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Oksi-84 [34.3K]
3 years ago
8

Help please. (Given: y ∥ x Prove: m∠5 + m∠2 + m∠6 = 180)

Mathematics
1 answer:
Minchanka [31]3 years ago
4 0

Answer:

Step-by-step explanation:

Concepts used :

sum of angles at a point on straight line is 180

if a transversal intersects two parallel lines then alternate angles are equal.

____________________________________________

∠∠∠∠∠

m∠1 + m∠2 + m∠3 = 180   ____________(A)

reason :sum of angles at a point on straight line is 180

these angles lie on LAM at point A

m∠1  = m∠5

Reason: alternate angles  y ∥ x and AC is transversal

m∠3  = m∠6

Reason: alternate angles  y ∥ x and AB is transversal

Substituting m∠1  with  m∠5 and m∠3  with m∠6

in equation A---m∠1 + m∠2 + m∠3 = 180

m∠5 + m∠2 + m∠6 = 180

Hence proved.

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A survey was given to 339 people asking whether people like dogs and/or cats.
lina2011 [118]

Answer:

80

Step-by-step explanation:

Think of it as a Venn diagram.  One circle is the people who like dogs, and one circle is the people who like cats.  The overlap is people who like both dogs and cats.

190 people in the survey said they like dogs.  That includes the people who like both dogs and cats.

141 people in the survey said they like cats.  That includes the people who like both dogs and cats.

If we simply add the two numbers together, we'll be counting the overlap twice.  So to find the total number of people who like dogs or cats, we have to subtract one overlap.

dogs or cats = 190 + 141 − x

Therefore:

190 + 141 − x + 88 = 339

419 − x = 339

x = 80

80 people said they liked both cats and dogs.

5 0
3 years ago
Patty is making a poster for science class. She spends. 50 minutes on each. Of 2 days. She completes 1/3 of the poster the first
Viktor [21]

Answer:

She has completed 2/3 of the poster

Explanation:

1/3 of the poster the first day

+

1/3 of the poster the next day

1/3 + 1/3 = 2/3

7 0
3 years ago
Given g(x)=−x−2, solve for x when g(x) =0
prohojiy [21]

Answer:

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5 0
2 years ago
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I need the answer for this question
joja [24]
3x+3=192 is the equation
To solve the equation, you would subtract 3 from both sides, 3-3 cancels out, so 192-3= 189. Then, you are left with 3x=189 so you divide both sides by 3, 3x divided by 3 cancels out, so you do 189 divided by 3 which is 63.
Answer to equation: x=63
Equation: 3x+3=192
8 0
4 years ago
(a) Find parametric equations for the line through (1, 4, 4) that is perpendicular to the plane x − y + 2z = 7. (Use the paramet
Alex777 [14]

Answer:

x=1+t\\y=4-t\\z=4+2t

Step-by-step explanation:

A vector perpendicular to the plane ax+by+cz+d=0 is of the form (a,b,c).

So, a vector perpendicular to the plane x − y + 2z = 7 is (1,-1,2).

The parametric equations of a line through the point (x_0,y_0,z_0) and parallel to the vector (a,b,c) are as follows:

x=x_0+at\\y=y_0+bt\\z=z_0+ct

Put (x_0,y_0,z_0)=(1,4,4) and (a,b,c)=(1,-1,2)

Therefore,

x=1+t\\y=4-t\\z=4+2t

xy-plane:

Put z = 0 ⇒ t = -2 ⇒x = - 1 , y = 6

So, at point (-1,6,0)

yz-plane:

Put x = 0 ⇒ t = -1 ⇒ y = 5, z =2

So, at point (0,5,2)

xz-plane:

Put y = 0 ⇒ t = 4 ⇒ x = 5, z = 12

So, at point (5,0,12)

5 0
3 years ago
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