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
Shalnov [3]
2 years ago
15

20 points!!!

Mathematics
1 answer:
Svetlanka [38]2 years ago
4 0
The answer is:  {4, 1} .
________________________________________________________
Explanation:
________________________________________
Given the equations:
________________________________________
      "12x = 54 −<span> 6y ;
     "-17x = -62 </span>− 6y ;
_________________________________________
Multiply the second equation (both sides) by "-1" ;
___________________________________________
  -1*{-17x = -62 − 6y} ;

to get: 

17x = 62 + 6y ;
___________________________________________
{Note: The reason we do this is that we notice the TWO "-6y" values; and by multiplying one of the entire equations by "-1" ; we can change said equation to an equation with a "(+6y)" value; and the "(+6y)" and the "(-6y)" values cancel out to "zero" ; providing an opportunity to isolate "x"; and to solve for "x".}.
___________________________________________
Now, rewrite the two equations:
___________________________________________

       12x = 54 − 6y ;
       17x = 62 +  6y ;
___________________________________________
↔  Rewrite; and then add the two together:

       6y + 62 = 17x 
      -6y + 54 = 12x 
____________________
       0  +  116 = 29x ;

↔ 29x = 116 ;

Divide EACH SIDE of the equation by "29" ; to isolate "x" on one side of the <span>equation ; and</span> to solve for "x" ;
________________________________________________
   29x / 29 = 116 / 29  ;
________________________________________________
to get:
________________________________________________
           x  = 4 .
______________________________________________
Now that we have the value for "x" , which is "4" ; let us plug in "4" for "x" for either of the original two equations, to solve for "y".  In fact, let us try substituing "4" for "x" ;  for BOTH of the two original equations; to see if the value is correct.
_____________________________________________
Our original two given equations are:
_____________________________________________
      "12x = 54 − 6y ;

     "-17x = -62 − 6y ;
_____________________________________________
 Let us start with the first equation:
 ________________________
      " 12x = 54 − 6y " ;
__________________________________
When "x = 4" ; what does "y" equal ?

Plug in "4" for "x" ; to solve for "y" ;

  12(4) = 54 − 6y ;

→ 48 = 54 − 6y ;

Subtract "54" from EACH SIDE of the equation;

→ 48 − 54 = 54 − 6y − 54 ;

to get:

→  -6 = -6y ; 

→ Divide EACH side of the equation by "-6" ; to isolate "y" on one side of the <span>equation ; and</span> to solve for "y" ; 

→ -6/-6 = -6y / -6 ;

to get:

1 = y ;  ↔ y = 1 ;  So, we have:  x = 4, y = 1 ;  or,  {4, 1}.
______________________________________________
Let us check to see, if the second (orginal equation) holds true when "x = 4" and "y = 1 " ;
______________________________________________
The second "original equation" given is:
______________________________________________
       " -17x = -62 − 6y " ;
______________________________________________
   →    -17(4) = ?  -62  − 6(1) ?

    →  -68 = ? -62 − 6 ?

    →  -68 = ? -68 ?  Yes!
________________________________________________________
The answer is:  {4, 1} .
________________________________________________________
You might be interested in
The length of a rectangle is 6 ft longer than its width. if the perimeter of the rectangle is 52 ft , find its area.
sveticcg [70]
Let its width be w and length= w+6
2(w+6+w)=52
4w+12=52
4w=40
w=10
Area=10*(10+6)=160
7 0
3 years ago
Which of the following is a proportion?
poizon [28]

Answer:

Option C, 14/21=9/21 is the proportion.

Step-by-step explanation:

Given:

a.5/7 = 10/12

b.9/15 = 12/18

c.4/6 = 8/12

d.14/21 = 9/12

We have to find the proportions.

In proportion two ratios are equal, as it has an equality sign in between so both side must be of same ratio in its simplest form.

Let's work with option C

⇒ \frac{4}{6}=\frac{8}{12}

To find the simplest form we have to divide the numerator and denominator with same digit (or its factor).

Simplest form of  \frac{8/2}{12/2} = \frac{4}{6} , \frac{4/2}{6/2}= \frac{2}{3}

Simplest form of \frac{4}{6} = \frac{2}{3}

Both sides in option C have equal ratios of 2/3.

So 4/6=8/12 is in proportion.

6 0
3 years ago
Elenas bed measures 3‘ x 6‘ on the scale drawing what are the actual measurements of her bed
Sonbull [250]

Using proportions, supposing a scale of 1 inch = 3 feet, the actual measurements of her bed are given by: 9 ft x 18 ft.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division, from the relations built in the problem.

One example of application of proportions is for scale problems, as the actual scale and the drawing length are compared to find the actual length of the object drawn.

In the context of this problem, the scale is given by:

1 inch = 3 feet.

The drawn length of the bed is given by:

3 inches x 6 inches.

Hence the actual length is given by:

9 feet x 18 feet.

As:

  • 3 x 3 = 9.
  • 6 x 3 = 18.

<h3>What is the missing information?</h3>

The scale of the drawing is missing, hence we are going to suppose that it is 1 inch = 3 feet.

More can be learned about proportions at brainly.com/question/24372153

#SPJ1

4 0
10 months ago
Hi, can somebody pretty please help me? Thank you!
dybincka [34]

Answer:

Honey, I don't know what you need help with. Nothing is linked.

Step-by-step explanation:

4 0
3 years ago
Consider circle E.<br>A<br>B<br>26<br>D<br>E<br>F<br>What is the mBC ?<br>mBC<br><br>Please help​
RSB [31]

Step-by-step explanation:

< AEB + < BEC = 180° {BEING LINEAR PAIR }

26° + < BEC = 180°

< BEC = 180° - 26°

< BEC = 154°

ARC BC = < BEC ( relation between arc and central angle)

Arc BC = 154°

Hope it will help :)

8 0
2 years ago
Other questions:
  • Which relationship is always correct for the angles x, y, and z of triangle ABC?
    13·2 answers
  • This problem has to do with Fahrenheit and Celsius
    7·1 answer
  • Plz help!
    13·2 answers
  • At a certain non-profit organization, 51% of employees are college graduates and 47% of employees have more than ten years of ex
    7·1 answer
  • How do you do this..........
    14·1 answer
  • Natalie baked 20 cupcakes for a fundraising event at school. On the way to the event she dropped 35% of the cupcakes on the floo
    12·1 answer
  • Written as a simplified polynomial in standard form, what is the result when (2x - 7) ^ 2 is subtracted from 1?
    8·1 answer
  • Whats The Answer Marking Brainliest, Please explain your answer:D...................<br> ..
    15·1 answer
  • HELP ME PLZ <br> What is the slope of a parallel to the line that passes through (- 3, 1) and (3, 7)
    6·2 answers
  • Which expression is equivalent to 64 2/3<br><br><br> PLS HELP
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!