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3 years ago

Solve the equation. |3 − w| = −2

2 answers:

7 0

The answer is 5 since there are no numbers in front you just subtract 3 from both sides leaving you with -w=-5 and a negative divided by a negative is a positive

gizmo_the_mogwai [7]3 years ago

3 0

Absolute value represents distance. Distances can't be negative.

So it's impossible to have |3-w| be some negative value.

Which is why $|3-w| = -2$ has no solutions

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3 years ago

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patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

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$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .

Verify that $(x + 2)\, (x + 3)$ indeed expands to the original polynomial:

$\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}$ .

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Read 2 more answers

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Ivahew [28]

I saw the image that should have been included in this problem.

It was a rectangular prism. It can also be identified as a right prism because its bases are aligned one directly above the other and its lateral faces are rectangular.

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3 years ago