The answer is 16 cm (or 0.16 m).
The scale is the ratio of the model to the real thing.
So, in the scale 1:50, the model is 1, while the real thing is 50.
Now, just make a proportion:
the model : the real thing = the model dimension : the real thing dimension
1 : 50 = x : 8m
From here:
x = 8m * 1 / 50 = 0.16 m = 0.16 * 100 cm = 16 cm.
[x-1]=5x+10
We have two equations:
1) x-1=5x+10
x-1=5x+10
x-5x=10+1
-4x=11
x=-11/4
2) x-1=-(5x+10)
x-1=-(5x+10)
x-1=-5x-10
x+5x=-10+1
6x=-9
x=-9/6=-3/2
we have two possible solutions:
solution₁; x=-11/4
solution₂: x=-3/2
we check it out:
1) x=-11/4
[x-1]=5x+10
[-11/4 - 1]=5(-11/4)+10
[(-11-4)/4]=-55/4 + 10
[-15/4]=(-55+40) /4
15/4≠-15/4 This solution don´t work.
2) x=-3/2
[x-1]=5x+10
[-3/2 - 1]=5(-3/2)+10
[(-3-2)/2]=-15/2 + 10
[-5/2]=(-15+20)/2
5/2=5/2; this solution works.
Therefore:
Answer: x=-3/2.
3 (4x + 6) = 21
4x + 6 = 21/3
4x + 6 = 7
4x = 7 - 6
4x = 1
x = 1/4
Given the quadratic function, to get the roots we factorize:
3x²-4x-7=0
3x²+3x-7x-7=0
3x(x+1)-7(x+1)=0
(3x-7)(x+1)=0
thus the roots are
x=-1 or x=3/7
thus the sum of the roots will be:
-1+3/7
=-4/7
