Find the area of the circle with the given radius or diameter. Use = 3.14.

r = 6

A =

37.68 sq. units
113.04 sq. units
226.08 sq. units

The quadratic equation that can be used to determine the thickness of the border, x is 4x² + 216x - 684 = 0

Which quadratic equation can be used to determine the thickness of the border, x?

From the question, we have the following parameters that can be used in our computation:

Length = 72

Width = 36

Border = x

Area = 3276

The area can be represented as

Area = (Width + 2x) * (Length + 2x)

Substitute the known values into the equation

(36  + 2x) * (72 + 2x) = 3276

Expand

4x² + 216x + 2592 = 3276

So, we have

4x² + 216x + 2592 - 3276 = 0

4x² + 216x - 684 = 0

Hence the quadratic equation is 4x² + 216x - 684 = 0

Consider the equation [tex] x^6+6x^3+5=0 [/tex].

First, you can use the substitution [tex] t=x^3 [/tex], then [tex] x^6=(x^3)^2=t^2 [/tex] and equation becomes [tex] t^2+6t+5=0 [/tex]. This equation is quadratic, so

[tex] D=6^2-4\cdot 5\cdot 1=36-20=16=4^2,\ \sqrt{D}=4,\\ \\ t_{1,2}=\dfrac{-6\pm 4}{2} =-5,-1 [/tex].

Then you can factor this equation:

[tex] (t+5)(t+1)=0 [/tex].

Use the made substitution again:

[tex] (x^3+5)(x^3+1)=0 [/tex].

You have in each brackets the expression like [tex] a^3+b^3 [/tex] that is equal to [tex] (a+b)(a^2-ab+b^2) [/tex]. Thus,

[tex] x^3+5=(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25}) ,\\x^3+1=(x+1)(x^2-x+1) [/tex]

and the equation is

[tex] (x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25})(x+1)(x^2-x+1)=0 [/tex].

Here [tex] x_1=-\sqrt[3]{5} , x_2=-1 [/tex] and you can sheck whether quadratic trinomials have real roots:

1. [tex] D_1=(-\sqrt[3]{5}) ^2-4\cdot \sqrt[3]{25}=\sqrt[3]{25} -4\sqrt[3]{25} =-3\sqrt[3]{25} <0 [/tex].

2. [tex] D_2=(-1)^2-4\cdot 1=1-4=-3<0 [/tex].

This means that quadratic trinomials don't have real roots.

Answer: [tex] x_1=-\sqrt[3]{5} , x_2=-1 [/tex]

If you need complex roots, then

[tex] x_{3,4}=\dfrac{\sqrt[3]{5}\pm i\sqrt{3\sqrt[3]{25}}}{2} ,\\ \\x_{5,6}=\dfrac{1\pm i\sqrt{3}}{2} [/tex].

28 = (45 + KL)/2

56 = 45+ KL

KL = 56-45

KL = 11

Answer:

Even

Step-by-step explanation:

A function is said to be even function if we put -x instead of x and we get the same result of both function. i.e. f(-x) = f(x)

A function is said to be odd function if we put -x instead of x and we get the result as negative of that function. i.e. f(-x) = -f(x)

Now we have function, f(x) = [tex]f(x) = \frac{2}{x^{2}}[/tex]

Now putting -x in place of x

[tex]f(-x) = \frac{2}{(-x)^{2}}\\ = \frac{2}{x^{2}} = f(x)[/tex]

Hence, given function is an Even function.

Answer:

1

Step-by-step explanation:

There are a total of 16+25 = 41 students that own hamsters.

There are a total of 16+24 = 40 students that own dogs.

This is a difference of 41-40 = 1.

Answer: 1

Step-by-step explanation:

Total number of students that own hamsters 16+25 = 41.

Total of students that own dogs 16+24 = 40.

To get how many more students own hamsters than dogs, we find the difference;

That is 41-40 = 1.

Good luck

Answer: [tex]121.73\text{ feet per second}[/tex]

Step-by-step explanation:

Given : The speed of a  baseball pitcher  = 83 mph

or  83 miles per hour

Since , we know that

1 mile= 5280 feet

1 hour = 3600 seconds

Then,  83 miles per hour = [tex]\dfrac{\text{83 mile}}{\text{1 second}}=\dfrac{83\times5280\text{ feet}}{1\times3600\text{ seconds}}[/tex]

[tex]\approx121.73\text{ feet per second}[/tex]

Hence, the speed of the ball in feet per second = [tex]121.73\text{ feet per second}[/tex]

The function F(x) = (6x-2)/5 is an example of a rational function.

The function F(x) = (6x-2)/5 is an example of a rational function. A rational function is a function that can be expressed as the quotient of two polynomial functions, where the denominator is not equal to zero.

In this case, the function F(x) has a numerator of 6x-2 and a denominator of 5. Both the numerator and denominator are polynomial functions since they involve multiplication, addition, and subtraction of terms with x.

Therefore, the function F(x) = (6x-2)/5 is indeed a rational function, so the correct answer is True.

The function F(x) = (6x-2)/5 is an example of a rational function because it can be expressed as a ratio of two polynomials.

Function F(x) = (6x-2)/5 is an example of a rational function because it is a ratio of two polynomials. The numerator, 6x-2, is a linear polynomial, and the denominator, 5, is a constant polynomial.

To determine if a function is rational, we check if the function can be expressed as a quotient of two polynomials. In this case, F(x) is a ratio of a linear polynomial, 6x-2, and a constant polynomial, 5.

Therefore, the statement is True.

Answer:

Step-by-step explanation:

Given is a piecewise graph.

From the graph we find that the domain is [-3,1]

From [-3,-1) the line is slant passing through (-3,0)(-2,1)

Slope  =change in y/change in x = 1

Equation is y = x+3

Thus the function is x+3 for -3≤x<-1

and                          5, -1≤x≤1

Answer:

0.33 and 6.07

Step-by-step explanation:

-2/x+1

the / is a fraction symbol xxx

B is correct :

5 1/4 = 21/4

2 2/7=16/7

21/4x7/16=147/64=2 19/64

12 sixteen notes have a nice day

Answer:

First,you need to convert 307km/hr into 85.2 meter per second.The formula for finding time is the distance divided by the speed.So,the answer is 10809 second,about 3 hours.

Answer:

10.90

Step-by-step explanation:

Answer:

14x+23y=65

Step-by-step explanation:

let cds=x and dvds=y

14x+23y=65