Which relations are functions?

Given: KLMN is a trapezoid, m∠N=m∠KML, FD=8, LM KN = 3 5 F∈ KL , D∈ MN , ME ⊥ KN KF=FL, MD=DN, ME=3 5 Find: KM

denis23 [38]

Answer:

The length of side KM is $\sqrt{109}$ units.

Step-by-step explanation:

Given information: KLMN is a trapezoid, ∠N= ∠KML, FD=8, LM:KN=3:5, F∈ KL, D∈ MN , ME ⊥ KN KF=FL, MD=DN, $ME=3\sqrt{5}$ .

From the given information it is noticed that the point F and D are midpoints of KL and MN respectively. The height of the trapezoid is $3\sqrt{5}$ .

Midsegment is a line segment which connects the midpoints of not parallel sides. The length of midsegment of average of parallel lines.

Since LM:KN=3:5, therefore LM is 3x and KN is 5x.

$\frac{3x+5x}{2}=8$

$\frac{8x}{2}=8$

$x=2$

Therefore the length of LM is 6 and length of KN is 10.

Draw perpendicular on KN form L and M.

$KN=KA+AE+EN$

$10=6+2(EN)$ (KA=EN, isosceles trapezoid)

$EN=2$

$KE=KN-EN=10-2=8$

Therefore the length of KE is 8.

Use pythagoras theorem is triangle EKM.

$Hypotenuse^2=base^2+perpendicular^2$

$(KM)^2=(KE)^2+(ME)^2$

$(KM)^2=(8)^2+(3\sqrt{5})^2$

$KM^2=64+9(5)$

$KM=\sqrt{109}$

Therefore the length of side KM is $\sqrt{109}$ units.

8 0

4 years ago

Read 2 more answers

The 3 by 3 grid below shows nine 1 cm × 1 cm squares and uses 24 cm of wire. What length of wire is required for a similar 20 by

Nady [450]

Answer:

840

Step-by-step explanation:

Hi there!

Usually, this kind of problem asks us the perimeter rather than the area. But when talking on this grid on how many cms are necessary to construct one made up of 9 squares 1cm x1 cm. We need to check one thing: Some line segments will be used twice. So this is not a classical perimeter question.

1) So we either manually and carefully count it avoiding not doing it twice the same common line segments.

Or.

2) By just applying an algorithm, Where n is the <em>nxn</em> grid

$n(n+1)+n(n+1)=Length \:of \:the \:wire$

So, for the 20x20 grid

$20(20+1)+20(20+1)=length\\\\20(21)+20(21)=length\\length=840 cm$

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4 years ago

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o-na [289]

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Step-by-step explanation:

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3 years ago

Match the hours (input) with the correct number of animals (output).

Aleksandr [31]

Answer:

1 -> 4

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Explanation:

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Andru [333]

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4 years ago