The sides of a triangle are given by the equations 4x-y-7=0,x+3y-31=0 and x+5y-7=0.determine the point of intersection of its al
titudes
details: class 12,algebra, 
title of chapter:
the general equations of straight lines.
 
      
                
     
    
    
    
    
    1 answer:
            
              
              
                
                
Hello,
1)Let's call A=inter (4x-y-7=0, x+3y-31=0)
4x-y=7
x+3y=31
==>13x=52==>x=4
and y=4*4-7=9
A=(4;9) 
2)Let's call B=inter (4x-y-7=0, x+5y-7=0)
4x-y=7
x+5y=7
==>21x=42
==>x=2 and y=4*2-7=1
B=(2,1)
3) Slope of BD: y=-x/3+31/3 ==> slope perpendicular=3
Line BD:y-1=3(x-2)==>y=3x+5
4) Slope AE: y=-x/5+7/5 ==>slope perpendicular=5
Line AE: y-9=5(x-4)==> y=5x-11
5) intersection (BD;AE):
y=5x-11
y=3x-5
==>2x=6==>x=3
and y=3*3-5=4
H=(3,4)
 
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Step-by-step explanation:
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Answer:
-15/8 or -1 7/8, 1.875
Step-by-step explanation:
 
        
             
        
        
        
None of them are correct.
        
             
        
        
        
Sum of the first two is:
-3x+5+7-4x = -7x+12
That subtracted from 5x+17:
5x+17-(-7x+12) = 12x+5
        
             
        
        
        
Step-by-step explanation:
g(x) = 3x² + 2
h(x) = 2x + 2
g(h(x)) = g([2x + 2]) = 3[2x+2]² + 2
 = 3[4x² + 8x + 4] + 2
 = 12x² + 24x + 12 + 2
 = 12x²+ 24x + 14