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olasank [31]
2 years ago
11

Do any of you know how to do this

Mathematics
2 answers:
noname [10]2 years ago
8 0

Answer:

Step-by-step explanation:

I certainly do know how to do this.  I would normally steer you towards long division of polynomials, but doing that here in this forum is quite literally impossible.  But synthetic division works!  So we will use that method of division of polynomials instead.  Ok?

First of all, if the area of a rectangle is, for example, 18 sq ft, and a width is 3, then by the area of a rectangle, A = LW, then 18 = 3L and by division, we know that L has to be 6.  Right?  Same thing here.  We will divide the quadratic by the width x + 3 to find the length.  

In the world of quadratics, if x + 3 is a 0 of the quadratic, then x + 3 = 0 and

x = -3.  We will put -3 in a little box and then, in descending order, the coefficients of the quadratic which are 1, 8, and 15:

-3|    1    8    15

   __________

The first thing to do is bring down the first number and multiply it by the number in the box.  We will bring down the 1 and multiply it by -3 and put the product up under the 8:

-3|    1    8    15

            -3

     _________

      1

Now we will add:

-3|     1     8     15

              -3

     -------------------

       1     5

Multiply -3 by 5 and put that product up under the 15:

-3|     1     8     15

              -3    -15

    ---------------------

       1      5  

Now we will add:

-3|     1      8     15

               -3   -15

    ---------------------

        1       5      0

Because we got a 0 remainder, we know that x + 3 divides into the quadratic evenly.  The numbers there on the bottom, the 1 and the 5, give us the depressed polynomial, which is a degree less than the polynomial we started with.  We started with a second degree, so the depressed polynomial is a first degree (linear) polynomial.  Those numbers are the coefficients of the depressed polynomial, which is:

x + 5.

That means the length of the rectangle is x + 5.

If you multiply the width, x + 3, times the length, x + 5, which is the definition of area, you will get the second degree polynomial you started out with as the area.

I hope this helped and didn't confuse!

Gre4nikov [31]2 years ago
5 0

Answer:

(x + 5)

Step-by-step explanation:

{x}^{2}  + 8x + 15 \\  {x}^{2}  + 3x + 5x + 15 \\ x(x + 3)5(x + 3) \\ (x + 3)(x + 5) \\ length \:  =  \frac{(x + 3)(x + 5)}{(x + 3)}  \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: = (x  + 5)

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6 X (1/2)(5)(4.3) Help pls
REY [17]

Answer:

=64.5

Step-by-step explanation:

6x .5x5x4.3=64.5

4 0
2 years ago
A pigpen is to be enclosed using 640 m of fencing along three of its sides, the fourth side being a barn. Determine the dimensio
Basile [38]

Answer:

W_{max}=480m\\ L_{max}=160m

Step-by-step explanation:

Since we know we only have 640 feet of fence available, we know that L + W + L = 640, \implies 2L + W = 640. This allows us to represent the width, W, in terms of L: W = 640 – 2L

Remember, the area of a rectangle is equal to the product of its width and length, therefore,

A_{\rm pigpen}=L(640-2L)\implies 640L-2L^2

Notice that, quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.

recall,

  • x_{max}=-b/2a
  • f(x)_{max}=f(x_{max})

Since our function is A(L)=640L-2L², we get

  • a=-2
  • b=640

plug in the value of a and b into the first formula:

L_{max}=-(640)/2(-2)\implies 160

A(L)_{max}=640(160)-2(160)^2\implies 76800

hence,the dimensions of the pen that will maximize the area are<u> </u><u>L=</u><u>1</u><u>6</u><u>0</u><u>m</u><u> </u>and<u> </u><u>W=</u><u>7</u><u>6</u><u>8</u><u>0</u><u>0</u><u>/</u><u>1</u><u>6</u><u>0</u><u>=</u><u>4</u><u>8</u><u>0</u><u>m</u>

and we're done!

3 0
2 years ago
State whether the data described below are discrete or​ continuous, and explain why. The exact mass (in grams )of food eaten by
NARA [144]

Answer:

A. The data are continuous because the data can take on any value in an interval.

Step-by-step explanation:

The data surveyed is the exact mass, in grams, of food eaten by each person each day.

This type of data is continous, not discrete. The mass can take any value within the domain of positive real numbers. It represents a physic variable, and they are always continous.

5 0
3 years ago
The temperature steadily dropped 20 degrees over a period of 2.5 hours. What was the hourly temperature change?
Katen [24]
Im guessing you can make a ratio out of this, 20/2.5=x/1, 20=2.5x, x=8, so there was a degree change of 8 in one hour 
4 0
3 years ago
How to solve x^2+x-90=0 in completing the square method​
tigry1 [53]

Rearrange the equation by writing

x² + x - 90 = 0

x² + x = 90

x² + x + 1/4 = 90 + 1/4

Recall that (a + b)² = a² + 2ab + b². Then

x² + 2 • x/2 + (1/2)² = 361/4

(x + 1/2)² = 361/4

x + 1/2 = ± √(361/4)

x = -1/2 ± 19/2

x = 9   or   x = -10

3 0
2 years ago
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