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raketka [301]
3 years ago
5

What would be the answer for this.

Mathematics
1 answer:
kvasek [131]3 years ago
4 0

Answer & Step-by-step explanation:

We are given that m∠1 = m∠2. We are to prove that line l is parallel to line m. So, let's make a proof. Your first statement should always be the given statement. You are given the statements. All we have to do is find the reasons for those statements.

  • m∠1 = m∠2 → Given
  • m∠1 = m∠3 → Vertical angles are equal
  • m∠2 = m∠3 → Substitution
  • l ║m → If corresponding angles are equal, then lines are parallel
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Oh my goodness !  You were doing such an absolutely beautiful job,
as far as you went, but then you ran into some rough road and quit.

You've got the correct expressions for the ages of the three people:

-- Will . . . w
-- Ben . . . w+3
-- Jan . . . 2(w+3)
You slipped up when you expanded Jan's age:  2(w+3) = <u>2w + 6</u> ,
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Let's do it again, together:

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Total:  (w + w + 2w) + (3 + 6) = 4w + 9

So the equation is:    <em><u>4w + 9 = 41</u></em>
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Subtract 9 from each side:   4w  =  32

Divide each side by 4:        <u>w = 8</u>

-- Will = w . . . . . 8 y.o.
-- Ben = w+3 . . . 11 y.o.
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When will Jan be twice as old as Will ?
That'll happen in 'x' years.
At that time, Will will be (8+x) and Jan will be (22+x),
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22 + x  =  2(8 + x)

22 + x  =  16 + 2x

Subtract 'x' from each side:    22  =  16 + x

Subtract  16  from each side:  <em>  6 = x</em>

<u>Check:</u>

In 6 years, Jan will be (22+6) = 28,
and Will will be (8+6) = 14 .

28 = twice as old as 14.      yay!

Can I make a little suggestion ?
I'm going to make it anyway:

Your problem was neatness.
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This is not an easy problem, but you definitely know your stuff. 
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