Ava is 23 cm taller than Olivia, and Olivia is half the height of Lucas. If Lucas is 1.78 m tall, how tall are Ava and Olivia? E
1 answer:
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By some properties of logarithms, rewrite the equation as
so that
(<em>a</em> - 2<em>b</em>)² = <em>ab</em>
Expand the left side:
<em>a</em> ² - 4<em>ab</em> + 4<em>b</em> ² = <em>ab</em>
Rearrange terms to get a quadratic equation in <em>a</em>/<em>b</em> :
<em>a</em> ² - 5<em>ab</em> + 4<em>b</em> ² = 0
<em>b</em> must be greater than 0, otherwise log(<em>b</em>) doesn't exist, and the same goes for <em>a</em>. So we can divide by <em>b</em> ² to get
<em>a</em> ²/<em>b</em> ² - 5<em>a</em>/<em>b</em> + 4 = 0
Factorize and solve for <em>a</em>/<em>b</em> :
(<em>a</em>/<em>b</em> - 4) (<em>a</em>/<em>b</em> - 1) = 0
==> <em>a</em>/<em>b</em> = 4 or <em>a</em>/<em>b</em> = 1
However, if <em>a</em>/<em>b</em> = 1, then <em>a</em> = <em>b</em> makes <em>a</em> - 2<em>b</em> = -<em>b</em>. But we must have <em>b</em> > 0, so we omit the second solution and end up with
<em>a</em>/<em>b</em> = 4
Answer:
Step-by-step explanation:
We know that,
The sum of interior angles of a triangle is 180 degrees.
So,
2x + 4 + 2x - 9 + x = 180
5x - 5 = 180
Add 5 to both sides
5x = 180 + 5
5x = 185
Divide both sides by 5
x = 185 / 5
x = 37
Hope this helped!
<h3>~AH1807</h3>