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
liberstina [14]
3 years ago
13

The length of one of the sides of a square was increased by 4 dm, and the other one was decreased by 6 dm. As a result, a rectan

gle was made with an area of 56 dm2. Find the length of the side of the square
Mathematics
2 answers:
Inga [223]3 years ago
5 0

Answer:

The answer to your question is 10 dm

Step-by-step explanation:

Data

length of a rectangle = x + 4

height of a rectangle = x - 6

Area of the rectangle = 56 dm²

length of the square = x

Process

1.- Find x with the information given for the rectangle

    Area = length x height

Substitution

    56 = (x + 4)(x - 6)

Expand

    56 = x² - 2x - 24

Equal to zero

            x² - 2x - 24 - 56 = 0

Simplify

             x² - 2x - 80 = 0

Factor

            (x - 10)(x + 8) = 0

Equal to zero

             x₁ -10 = 0          x₂ + 8 = 0

             x₁ = 10               x₂ = -8

2.- Conclusion

The length of the square is 10 dm because there are no negative lengths.                  

lapo4ka [179]3 years ago
5 0

Answer:the length of the side of the square is 10 dm

Step-by-step explanation:

Let x represent the length of each side of the square.

The length of one of the sides of a square was increased by 4 dm, and the other one was decreased by 6 dm. This means that the length of one side of the rectangle formed is (x + 4) dm and the length of the other side of the rectangle is

(x - 6) dm

The are of the rectangle is 56dm². This means that

(x - 6)(x + 4) = 56

x² + 4x - 6x - 24 = 56

x² - 2x - 24 - 56 = 0

x² - 2x - 80 = 0

x² + 8x - 10x - 80 = 0

x(x + 8) - 10(x + 8) = 0

x - 10 = 0 or x + 8 = 0

x = 10 or x = - 8

Since the length of each side of the square cannot be negative, then

x = 10

You might be interested in
Dolores spent $ 13.00 of the $20.00 in her wallet. Which decimal represents the fraction of the $20.00 Dolores spent?
Veronika [31]

Answer:

In order to find the fraction of the 20 dollars that has been spent, we have to divide the amount spent by the total amount. So 0.65 is the fraction of 20 that is spent.

Step-by-step explanation:

6 0
2 years ago
PLEASE SHOW ALL YOUR WORK TO GET BRAINLIEST AWARD
krek1111 [17]
<span> 7x+2y=5;13x+14y=-1 </span>Solution :<span><span> {x,y} = {1,-1}</span>  </span>System of Linear Equations entered :<span><span>  [1] 7x + 2y = 5 </span><span>  [2] 13x + 14y = -1 </span></span>Graphic Representation of the Equations :<span> 2y + 7x = 5 14y + 13x = -1 </span>Solve by Substitution :

// Solve equation [2] for the variable  y  
 

<span> [2] 14y = -13x - 1 [2] y = -13x/14 - 1/14</span>

// Plug this in for variable  y  in equation [1]

<span><span>  [1] 7x + 2•(-13x/14-1/14) = 5 </span><span>  [1] 36x/7 = 36/7 </span><span>  [1] 36x = 36 </span></span>

// Solve equation [1] for the variable  x  

<span><span>  [1] 36x = 36</span>  <span>  [1] x = 1</span> </span>

// By now we know this much :

<span><span>  x = 1</span> <span>  y = -13x/14-1/14</span></span>

<span>// Use the  x  value to solve for  y  
</span>

<span>   y = -(13/14)(1)-1/14 = -1 </span>Solution :<span><span> {x,y} = {1,-1}</span>  <span> Processing ends successfully</span></span>
8 0
3 years ago
Solve the following automotive-services problems based on the examples shown previously. Choose the correct answer.
Radda [10]
Transmission must be in third gear as both are running at the same speed ! so third gear !!!
7 0
3 years ago
Read 2 more answers
3. What is the slope of the line represented by the equation
dusya [7]

Answer:

Slope = -1/2

Step-by-step explanation:

Use y = mx + b to find the slope (m) Write the expression as an equation (-14y)-7x=0. Rewrite in slope-intercept form by removing the parentheses, adding 7x to both sides, dividing each term by -14, then writing in y = mx + b form, which is m=-1/2x. Remove the variable, it becomes your answer of -1/2.

5 0
3 years ago
1) 1, 4, 16, 64, ...<br>CR=L<br>Next 3 Terms:​
avanturin [10]

Answer:

256, 1024, 4096.

Step-by-step explanation:

The rule is x*4.

--> 1*4 = 4.

--> 4*4 = 16.

-->  16*4 = 64.

--> 64*4 = 256.

--> 256*4 = 1024.

--> 1024*4 = 4096.

4 0
3 years ago
Read 2 more answers
Other questions:
  • Help with this question
    13·1 answer
  • Which products are negative?
    11·1 answer
  • Henry had 2.5 lb of apples for a fruit salad. The recipe says that 5 lb of apples are needed for the salad. Henry went to the st
    12·1 answer
  • 20 POINTS! Please help, best answer will recessive brainliest answer points as well as 5 stars and a thank you. :)
    14·1 answer
  • Help 8th grade math need answers quick
    6·1 answer
  • BEST ANSWER GET BRAINLIEST
    11·2 answers
  • Noah drew 26 hearts, 21 stars, and 38 circles. what is the ratio of stars to hearts to circles?
    14·1 answer
  • Ill give you 25 points
    9·1 answer
  • Help me please :) . <br> I’ll mark you as a brainliest.
    13·2 answers
  • Fight!Fight!Fight!
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!