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CaHeK987 [17]
2 years ago
7

Which of the following are arithmetic sequences? Check all that apply.

Mathematics
1 answer:
telo118 [61]2 years ago
3 0

a c and d

ub9uyuyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy

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The math test scores of Mrs. Hunter's class are shown below:
pishuonlain [190]

Answer:

82

Step-by-step explanation:

Well since everything is already in order from least to greatest:

48, 56, 68, 72, 72, 78, 78, 80, 82, 84, 88, 88, 88, 90, 94, 98, 100

The median is the number in the middle

So 82 is the median

Hope this helps!

Feel free to comment any questions you have!

6 0
3 years ago
In a certain year, there were 88 female officials in Congress, which is comprised of the House of Representatives and the Senate
Ainat [17]

Answer:

  • 71 in House of Representatives
  • 17 in Senate

Step-by-step explanation:

Let h and s represent the numbers in the House and Senate, respectively. Then we have ...

  h + s = 88

  h - s = 54

Subtracting the second equation from the first gives ...

  (h +s) -(h -s) = (88) -(54)

  2s = 34 . . . . . simplify

  s = 17 . . . . . . . divide by 2

  h = 88 -17 = 71 . . . . find the other value using the sum equation

There were 71 females in the House of Representatives, and 17 females in the Senate.

3 0
2 years ago
A small fishing boat's outboard motor requires a mixture of gasoline and oil for fuel. The mixture called for in the owner's man
NARA [144]
I hope this helped:)

5 0
3 years ago
Is 32.725 = to 32.735
Arturiano [62]

Answer:

no it is not 32.725 is 0.01 less than

8 0
3 years ago
BRAINLIESSTTTT ASAP !!!!!!!!!! 20 pointssss
Mars2501 [29]
Answers:  
_____________________________________________________
   Part A)  " (3x + 4) " units  . 
_____________________________________________________
   Part B)  "The dimensions of the rectangle are:

                             " (4x + 5y) " units ;  <u>AND</u>:  " (4x − 5y)"  units."
_____________________________________________________

Explanation for  Part A):
_____________________________________________________

Since each side length of a square is the same; 
   
    Area = Length * width = L * w ;  L = w  = s = s ;

      in which:  " s = side length" ;

So, the Area of a square, "A"  = L * w = s * s = s² ;

{<u>Note</u>:  A "square" is a rectangle with 4 (four) equal sides.}.

→  Each side length, "s", of a square is equal.

Given:  s² = "(9x² + 24x + 16)" square units ;

Find "s" by factoring: "(9x² + 24x + 16)" completely:

   →  " 9x² + 24x + 16 ";

Factor by "breaking into groups" :

"(9x² + 24x + 16)"  = 

    →  "(9x² + 12x) (12x + 16)" ;
_______________________________________________________

Given:   " (9x² + 24x + 16) " ; 
_______________________________________________________
Let us start with the term:
_______________________________________________________

" (9x² + 12x) " ; 

    →  Factor out a "3x" ;  → as follows:
_______________________________________

    → " 3x (3x + 4) " ; 

Then, take the term:
_______________________________________
    → " (12x + 16) " ;

And factor out a "4" ;   →  as follows:
_______________________________________

    → " 4 (3x + 4) " 
_______________________________________
We have:

" 9x² + 24x + 16 " ;

    =  " 3x (3x + 4)  +  4(3x + 4) " ;
_______________________________________
Now, notice the term:  "(3x + 4)" ; 

We can "factor out" this term:

3x (3x + 4)  +  4(3x + 4)  = 

     →  " (3x + 4) (3x + 4) " .  → which is the fully factored form of:

                                                   " 9x² + 24x + 16 "  ; 
____________________________________________________
     →  Or; write:  "  (3x + 4) (3x + 4)" ; as:  " (3x + 4)² " .
____________________________________________________
     →  So,  "s² = 9x² + 24x + 16 " ; 

Rewrite as:  " s² = (3x + 4)² " .

     →  Solve for the "positive value of "s" ; 

     →  {since the "side length of a square" cannot be a "negative" value.}.
____________________________________________________
     →  Take the "positive square root of EACH SIDE of the equation; 
              to isolate "s" on one side of the equation; & to solve for "s" ;

     →  ⁺√(s²)  =  ⁺√[(3x + 4)²]   '

To get:

     →  s  = " (3x + 4)" units .
_______________________________________________________

Part A):  The answer is:  "(3x + 4)" units.
____________________________________________________

Explanation for Part B):

_________________________________________________________<span>

The area, "A" of a rectangle is:

    A = L * w ;  

 in which "A" is the "area" of the rectangle;
                "L" is the "length" of the rectangle; 
                "w" is the "width" of the rectangle; 
_______________________________________________________
  Given:  " A = </span>(16x² − 25y²) square units" ;  
   
       →  We are asked to find the dimensions, "L" & "w" ;
       →  by factoring the given "area" expression completely:
____________________________________________________
  → Factor:  " (16x² − 25y²) square units " completely '

Note that:  "16" and: "25" are both "perfect squares" ;
      
We can rewrite: " (16x² − 25y²) "  ;   as:

       =   " (4²x²)  −  (5²y²) " ; and further rewrite the expression:
________________________________________________________
Note:  
________________________________________________________
" (16x²) " ;  can be written as:  "(4x)² " ;

 ↔ " (4x)²  =  "(4²)(x²)" = 16x² "


Note:  The following property of exponents:

         →  (xy)ⁿ = xⁿ yⁿ ;    →  As such:  " 16x² = (4²x²) = (4x)² " . 
_______________________________________________________
Note:
_______________________________________________________

     →   " (25x²) " ;  can be written as:  " (5x)² " ; 

        ↔   "( 5x)²  =  "(5²)(x²)" = 25x² " ; 

Note:  The following property of exponents:

         →  (xy)ⁿ = xⁿ yⁿ ;    →  As such:  " 25x² = (5²x²) = (5x)² " . 
______________________________________________________

→  So, we can rewrite:  " (16x² − 25y²) " ;  

as:  " (4x)² − (5y)² " ;   
 
    → {Note:  We substitute: "(4x)² "  for "(16x²)" ; & "(5y)² "  for "(25y²)" .} . ; 
_______________________________________________________
→  We have:  " (4x)² − (5y)² " ;

→  Note that we are asked to "factor completely" ; 

→  Note that:  " x² − y² = (x + y) (x − y) " ;

      → {This property is known as the "<u>difference of squares</u>".}.

→ As such:  " (4x)² − (5y)² " = " (4x + 5y) (4x − 5y) " .
_______________________________________________________
Part B):  The answer is:  "The dimensions of the rectangle are:

                              " (4x + 5y) " units ;  AND:  " (4x − 5y)"  units."
_______________________________________________________
7 0
3 years ago
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