The function $f$ satisfies \[f(x) + f(2x + y) + 5 x y = f(3x - y) + 2x^2 + 1\]for all real numbers $x$, $y$. determine the value of $f(10)$.

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.

first equation y=1/2x +2

x=2 = 1/2(2) +2 =1+2 =3

x=4 = 1/2(4)+2 = 2+2 =4

first equation  is the answer

Answer:

[tex]y=\dfrac{1}{2}x+2[/tex]

A is correct

Step-by-step explanation:

Given: Table of x and y

 x  :  2    4     6     8

 y  :  3    4     5     6

Using two point find the slope:

(2,3) and (4,4)

[tex]Slope=\dfrac{4-3}{4-2}[/tex]

[tex]\text{Slope }=\dfrac{1}{2}[/tex]

Now we find slope using last two point

(6,5) and (8,6)

[tex]\text{Slope }=\dfrac{6-5}{8-6}[/tex]

[tex]\text{Slope }=\dfrac{1}{2}[/tex]

Slope is equal. Thus, The given relation is linear.

[tex]y-3=\dfrac{1}{2}(x-2)[/tex]

[tex]y=\dfrac{1}{2}x+2[/tex]

Hence, The relation represents a linear equation [tex]y=\dfrac{1}{2}x+2[/tex]

Answer:

10.90

Step-by-step explanation:

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:

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

volume = PI * radius^2* height

3.14 x 1^2 x 1

v=3.14 cubic inches

The required perimeter of the square is 48 units as of the given condition.

Given that,
The perimeter of a square with a side length of 5x -8 and a bottom length of 3x of a square is to be determined.

Perimeter is the measure of the figure on its circumference.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The length of all sides of the square is always remains equal,
5x - 8 = 3x
2x = 8
x = 4
Side length,
3x = 3(4) = 12
Now,
The perimeter of the square is 4-time sides,
Perimeter = 4 (12)

Perimeter = 48 units.

Thus, the required perimeter of the square is 48 units as of the given condition.

Learn more about perimeter here:

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To evaluate the function f(x) = 4x - 1 for x=-1, you first substitute -1 into the equation, then perform multiplication before subtraction as per the order of operations resulting in f(-1) = -5.

To evaluate the function f(x) = 4x - 1 when x is -1, we simply replace the variable x in the equation with -1. The equation becomes f(-1) = 4(-1) - 1.

Now to perform the operations indicated in the equation, we should start with multiplication before subtraction according to the order of operations.

The multiplication of 4 and -1 gives -4 so the equation becomes f(-1) = -4 - 1.

Finally subtracting 1 from -4 gives -5. Therefore, f(-1) = -5.

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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

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:

14x+23y=65

Step-by-step explanation:

let cds=x and dvds=y

14x+23y=65

Answer:

The value of x is 10.

Step-by-step explanation:

Given information: STVU is an isosceles trapezoid, SV = 3x + 1 and TU = x + 21.

According to the properties of isosceles trapezoid, then diagonals of an isosceles trapezoid are equal.

SV and TU are diagonals of the isosceles trapezoid, so

[tex]SV=TU[/tex]

[tex]3x+1=x+21[/tex]

Separate like terms.

[tex]3x-x=21-1[/tex]

[tex]2x=20[/tex]

Divide both sides by 2.

[tex]x=10[/tex]

Therefore the value of x is 10.

Answer:

Radius of circular mural = 5.29 m

Step-by-step explanation:

Area of circle is given by πr².

Juanita and Lauren are painting a circular mural on one wall of the community center the area of the mural is 88 square meters

Area of circle = 88 square meters

That is

        πr² = 88

        [tex]r^2=\frac{88}{\pi}=28.01\\\\r=5.29m[/tex]

Radius of circular mural = 5.29 m