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nikklg [1K]
2 years ago
8

Find the value of x.

Mathematics
1 answer:
Vladimir79 [104]2 years ago
4 0

Answer:

x= 2√37

Step-by-step explanation:

First thing you want to do is find the length of the missing side where the the right angle is at. You can find that with the pythagorean theorem of the other triangle, since you are already given 2 sides.

Pythagorean Theorem

{a}^{2}  +  {b}^{2}  =  {c}^{2}

a=2

b=?

c=2√2

Plug in and solve for b.

2^2+b^2=(2√2)^2

4+b^2=8

b^2=4

b=2

Now use the pythagorean theorem again to find your x side.

a=2

b=12

c=?

2^2+12^2=c^2

4+144=c^2

148=c^2

c=√148

c=2√37

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Step-by-step explanation:

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2 years ago
The sum of 6 consecutive even numbers is 270.What is the second number in this sequence?
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Step-by-step explanation:

Let the six consecutive even numbers be x , x+2 , x+4 ,x+6 ,x+8 ,x+10.

Then According to the question , we have

x+(x+2)+(x+4)+(x+6)+(x+8)+(x+10)=270\\\\\Rightarrow\ x+x+2+x+4+x+6+x+8+x+10=270\\\\\Rightarrow\6x+30=270\\\\\Rightarrow\ 6x=270-30\\\\\Rightarrow\ 6x=240\\\\\Rightarrow\ x=40

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10. 10. If AB bisects CAF, and m&lt;EAF = 72°,<br>then the m&lt;BAF =​
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The measure of ∠BAF is 54°.

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m∠EAF = 72° and AB bisects ∠CAF.

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Vertical angle theorem:

<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>

∠DAC ≅ ∠EAF

m∠DAC = 72°

<em>Sum of the adjacent angles in a straight line = 180°</em>

m∠DAE + m∠EAF = 180°

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Subtract 72° from both sides.

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m∠CAB + m∠BAF = 108°

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Divide by 2 on both sides, we get

m∠BAF = 54°

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