Answer:
- The first one is 6
x^
3  +  6
x^
2  -  36
x
and the second one is 3x^2 + 21x - 54
 
        
                    
             
        
        
        
Let l and l-6 be the length and width, respectively, of the rectangle. Then:
l(l-6)=40
l²-6l-40=0
(l-10)(l+4)=0
l=10,-4
The rectangle is 10" by 4". ☺☺☺☺
        
             
        
        
        
<u>Step-by-step explanation:</u>
transform the parent graph of f(x) = ln x        into f(x) = - ln (x - 4)  by shifting the parent graph 4 units to the right and reflecting over the x-axis 
(???, 0): 0 = - ln (x - 4)
             
             0 = ln (x - 4)
             
              1 = x - 4
           <u> +4 </u>  <u>    +4 </u>
              5 = x
(5, 0)
(???, 1): 1 = - ln (x - 4)
             
             1 = ln (x - 4)
             
              e = x - 4
           <u> +4 </u>   <u>    +4 </u>
          e + 4 = x
           6.72 = x
(6.72, 1)
Domain: x - 4 > 0
                 <u>  +4 </u>  <u>+4  </u>
                x       > 4
(4, ∞)
Vertical asymptotes: there are no vertical asymptotes for the parent function and the transformation did not alter that
No vertical asymptotes
*************************************************************************
transform the parent graph of f(x) = 3ˣ        into f(x) = - 3ˣ⁺⁵  by shifting the parent graph 5 units to the left and reflecting over the x-axis 
Domain: there is no restriction on x so domain is all real number
(-∞, ∞)
Range: there is a horizontal asymptote for the parent graph of y = 0 with range of y > 0.  the transformation is a reflection over the x-axis so the horizontal asymptote is the same (y = 0) but the range changed to y < 0.
(-∞, 0)
Y-intercept is when x = 0:
 f(x) = - 3ˣ⁺⁵
       = - 3⁰⁺⁵
       = - 3⁵
       = -243
Horizontal Asymptote: y = 0  <em>(explanation above)</em>
 
        
             
        
        
        
Answer:
<h3> The equation has one valid solution and no extraneous of solutions.</h3>
Step-by-step explanation:
Given the expression;
4x/3x+1 = x/2x+10
We are to get the nature of the value of x
Cross multiply;
x(3x+1) = 4x(2x+10)
3x²+x = 8x²+40x
Collect like terms;
3x²-8x² + x - 40x = 0
-5x²+x -40x = 0
-5x²-39x = 0
-5x² = 39x
-5x = 39
x = -39/5
<em>Since we have just one value of x hence, the equation has one valid solution and no extraneous of solutions.</em>
<em></em>
<em></em>
 
        
                    
             
        
        
        
Answer:
Step-by-step explanation:
m3/9=3
We move all terms to the left:
m3/9-(3)=0
We multiply all the terms by the denominator
m3-3*9=0
We add all the numbers together, and all the variables
m^3-27=0
#learnwithbrainly