x^2+3x-1 is a factor of x^4+3x^3-2x^2-3x+1 true or false?

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Answer:

Yes, it is true that $x^2+3x-1$ is a factor of $x^4+3x^3-2x^2-3x+1$ .

Step-by-step explanation:

Let us try to factorize $x^4+3x^3-2x^2-3x+1$

$x^4+3x^3-2x^2-3x+1\\\Rightarrow x^4-2x^2+1-3x+3x^3$

Let us try to make a whole square of the given terms:

$\Rightarrow (x^2)^2-2\times x^2 \times 1+1^2+3x^3-3x\\\Rightarrow (x^2-1)^2+3x^3-3x\\$

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Formula used above:

$a^{2} -2 \times a \times b +b^{2} = (a-b)^2$

In the above equation, we had $a = x, b = 1$ .

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Further solving the above equation, taking $3x$ common out of $3x^3-3x$

$\Rightarrow (x^2-1)^2+3x(x^2-1)\\$

Taking $(x^{2} -1)$ common out of the above term:

$\Rightarrow (x^2-1)((x^2-1)+3x)\\\Rightarrow (x^2-1)(x^2+3x-1)$

So, the two factors are $(x^2-1)\ and\ (x^2+3x-1)$ .

$\therefore$ The statement that $x^2+3x-1$ is a factor of $x^4+3x^3-2x^2-3x+1$ is <em>True.</em>

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2 years ago