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
finlep [7]
3 years ago
6

10 POINTS!

Mathematics
1 answer:
aksik [14]3 years ago
3 0

Answer:

C

Step-by-step explanation:

You might be interested in
The sum of twice a first number and five times a second number is 78. If the second number is subtracted from five times the fir
ss7ja [257]
The numbers are:  "9" and "12" .
___________________________________
Explanation:
___________________________________
Let:  "x" be the "first number" ; AND:

Let:  "y" be the "second number" .
___________________________________
From the question/problem, we are given:
___________________________________
     2x + 5y = 78 ;  → "the first equation" ; AND:

     5x − y = 33 ;  → "the second equation" .
____________________________________
From "the second equation" ; which is:

   " 5x − y = 33" ; 

→ Add "y" to EACH side of the equation; 

              5x − y + y = 33 + y ;

to get:  5x = 33 + y ; 

Now, subtract: "33" from each side of the equation; to isolate "y" on one side of the equation ; and to solve for "y" (in term of "x");

            5x − 33 = 33 + y − 33 ;

to get:   " 5x − 33 = y " ;  ↔  " y = 5x − 33 " .
_____________________________________________
Note:  We choose "the second equation"; because "the second equation"; that is;  "5x − y = 33" ;  already has a "y" value with no "coefficient" ; & it is easier to solve for one of our numbers (variables); that is, "x" or "y"; in terms of the other one; & then substitute that value into "the first equation".
____________________________________________________
Now, let us take "the first equation" ; which is:
  "  2x + 5y = 78 " ;
_______________________________________
We have our obtained value; " y = 5x − 33 " .
_______________________________________
We shall take our obtained value for "y" ; which is: "(5x− 33") ; and plug this value into the "y" value in the "first equation"; and solve for "x" ;
________________________________________________
Take the "first equation":
 ________________________________________________
      →   " 2x + 5y = 78 " ;  and write as:
________________________________________________ 
      →   " 2x + 5(5x − 33) = 78 " ;
________________________________________________
Note the "distributive property of multiplication" :
________________________________________________
     a(b + c) = ab + ac ; AND:

     a(b − c) = ab − ac .
________________________________________________
So; using the "distributive property of multiplication:

→   +5(5x − 33)  = (5*5x) − (5*33) =  +25x − 165 .
___________________________________________________
So we can rewrite our equation:

          →  " 2x + 5(5x − 33) = 78 " ;

by substituting the:  "+ 5(5x − 33) " ;  with:  "+25x − 165" ; as follows:
_____________________________________________________

          →  " 2x + 25x − 165 = 78 " ;
_____________________________________________________
→ Now, combine the "like terms" on the "left-hand side" of the equation:

              +2x + 25x = +27x ; 

Note:  There are no "like terms" on the "right-hand side" of the equation.
_____________________________________________________
    →  Rewrite the equation as:
_____________________________________________________
         →   " 27x − 165 = 78 " ;

      Now, add "165" to EACH SIDE of the equation; as follows:

         →    27x − 165 + 165 = 78 + 165 ;

        →  to get:      27x = 243  ;
_____________________________________________________
      Now, divide EACH SIDE of the equation by "27" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
_____________________________________________________
               27x / 27  =  243 / 27 ; 

       →   to get:    x = 9 ; which is "the first number" .
_____________________________________________________
Now;    Let's go back to our "first equation" and "second equation" to solve for "y" (our "second number"):

     2x + 5y = 78 ; (first equation);
     
      5x − y = 33 ; (second equation); 
______________________________
Start with our "second equation"; to solve for "y"; plug in "9" for "x" ;

→ 5(9) − y = 33 ;  

    45 − y = 33;  
   
Add "y" to each side of the equation:
 
   45 − y + y = 33 + y ;  to get:

   45 = 33 + y ;  

↔ y + 33 = 45 ;  Subtract "33" from each side of the equation; to isolate "y" on one side of the equation ; & to solve for "y" ;  
 
 → y + 33 − 33  = 45 − 33 ;

to get:  y = 12 ;

So;  x = 9 ; and y = 12 .  The numbers are:  "9" and "12" .
____________________________________________
 To check our work:
_______________________
1)  Let us plug these values into the original "second equation" ; to see if the equation holds true (with "x = 9" ; and "y = 12") ; 

→ 5x − y = 33 ;  → 5(9) − 12 =? 33 ?? ;  → 45 − 12 =? 33 ?? ;  Yes!
________________________
2)  Let us plug these values into the original "second equation" ; to see if the equation holds true (with "x = 9" ; and "y = 12") ;

→ 2x + 5y = 78 ; → 2(9) + 5(12) =? 78?? ; → 18 + 60 =? 78?? ; Yes!
_____________________________________
So, these answers do make sense!
______________________________________
3 0
3 years ago
If a=12 and b=23 what is the area of pencil decoration
Allushta [10]
I think the answer is 276
12 * 23 = 276
hope it helps
7 0
3 years ago
Read 2 more answers
Help me pls UoU Uwu<br> \djjn
Nataly [62]

Answer:

y = 4x + 14

Step-by-step explanation:

slope-intercept form: y = mx + b

Slope formula: \frac{y2-y1}{x2-x1}

To write the equation in y = mx + b form, we need to find the slope(m) and the y-intercept(b) of the equation.

To find the slope, take two points from the table(in this example I'll use points (0, 14) and (1, 18)) and input them into the slope formula:

\frac{18-14}{1-0}

Simplify:

18 - 14 = 4

1 - 0 = 1

\frac{4}{1}=4

The slope is 4.

To find the y-intercept, input the values of the slope and one point(in this example I'll use point (1, 18)) into the equation format and solve for b:

y = mx + b

18 = 4(1) + b

18 = 4 + b

14 = b

The y-intercept is 14.

Now that we know the slope and the y-intercept, we can write the equation:

y = 4x + 14

3 0
3 years ago
Which simplified fraction is equal to 0.53 repeating?
GalinKa [24]

Answer: I believe its 5/9

Step-by-step explanation:  

As you can see, the only fraction that doesn't equal 0.53, or the outlier, is 5/9 or 0.5556

5 0
3 years ago
Difference between a number line and a number track
harkovskaia [24]

Answer:

What's the difference between a number track and a number line? A number track is a sequence of numbers, each inside its own square. ... Whereas, a number line is where the numbers are attached to markers on a line. This method of addition / subtraction comes later.

3 0
2 years ago
Other questions:
  • What's the value of a?
    15·1 answer
  • What does the notation f(2) mean? multiply f by 2 the output (y-value) when x = 2 the value of x when the output is 2
    15·2 answers
  • Can anyone help me with this e?I need the answer quickly.(FINALS ON MONDAY)​
    9·2 answers
  • 1) Jan is buying new flooring for her kitchen. The kitchen is a rectangle that is 3
    11·1 answer
  • How many time can 21 go into 6
    8·2 answers
  • A chocolate shop sells chocolates with a variety of different fillings.
    12·1 answer
  • One of the legs of a right triangle measures 6 cm and its hypotenuse measures 10 cm. Find the measure of the other leg. If neces
    11·1 answer
  • I need help with Geometry
    11·1 answer
  • An investigation of the relationship between height of a child and age (in months) found that age explained 64% of the variation
    8·1 answer
  • COMPLETE ANSWER
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!