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
Ede4ka [16]
3 years ago
12

The length plus the width of a rectangle is 10. Let x represent the length. The equation for the area y of the

Mathematics
1 answer:
yuradex [85]3 years ago
8 0

Answer:

length of rectangle = 5

width of rectangle = 5

Area of rectangle = 25

Step-by-step explanation:

Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:

y=x\,(10-x)=10x-x^2

Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.

Recall that the formula for the x of the vertex of a quadratic of the form :

y=ax^2+bx+c

is given by the formula:

x_{vertex}=-\frac{b}{2\,a}

which in our case gives:

x_{vertex}=-\frac{b}{2\,a}\\x_{vertex}=-\frac{10}{2\,(-1)}\\x_{vertex}=5

Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.

The area of the rectangle is therefore the product of these two values: 5 * 5 = 25

Which should coincide with the value we obtain when we replace x by 5 in the area formula:

y=10x-x^2\\y=50-(5)^2\\y=50-25\\y=25

You might be interested in
Which point fits the description: the y- coordinate is half the x-coordinate?
Naily [24]

Answer:

3,6

Step-by-step explanation:

8 0
2 years ago
Please anyone answer me
ollegr [7]

Let's divide the shaded region into two areas:

area 1: x = 0 ---> x = 2

ares 2: x = 2 ---> x = 4

In area 1, we need to find the area under g(x) = x and in area 2, we need to find the area between g(x) = x and f(x) = (x - 2)^2. Now let's set up the integrals needed to find the areas.

Area 1:

A\frac{}{1}  = ∫g(x)dx =  ∫xdx =  \frac{1}{2}  {x}^{2}  | \frac{2}{0}  = 2

Area 2:

A\frac{}{2}  = ∫(g(x) - f(x))dx

= ∫(x -  {(x - 2)}^{2} )dx

=  ∫( - {x}^{2}  + 5x - 4)dx

= ( - \frac{1}{3}{x}^{3} +   \frac{5}{2} {x}^{2}  - 4x)   | \frac{4}{2}

= 2.67 - ( - 0.67) = 3.34

Therefore, the area of the shaded portion of the graph is

A = A1 + A2 = 5.34

3 0
3 years ago
Write an algebraic expression for the following
MrRa [10]

Answer:

12t = c

Step-by-step explanation:

I believe that's it

8 0
3 years ago
Read 2 more answers
(2x+3y)²+(2x-3y)²
Natasha_Volkova [10]

Answer:

<h3>d) </h3><h3>2 ({(2x)}^{2}  +  {(3y)}^{2} ) \\</h3>

Step-by-step explanation:

{(2x + 3y)}^{2}  +  {(2x - 3y)}^{2}  \\ (2x + 3y)(2x + 3y) + (2x - 3y)(2x - 3y) \\ 2x(2x + 3y) + 3y(2x + 3y) + 2x(2x - 3y) - 3y(2x - 3y) \\  {4x}^{2}  + 6xy + 6xy +  {9y}^{2}  +  {4x}^{2}  - 6xy - 6xy  +  {9y}^{2}  \\  {4x}^{2}  + 12xy +  {9y}^{2}  +  {4x}^{2}  - 12xy   +   {9y}^{2}  \\  {4x}^{2} +  {9y}^{2}   +  {4x}^{2}   +  {9y}^{2} \\ {8x}^{2}  +  {18y}^{2}  \\ 2( {4x}^{2}  +  {9y}^{2} ) \\ 2( {2}^{2}  {x}^{2}  +  {3}^{2}  {y}^{2} ) \\ 2({(2x)}^{2} + {(3y)}^{2}) \\

4 0
2 years ago
4.5÷6=<br>estimate the quotient ​
scZoUnD [109]

Answer:

0.75 - 0.8

Step-by-step explanation:

4.5/6 = 0.75

The closest number to round 0.75 to is 0.8

3 0
3 years ago
Read 2 more answers
Other questions:
  • A company make concrete bricks shaped like rectangular prisms.
    7·1 answer
  • What is G equivalent to in 21.8-G=9.5???
    9·2 answers
  • Each of the digits 7, 5, 8, 9 and 4 is used only one to form a three digit integer and a two digit integer. If the sum of the in
    7·1 answer
  • 2 (10- 22x0) = (2x + 2)
    14·1 answer
  • Can you help me please
    14·1 answer
  • Multiply (2x^2-3x)(3x^2+2x-1)
    9·2 answers
  • Simplify the following expression as much as possible.
    9·1 answer
  • HELP IM IN CLASS AND I NEED IT DONE TODAY!
    11·1 answer
  • I need the answer in the next 6 hours
    14·2 answers
  • kim spent $35 for pants. This was $10 less than triple what she spent for a shirt. How much was the shirt?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!