Given:
![\Delta DHE\sim \Delta DGF](https://tex.z-dn.net/?f=%5CDelta%20DHE%5Csim%20%5CDelta%20DGF)
To find:
The value of x.
Solution:
We know that, corresponding sides of similar triangles are proportional.
Since,
, therefore
![\dfrac{HE}{GF}=\dfrac{DE}{DF}](https://tex.z-dn.net/?f=%5Cdfrac%7BHE%7D%7BGF%7D%3D%5Cdfrac%7BDE%7D%7BDF%7D)
On substituting the values from the figure, we get
![\dfrac{8}{12}=\dfrac{x}{x+2}](https://tex.z-dn.net/?f=%5Cdfrac%7B8%7D%7B12%7D%3D%5Cdfrac%7Bx%7D%7Bx%2B2%7D)
![\dfrac{2}{3}=\dfrac{x}{x+2}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B3%7D%3D%5Cdfrac%7Bx%7D%7Bx%2B2%7D)
On cross multiplication, we get
![2(x+2)=3x](https://tex.z-dn.net/?f=2%28x%2B2%29%3D3x)
![2x+4=3x](https://tex.z-dn.net/?f=2x%2B4%3D3x)
![4=3x-2x](https://tex.z-dn.net/?f=4%3D3x-2x)
![4=x](https://tex.z-dn.net/?f=4%3Dx)
Therefore, the value of x is 4.
Step-by-step explanation:
if there is nothing missing, we have
x + 25/-8 = -6
in order to compare or add or subtract fractions, we need to bring them all to the same denominator (bottom part).
remember, integer numbers are fractions too. like here
-6 = -6/1
25/-8 = -25/8
so, how can we bring -6/1 to .../8 ?
by multiplying 1 by 8.
but we cannot multiply only the denominator by 8. otherwise we would suddenly have
-6/8
and is -6/8 = -6/1 ? no, certainly not.
to keep the original value of the fraction we have to do the same multiplication also with the numerator (top part).
so, we actually do
-6/1 × 8/8 = -48/8
with this little trick we have now .../8 to operate with, and our transformed fraction has still the same value
-6/1 = -48/8 indeed.
so, we have
x + -25/8 = -48/8
x - 25/8 = -48/8
x = -48/8 + 25/8 = -23/8
Answer:
384/12 or 192/6 or 96/3
Step-by-step explanation:
Answer:
x = -4
Step-by-step explanation:
5x-9 = 15+11x
5x - 11x = 15 + 9
-6x = 24
x = -4
Set up the equation in long division form with x-5 outside of the box. Then you want to input the values as you go. Let me know if you want me to clarify my steps.