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Hitman42 [59]
3 years ago
8

Hi, i need help on these. thank you very much [urgent]

Mathematics
1 answer:
stepladder [879]3 years ago
7 0

(4y - 3x) \times (4y + 3x)

( {11a}^{5}  -  {b}^{4} ) \times ( {11a}^{5}  +  {b}^{4} )

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The area of a rectangle is 980 in squared. the ratio of the length to the width is 5 : 4. find the length and the width.
ella [17]
Answer:   The length of the rectangle is 35 in.

                 The width of the rectangle is 28 in.
_________________________________________________________
Explanation:
_________________________________________________________
The formula for the area, "A", of a rectangle:

Area (A) = length (L) * width (w) ; 
 
  that is:   "  A  =  L  *  w  "  ;

A = 980 in²  (given);

ratio of the length to the width is:  " 5 : 4 " (given); 

→   Find the length (L) and the width (w).
_________________________________________________________

→  980 in²  =  (5x) * (4x) ; 

in which:  " 980 in² " is the area of the triangle; 

                 " 5x" = the length (L) of the rectangle, for which we shall solve; 

                 " 4x" = the width (w) of the rectangle, for which we shall solve.
_______________________________________________________
If we find solve for "x" ; we can solve for  "5x" and "4x" (the "length" and the "width", respectively);  by plugging in the solved value for "x" ; 
_______________________________________________________

   →  980 in²  =  (5x) * (4x) ; 

   ↔   (5x) * (4x) = 980 in²  ; 

   →   (5x) * (4x) = (5) * (4) * (x) * (x)  = 20 * x² = 20x² ;

   →  20x²  =  980 ;

Divide each side by "10" ; by canceling out a "0" on each side of the equation:

   →  2x² = 98 ; 

Now, divide each side of the equation by "2" ;

   → 2x² / 2  =  98 / 2 ; 

to get:  

→  x² = 49 ; 

Now, take the "positive square root" of each side of the equation;  (since a "length or width" cannot be a "negative value") ; 
    to isolate "x" on one side of the equation; & to solve for "x" ; 

→  ⁺√(x²) = √49 ; 

to get:

→  x = 7 ;
______________________________________________________
Now, we can solve for the "length" and the "width" ; 

→  The length is:  "5x" ;   

     5x = 5(7) =  " 35 in " ; 
______________________________________________________
→  The width is:  "4x" ; 

     4x =  4(7) =  "28 in."
______________________________________________________
Let us check our answer:

    →  A = L * w ; 

    →  980 in² = ?  35 in. * 28 in. ?? ; 

   Using a calculator:  "35 * 28 = 980" .  Yes!   ;
____________________________________________________
 { Also note:  " in * in = in² " ?  Yes! } .
____________________________________________________
3 0
3 years ago
Consider a sequence whose first five terms are: -3,0,3, 24, 81.
vfiekz [6]
D is the correct answer
6 0
3 years ago
Let y = f(x) be a function with domain D = [−6, 10] and range R = [−8, 12]. Find the domain D and range R for each function. Ass
bogdanovich [222]
A) The domain remains the same.
Since, in y = - 2 f(x) , the y is whats being multiplied and therefore changed, not the x  or domain.
Therefore D[-6,10] <span>
The range is what changes by a factor of -2.
If the original range was [-8,12], then the new one is 
[(-8 x -2),(12 x -2)] = [16 , -24].

However, you must flip the numbers to make the interval true, giving you R [-24,16]</span>
7 0
3 years ago
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The area of polygon MNOPQR = area of a rectangle that is 15 square units + area of a rectangle that is ___ square units. (input
shutvik [7]
The area of the small rectangle is 3 units square.

3 0
3 years ago
The points R(−4, −1) and S(2, −5) are two vertices of right triangle RST. The hypotenuse of the triangle is RS.
Nostrana [21]
      If RS is the hypotenuse of the triangle RST and point T is in Quadrant 3, then point T must be the intersection of the lines: x = - 4 and y = - 5.
       Therefore, the coordinates of point T are ( x, y ) = ( - 4, - 5 ) 
       Answer:
       T ( - 4, - 5 )
6 0
3 years ago
Read 2 more answers
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