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
charle [14.2K]
3 years ago
12

The length of a rectangle is 5m less than three times the width, and the area of the rectangle is 50m^(2). Find the dimensions o

f the rectangle
Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
6 0

Answer:

The width is 5m and the length is 10m.

Step-by-step explanation:

Rectangle:

Has two dimensions: Width(w) and length(l).

It's area is:

A = w*l

The length of a rectangle is 5m less than three times the width

This means that l = 3w - 5

The area of the rectangle is 50m^(2)

This means that A = 50. So

A = w*l

50 = w*(3w - 5)

3w^{2} - 5w - 50 = 0

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

In this question:

3w^{2} - 5w - 50 = 0

So

a = 3, b = -5, c = -50

\bigtriangleup = (-5)^{2} - 4*3*(-50) = 625

w_{1} = \frac{-(-5) + \sqrt{625}}{2*3} = 5

w_{2} = \frac{-(-5) - \sqrt{625}}{2*3} = -3.33

Dimension must be positive result, so

The width is 5m(in meters because the area is in square meters).

Length:

l = 3w - 5 = 3*5 - 5 = 10

The length is 10 meters

You might be interested in
The graph below is the graph of a function.<br> 10<br> - 10<br> 10<br> - 10<br> True<br> B. False
Dimas [21]

Answer:

hgfyjtdjtrxgfyfguktfkgh

Step-by-step explanation:

hgfytrdutrc

6 0
3 years ago
Can you pls solve this 2x² + 5x - 7​
Studentka2010 [4]

Answer:

not solvable

Step-by-step explanation:this statement is impossible to simplify without more information.

5 0
4 years ago
Students on the softball team on $295 from the car wash how many team banners can they buy each banner cost eight dollars
NISA [10]

Answer:

the students can buy 36 banners with 7 dollars left.

4 0
4 years ago
Read 2 more answers
What properties of a figure are preserved under a rotation?
Mekhanik [1.2K]
Isometries I'm guessing<span>

</span>
3 0
3 years ago
The sum of the fractions 2/y-3 and 6/y+3 is equal to their
Sphinxa [80]

Step-by-step explanation:

Move expression to the left side and change its sign

5

y

−

3

+

10

y

2

−

y

−

6

−

y

y

+

2

=

0

Write

−

y

as a sum or difference

5

y

−

3

+

10

y

2

+

2

y

−

3

y

−

6

−

y

y

+

2

=

0

Factor out

y

and

−

3

from the expression

5

y

−

3

+

10

y

(

y

+

2

)

−

3

(

y

+

2

)

−

y

y

+

2

=

0

Factor out

y

+

2

from the expression

5

y

−

3

+

10

(

y

+

2

)

(

y

−

3

)

−

y

y

+

2

=

0

Write all numerators above the least common denominator

5

(

y

+

2

)

+

10

−

y

(

y

−

3

)

(

y

+

2

)

(

y

−

3

)

=

0

Distribute

5

and

−

y

through the parenthesis

5

y

+

10

+

10

−

y

2

+

3

y

(

y

+

2

)

(

y

−

3

)

=

0

Collect the like terms

8

y

+

20

−

y

2

(

y

+

2

)

(

y

−

3

)

=

0

Use the commutative property to reorder the terms

−

y

2

+

8

y

+

20

(

y

+

2

)

(

y

−

3

)

=

0

Write

8

y

as a sum or difference

−

y

2

+

10

y

−

2

y

+

20

(

y

+

2

)

(

y

−

3

)

=

0

Factor out

−

y

and

−

2

from the expression

−

y

(

y

−

10

)

−

2

(

y

−

10

)

(

y

+

2

)

(

y

−

3

)

=

0

Factor out

−

(

y

−

10

)

from the expression

−

(

y

−

10

)

(

y

+

2

)

(

y

+

2

)

(

y

−

3

)

=

0

Reduce the fraction with

y

+

2

−

y

−

10

y

−

3

=

0

Determine the sign of the fraction

−

y

−

10

y

−

3

=

0

Simplify

10

−

y

y

−

3

=

0

When the quotient of expressions equals

0

, the numerator has to be

0

10

−

y

=

0

Move the constant,

10

, to the right side and change its sign

−

y

=

−

10

Change the signs on both sides of the equation

y

=

10

Check if the solution is in the defined range

y

=

10

,

y

≠

3

,

y

≠

−

2

∴

y

=

10

6 0
3 years ago
Read 2 more answers
Other questions:
  • 7. The box plots show the average gas mileage of
    5·2 answers
  • 35 % of what number is 12?
    13·2 answers
  • The formula i = prt where i = interest, p= principal, r= rate, and t= time is used to calculate the amount of simple interest ea
    9·1 answer
  • What does X equal. PLEASE HELP!!!
    9·2 answers
  • Tod has baseball and basketball trading cards. He has 10 more baseball cards than basketball cards. He has 38 cards in all. How
    13·1 answer
  • perimetrul unui paralelogram este de 30 cm.una dintre laturi are lungimea de 6 metri . dterminati lungimile celolrarte laturi
    7·1 answer
  • One day,the state fair total attendance was 126,945. Round 126,945 to the nearest hundred thousand, nearest ten thousand,And nea
    9·2 answers
  • How are mean and median similar?
    10·1 answer
  • The mathematical expressions of the thermal conditions at the boundaries are called the _____ conditions.
    9·1 answer
  • 15. Juan has a fair six-sided die, if Juan rolls the die
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!