To me it looks like your right
I’m a little confused by the question and the problem, is there a picture of the problem you could add?
Took me a minute to think.
Form ratios.
x, the small triangle, forms a ratio with 6, the big triangle.
The part of the side that is equal(with the dash) that is part of the small triangle
is equal to 6-x, the big triangle.
Yes, you can cross-multiply here!
<em>Now,</em><em> </em>cross multiply.
P.S. Use distributive property.
36-6x = 8x
Add 6x on both sides.
36=14x
Divide by 14 on both sides.
x =
=
<span><span>(<span>7y+2<span>y2</span>−7</span>)</span>−<span>(<span>3−4y</span>)</span></span>
<span>=<span>7y</span><span>+4y</span>+2<span>y2</span><span>−7</span><span>−3</span></span>
<span>=11y−2<span>y2</span>−<span>10</span></span>
Hope this helps
The given equation
x/2 = y/3 = z/4
can be broken into three separate equations which I'll call equations (A), (B) and (C)
- x/2 = y/3 ..... equation (A)
- y/3 = z/4 .... equation (B)
- x/2 = z/4 .... equation (C)
We'll start off solving for z in equation (C)
x/2 = z/4
4x = 2z ... cross multiply
2z = 4x
z = 4x/2 ... divide both sides by 2
z = 2x
Now let's solve for y in equation (A)
x/2 = y/3
3x = 2y
2y = 3x
y = 3x/2
y = (3/2)x
y = 1.5x
The results of z = 2x and y = 1.5x both have the right hand sides in terms of x. This will allow us to replace the variables y and z with something in terms of x, which means we'll have some overall expression with x only. The idea is that expression should simplify to 3 if we played our cards right.
We won't be using equation (B) at all.
---------------------
The key takeaway from the last section is that
Let's plug those items into the expression (2x-y+5z)/(3y-x) to get the following:
(2x-y+5z)/(3y-x)
(2x-y+5(2x))/(3y-x) ..... plug in z = 2x
(2x-y+10x)/(3y-x)
(12x-y)/(3y-x)
(12x-1.5x)/(3(1.5x)-x) .... plug in y = 1.5x
(12x-1.5x)/(4.5x-x)
(10.5x)/(3.5x)
(10.5)/(3.5)
3
We've shown that plugging z = 2x and y = 1.5x into the expression above simplifies to 3. Therefore, the equation (2x-y+5z)/(3y-x) = 3 is true when x/2 = y/3 = z/4. This concludes the proof.
