Select the graph for the solution of the open sentence. Click until the correct graph appears. 2|x| < 4

Mathematics

1 answer:

sdas [7]3 years ago

3 0

Answer:

<em>We have to plot the graph of the inequality:</em>

$2|x|$

i.e. $|x|$

the graph is a number line representing the possible values of 'x' by solving the inequality.

the inequality is solved as:

-2<x<2

i.e. the region is: (-2,2); i.e. we have all the real values between -2 and 2 such that 2 and -2 is not included hence there is a open circle at 2 and -2.

the graph of the solution is attached to the answer.

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1. N is a midpoint of the segment KL, then N has coordinates

$\left(\dfrac{x_K+x_L}{2},\dfrac{y_K+y_L}{2} \right) =\left(\dfrac{0+2a}{2},\dfrac{2b+0}{2} \right) =(a,b).$

2. To find the area of △KNM, the length of the base MK is 2b, and the length of the height is a. So an expression for the area of △KNM is

$A_{KMN}=\dfrac{1}{2}\cdot \text{base}\cdot \text{height}=\dfrac{1}{2}\cdot 2b\cdot a=ab.$

3. To find the area of △MNL, the length of the base ML is 2a and the length of the height is b. So an expression for the area of △MNL is

$A_{MNL}=\dfrac{1}{2}\cdot \text{base}\cdot \text{height}=\dfrac{1}{2}\cdot 2a\cdot b=ab.$

4. Comparing the expressions for the areas you have that the area $A_{KMN}$ is equal to the area $A_{MNL}$ . This means that the segment from the midpoint of the hypotenuse of a right triangle to the opposite vertex forms two triangles with equal areas.