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3 years ago

I NEED HELP WITH MY MATHS HOMEWORK PLEASE!!

Mathematics

2 answers:

Inessa05 [86]3 years ago

8 0

<h3>Answer: 1/12</h3>

Explanation:

The notation $A \cap B$ means "the overlapped region between circles A and B". There is only one value in this region, and it is the "8". This is in the lower half of this region as the upper half is empty.

There are 12 values in the set {2,4,6,8,10,12,14,16,18,20,24} which we can see by counting them out, or we can note how 24 = 2*12 and how we started with 2 = 2*1. So basically we have...

2 = 2*1
4 = 2*2
6 = 2*3
8 = 2*4
10 = 2*5
12 = 2*6
14 = 2*7
16 = 2*8
18 = 2*9
20 = 2*10
22 = 2*11
24 = 2*12

So again we have 1 value in the overlapped region between A and B, out of 12 values total. So that's why the answer is 1/12.

german3 years ago

6 0

Answer:

What is your exact question?

Step-by-step explanation:

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3 years ago

Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL

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Answer:

$KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08\\ \\KN=45\sin 50^{\circ}\approx 34.47$

Step-by-step explanation:

Given:

KL ║ NM ,

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NL ⊥ LM

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1. Consider triangle NLM. This is a right triangle, because NL ⊥ LM. In this triangle,

LM = 45

m∠M = 50°

So,

$\tan \angle M=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{NL}{LM}=\dfrac{NL}{45}\\ \\NL=45\tan 50^{\circ}$

Also

$m\angle LNM=90^{\circ}-50^{\circ}=40^{\circ}$ (angles LNM and M are complementary).

2. Consider triangle NKL. This is a right triangle, because KN ⊥ NM . In this triangle,

$NL=45\tan 50^{\circ}$

$m\angle KLN=m\angle LNM=40^{\circ}$ (alternate interior angles)

$m\angle KNL=90^{\circ}-40^{\circ}=50^{\circ}$ (angles KNL and KLN are complementary).

So,

$\sin \angle KNL=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{KL}{LN}=\dfrac{KL}{45\tan 50^{\circ}}\\ \\KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08$

and

$\cos \angle KNL=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{KN}{LN}=\dfrac{KN}{45\tan 50^{\circ}}\\ \\KN=45\tan 50^{\circ}\cos 50^{\circ}=45\sin 50^{\circ}\approx 34.47$

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Hey there :)

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