What is the length of line segment AB?1 inchv3 inches4 inches475 inches

Mathematics

1 answer:

drek231 [11]3 years ago

5 0

Answer:

$AB=\sqrt{3}\ in$

Step-by-step explanation:

The correct question is

The diagonal of rectangle ABCD measures 2 inches in length.

What is the length of line segment AB?

The picture of the question in the attached figure

we know that

In the right triangle ABD

$cos(30^o)=\frac{AB}{BD}$ ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

$cos(30^o)=\frac{AB}{2}$

Remember that

$cos(30^o)=\frac{\sqrt{3}}{2}$

$\frac{AB}{2}=\frac{\sqrt{3}}{2}$

$AB=\sqrt{3}\ in$

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Express f(x) = |x-2| +|x+2| in the non-modulus form. Hence, sketch the graph of f.

alexgriva [62]

Recall that

$|x|=\begin{cases}x&\text{if }x\ge0\\-x&\text{if }x$

There are three cases to consider:

(1) When $x+2$ , we have $|x+2|=-(x+2)$ and $|x-2|=-(x-2)$ , so

$|x-2|+|x+2|=-(x-2)-(x+2)=-2x-4$

(2) When $x+2\ge0$ and $x-2$ , we get $|x+2|=x+2$ and $|x-2|=-(x-2)$ , so

$|x-2|+|x+2|=-(x-2)+(x+2)=4$

(3) When $x-2\ge0$ , we have $|x+2|=x+2$ and $|x-2|=x-2$ , so

$|x-2|+|x+2|=(x-2)+(x+2)=2x$

So

$|x-2|+|x+2|=\begin{cases}-2x-4&\text{if }x$