1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
myrzilka [38]
3 years ago
7

Trina has two brothers. one brother is 7 years older than trina and the other brother is 7 years younger than trina. the product

of her brothers age is 95.
a. if x represents trinas age, write an equation to describe the product of her brothers ages.
b. solve the equation for x how old is trina.
Mathematics
1 answer:
AlladinOne [14]3 years ago
7 0
(a) 95 = (x+7)*(x-7)

(b) 95 = (x+7)*(x-7) 
Expand the brackets:
95 = x² -7x + 7x -49 = x² - 49
Subtract x² from both sides:
95-x² = -49
Subtract 95 from both sides:
-x²=-49-95 
-x²= -144
Divide both sides by -1 to get rid of the negative numbers:
-x²/-1=-144/-1
x²=144
Take the square root of 144:
x = ± squareroot of 144
x = 12 or -12
x = 12 because you cannot have a negative age so Trina is 12 years old.
     
You might be interested in
PLEASE HELP
adell [148]
We know that
in a right triangle
Applying the Pythagoras Theorem
c²=a²+b²

in this problem
c=√87 yd
a=√23 yd
b=?
so
b²=c²-a²-----> b²=(√87)²-(√23)²----> b²=87-23----> b²=64----> b=8 yd

the answer is
8 yd
4 0
3 years ago
Read 2 more answers
Some friends of yours collected books for a book drive. They collected 64 Fiction, and 48 Non-Fiction books. They asked you to m
Cloud [144]

As all of the bundles have the same content inside, so assuming that there is x number of Fiction books and y number of Non-fiction books in each bundle.

Let n be the total number of bundles that my team can send.

There are 64 Fiction books, so

nx=64 ...(i)

Or x=64/n ...(ii)

also, there are 48 Non-Fiction books, so

ny=48 ...(iii)

Or y=48/n ...(iv)

Observing that the numbers x, y, and n are counting numbers and from equations (i) and (iii), n is the common factor of 64 and 48.

The possible common factors of 64 and 48 are,

n=1,2,4,8, and 16.

So, my team can send 1,2,3,4,8 or 16 bundles of books.

Now, from equations (ii) and (iv),

For n=1:

x=64/1=64

y=48/1=48

So, for 1 bundle the number of Fiction and Non-fictions books are 64 and 48 respectively.

For n=2:

x=64/2=32

y=48/2=48

So, for 2 bundles, the number of Fiction and Non-fictions books are 32 and 24 respectively.

For n=4:

x=64/4=16

y=48/4=12

So, for 4 bundles, the number of Fiction and Non-fictions books are 16 and 12 respectively.

For n=8:

x=64/8=8

y=48/8=6

So, for 8 bundles, the number of Fiction and Non-fictions books are 8 and 6 respectively.

For n=16:

x=64/16=4

y=48/16=3

So, for 16 bundles, the number of Fiction and Non-fictions books are 4 and 3 respectively.

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
-3x-8/4=10<br><br> What’s is value of x
dlinn [17]

Answer:

x= -16

Step-by-step explanation:

-3x-8/ 4 = 10

Here we can try to isolate x and so we have to first multiply 4 on each side.

-3x-8= 40

Then we can add the 8 to each side.

-3x= 48

Next, divide the -3 onto each side and we can get the answer!

x= -16

6 0
3 years ago
Match the set of two interior angle measurements with the third interior angle measurement that can make a triangle.
ioda

Answer:

40^\circ,50^\circ$ and 90^\circ

42^\circ,66^\circ$ and 72^\circ

60^\circ,60^\circ$ and 60^\circ

Step-by-step explanation:

The sum of angles in a triangle is 180 degrees

(a)Given the angles 40° and 50°

The third angle is, therefore: 180^\circ-(40^\circ+50^\circ)=90^\circ

We, therefore, have the set: 40^\circ,50^\circ$ and 90^\circ

(b)Given the angles 42° and 66°

The third angle is, therefore: 180^\circ-(42^\circ+66^\circ)=72^\circ

We, therefore, have the set: 42^\circ,66^\circ$ and 72^\circ

(c)Given the angles 60° and 60°

The third angle is, therefore: 180^\circ-(60^\circ+60^\circ)=60^\circ

We, therefore, have the set: 60^\circ,60^\circ$ and 60^\circ

6 0
3 years ago
Other questions:
  • Can someone PLEASE help ME with this math problem????? Nobody knows how to complete it!
    15·1 answer
  • A triangle has an area of 10.510.5 square feet. the base of the triangle is 66 feet. what is the height?
    10·1 answer
  • Grace hit 12 balls in the batting cage out of 20 pitches. Tomorrow she is going to go to the same batting cage and get 30 pitche
    5·1 answer
  • 4x + 3y - 8z<br> -5x + 7y + 10Z<br> (+) - 4x – 3y - 8z
    5·1 answer
  • Cedric is constructing a kite in the shape of a rhombus.The spars of the kite measure 15 inches and 24 inches.How many fabric wi
    9·1 answer
  • SQUARE ROOTS<br> 2x2 +50 =-166
    7·1 answer
  • Open in Desktop App
    15·1 answer
  • Interval of [0⁰,360⁰]<br><br><br>3 sin² tan 0-3 sin²0 = 0<br><br><br>20 points​
    5·1 answer
  • Which graph represents a function?
    6·2 answers
  • Which expressions represents a 20% discount off the price of an item that originally cost d dollars
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!