Answer:
x = 6
Step-by-step explanation:
∠ DBC + ∠ ABC = ∠ ABD , substitute values
5x - 4 + 8x - 3 = 79
13x + 1 = 79 ( subtract 1 from both sides )
13x = 78 ( divide both sides by 13 )
x = 6
 
        
             
        
        
        
9514 1404 393
Answer:
   A
Step-by-step explanation:
The axis of symmetry of quadratic ax²+bx+c is x=-b/(2a). For the given equation, the axis of symmetry is ...
   x = -4/(2(3/2)) = -4/3
The only graph with its vertex at x=-4/3 is graph A.
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<em>Additional comment</em>
You can also make the correct choice by evaluating the equation at a couple of different values of x. Convenient ones are x= -1, or 0, or +1. The value at x=0 is the y-intercept, (0, -2), which seems to be a point on all of the graphs. The value at x=1 is 3/2+4-2 = 3.5, which looks like it is only seen on graph A.
 
        
             
        
        
        
Answer:
y = 2/5x + 18.
Step-by-step explanation:
The line will have the same slope of 2/5.
Using the point-slope form of a line:
y - 12 = 2/5(x - -15)
y - 12 = 2/5(x + 15)
y = 2/5x + 6 + 12
y = 2/5x + 18.
 
        
                    
             
        
        
        
Answer:
The numbers are 12 and 3. 
Step-by-step explanation:
We can solve this problem by working with the information we have and setting up some equations. 
We know that one number is four times as large as another. So, let the smaller number be represented by the variable x and the bigger number be represented by 4x, since it is four times as large. 
Now, we know that if the numbers are added together, then the result is six less than seven times the smaller number. This can also be represented by the equation 4x + x = 7x - 6. 
Let's solve that equation like so: 

So, the smaller number must be 3 (remember that x represented the smaller number). To find the bigger number, all we need to do is multiply 3 by 4, which gives us 12. Therefore, the numbers are 12 and 3.