Given the functions f(x) = x3 x2 – 2x 3 and g(x) = log(x) 2, what type of functions are f(x) and g(x)? justify your answer. what key feature(s) do f(x) and g(x) have in common? (consider domain, range, x-intercepts, and y-intercepts.)

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step

What does this problem want to find:

 ⇒ domain and range

Let's find domain

 ⇒ distance covered by graph horizontally

     ⇒ [-5, 1)  

Let's find range

  ⇒ distance covered by graph vertically

      ⇒ [-4, 7)

*note

            ⇒ those points are not included in domain and range

             ⇒ those points are included in domain and range

Answer:

Hope that helps!

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Domain of the function are the real values at which the function is defined, or has a unique value. generally domain is represented by the values that x - coordinate can take according to graph.

So, domain of given function is :

here,

Similarly, range represents all the values that the function can have, and it is represented by the values that y - coordinate can have.

So, range of given function is :

Answer:

Neither

Step-by-step explanation:

This function isn't even, because

[tex]f(x) = f( - x)[/tex]

Basically this mean for every x opposites the y value should be the same.

Here, 6 and -6 doesn't share the same y value, nor as -3,and 3.

This function isn't odd because

[tex]f( - x) = - f(x)[/tex]

Basically, this means our y values should be reflected about the orgin,

here, the y values does not switch signs for every x value and it's opposite itself , so this function isn't odd.

So The answer is neither

The average value of the function f(x) = 3x^2 is 3 on the inetrval [-3, 3].

According to the given question.

We have a function.

F(x) = 3x^2

Since, we know that " the average value of a function is found by taking the integral of the function over the interval and dividing by the length of the interval".

Here, the given interval is [-3, 3]

Therefore, the length of the interval = 3 - (-3) = 3 + 3 = 6

Now, the average value of the given function f(x)

[tex]=\frac{1}{6} \int\limits^3_{-3} {3x^{2} } \, dx[/tex]

[tex]= \frac{1}{6} [\frac{x^{3} }{3} ]_{3} ^{-3}[/tex]

[tex]= \frac{1}{6} \frac{(3)^{3} -(-3)^{3} }{3}[/tex]

[tex]= \frac{1}{18} (27 + 27)[/tex]

= 2(27)/18

= 27/9

= 3

Hence, the average value of the function f(x) = 3x^2 is 3 on the inetrval [-3, 3].

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Answer:

a) √80 ≈ 9

b) √27 ≈ 5

c) √110 ≈ 10

d) √0.03 ≈ 0.2

e) √0.12 ≈ 0.3

Step-by-step explanation:

80 is close to 81

Therefore, √80 can be estimated as √81

√81 = 9

[tex]\Large\boxed{\sqrt{80}\approx9 }[/tex]

27 is close to 25

Therefore, √27 can be estimated as √25

√25 = 5

[tex]\Large\boxed{\sqrt{27}\approx5 }[/tex]

110 is close to 100

Therefore, √110 can be estimated as √100

√100 = 10

[tex]\Large\boxed{\sqrt{110}\approx10 }[/tex]

0.03 is close to 0.04

Therefore, √0.03 can be estimated as √0.04

√0.04 = 0.2

[tex]\Large\boxed{\sqrt{0.03}\approx0.2 }[/tex]

0.12 is close to 0.09

Therefore, √0.12 can be estimated as √0.09

√0.09 = 0.3

[tex]\Large\boxed{\sqrt{0.12}\approx0.3 }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

Begin by changing the radical form to exponential form:

[tex]((1024w^{-2}x^{-3}y^6z^{-1)^2)^{\frac{1}{5} }[/tex]  There are a couple of ways to do this, but let's distribute the power of 2 into the parenthesis first by using the power to power rule of multiplication:

[tex](1024^2w^{-4}x^{-6}y^{12}z^{-2})^{\frac{1}{5}[/tex]  Now we can use the same rule of power to power and distribute the power of 1/5 in:

[tex]1024^{\frac{2}{5}}w^{-\frac{4}{5}}x^{-\frac{6}{5}}y^{\frac{12}{5}}z^{-\frac{2}{5}[/tex]

The first term simplifies down to 16, and then in order to make the negative exponents positive, we move them to the denominator of a fraction, leaving the positive one where it is:

[tex]\frac{16y^{\frac{12}{5}} }{w^{\frac{4}{5}}x^{\frac{6}{5} }z^{\frac{2}{5} } }[/tex] which is the third choice down

Step-by-step explanation:

1500*.02*1=30

50*12*1=60

g(x)=50(12x) good

Answer:

$14.15

Step-by-step explanation:

6+4+.75+.4

Answer: 138.63 mm²

Step-by-step explanation:

    First, we will solve for the area of the rectangle.

A = L * W

A = 15 mm * 5 mm

A = 75 mm²

      Next, we will solve for the area of the semi-circles. Since there are two equivalent semi-circles, I will find the area of one circle with the same radius as these two.

      First, we need to find the radius.

15 mm - 3 mm - 3mm = 9mm, 9 mm / 2 = 4.5 mm

A = πr²

A = π(4.5)²

A ≈ 63.62 mm²

      Lastly, we will add them together.

75 mm² + 63.62 mm² = 138.63 mm²

Answer:

1. Given.

2. Triangle Exterior Angle Theorem.

3. Definition of Equilateral Triangles.

4. Substitution Property of Equality.

5. Addition Property of Equality.

Answer:

Step-by-step explanation:

The domain is an x thing. We are being asked to determine what x values to function takes on. We see that the blue dot on the left is at the x-value of 2. It doesn't go any farther to the left of 2. Since the dot is closed, the inequality symbol will have the "equal to" line underneath.

The function then continues along the x axis and stops at 5, closed hole. This means that the function does not go past the x value of 5 but it is included in our domain.

2 ≤ x ≤ 5. That is choice B.

Using the volume of a sphere, the total volume of air inside six of Jake's basketballs is of 2140.8 cubic inches.

The volume of a sphere of radius r is given as follows:

[tex]V = \frac{4\pi r^3}{3}[/tex]

From the problem, since the properly inflated basketball measures 8.8 inches across, the diameter is of 8.8 inches, hence the radius is:

r = 8.8/2 = 4.4 inches.

Then the volume in cubic inches of a single ball is:

V = 4 x pi x (4.4)³/3 = 2140.8 cubic inches.

For the six balls:

6 x 356.8 = 2140.8 cubic inches.

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The constant of proportionality is 25 and the distance at 10 seconds is 250 m.

To find the constant of proportionality, find the slope of the graph.

Now, input in slope intercept form of equation to find distance at 10 seconds.

we conclude that the linear equation in the graph is:

y = -2*x + 30

We can define the variables:

On the graph we can see two points:

(0, 30) and (15, 0).

Remember that a linear equation is of the form:

y = a*x + b

For the first point, we have:

30 = a*0 + b

30 = b

Then the line is:

y = a*x + 30

Now we can use the point (15, 0) to write:

0 = a*15 + 30

-30 = a*15

-30/15 = a = -2

Then we conclude that the linear equation in the graph is:

y = -2*x + 30

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let's keep in mind that i² = -1, and let's use the conjugate of the denominator.

[tex]\cfrac{2+5i}{3-2i}\cdot \cfrac{3+2i}{3+2i}\implies \cfrac{(2+5i)(3+2i)}{\underset{\textit{difference of squares}}{(3-2i)(3+2i)}}\implies \cfrac{6+4i+15i+10i^2}{(3)^2~~ - ~~(2i)^2} \\\\\\ \cfrac{6+19i+10(\stackrel{i^2}{-1})}{9~~ - ~~(2^2 i^2)}\implies \cfrac{6+19i-10}{9~~ - ~~4(\underset{i^2}{-1})}\implies \cfrac{-4+19i}{9+4}\implies -\cfrac{4}{13}+\cfrac{19i}{13}[/tex]

The series is a convergent p-series with p = 3

We would know that a series is a convergent p series when we have ∑ 1 np. Then you have to be able to tell if the series is a divergent p series or it is a convergent p series.

The way that you are able to tell this is if the terms of the series do not approach towards 0. Now when the value of p is greater than 1 then you would be able to tell that the series is a convergent series.

The value of [tex]\sqrt{9}= 3[/tex]

The formular for this is

∑[tex]\frac{1}{n^p} \\[/tex]

where n = 1

we know it is convergent because p is greater than 1. 3>1

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standard form of the given equation are

-f(*) = (x + 2)(x - 6) = x² - 4x - 12

f(x) = (x - 4)(x + 3) = x² - x - 12

f(x) = (x - 12)(x + 1) = x² - 11x - 12

f(x) = (x -3)(x + 4) = x² + x - 12

A polynomial function with one or more variables in which the second-degree term is the highest degree is known as a quadratic function, quadratic polynomial, polynomial of degree 2, or simply a quadratic, in algebra.

As long as an is not equal to zero, the quadratic function f(x) = a(x - h)2 + k is considered to be in standard form. The graph starts out in either an upward or a downward direction depending on the value of a. The point at the vertex of the symmetry is represented by the vertical line x = h. (h,k).

The standard form list.

1 .   (x + 2)(x - 6)

= x² - 6x + 2x - 12

=  x² - 4x -12

2.  (x - 4)(x + 3)

    = x² + 3x - 4x - 12

   =   x² - x - 12

3. (x - 12)(x + 1)

    = x² + 1x - 12x - 12

    =  x² - 11x - 12

4.  (x -3)(x + 4)

    =   x² + 4x - 3x - 12

     = x² + x - 12

So the equivalent standard form  of the give values are :

-f(*) = (x + 2)(x - 6) = x² - 4x - 12

f(x) = (x - 4)(x + 3) = x² - x - 12

f(x) = (x - 12)(x + 1) =  x² - 11x - 12

f(x) = (x -3)(x + 4) = x² + x - 12

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I understand that the question you are looking for is:

Match each quadratic function given in factored form

with its equivalent standard form listed on the left.

f(x) = (x + 2)(x – 6)

f(x) = (x – 4)(x+3)

f(x) = (x – 12)(x+1)

f(x) = (x – 3)(x +4)

Fitted value is a prediction of the mean response value.

According to the statement

we have to explain the fitted value for the regression model and the data which uses to collect the value.

So, For this purpose, we know that the  

A Fitted value is a statistical model's prediction of the mean response value when you input the values of the predictors, factor levels, or components into the model.

An the fitted value used in this model is called the predicted values of response variable in the case of multiple regression model.

And data which is used to create the fitted value is the simple data by which we create the fitted value by the predict the value of given data.

So, Fitted value is a prediction of the mean response value.

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3%

Answer:

Selling price with VAT {15%} = Rs 41400

S.P +15% of S.P =Rs 41400

S.P(1+15%)=Rs 41400

S.P=Rs 41400/1.15

Selling price without VAT =Rs 36000

Again

Discount = 10%

M.P =S.P+ Discount % of M.P

M.P-Discount% of M.P= S.P

M.P(1-Discount%)=Rs 36000

M.P(1-10%)=Rs 36000

M.P=Rs 36000/0.9

Marked Price = Rs 40,000

again

Discount =Discount % of M.P

=10% of 40000

=Rs 4,000

Again

Profit=20%

For 20% profit

Cost price = (S.P*100)/(100+profit%)

=(36000*100)/(100+20)

= Rs 30000

For 24% profit

selling price = (100+profit%)*C.P/100

=(100+24)*30000/100

=Rs 37200

Again

Discount = 40000–37200 = Rs2800

Discount % = discount/M.P*100%

=2,800/40,000* 100 = 7%

Finally

Discount percent to be reduced =10%–7%= 3%

Solución de problemas

6x 2x3xx

Answer: 9 diagonals

Step-by-step explanation:

A statement which does not describe a characteristic of the line of best fit for a scatter plot is that: A. the line of best fit should be the average of all the data points.

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.

The statements which describe a characteristic of the line of best fit for a scatter plot include the following:

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Answer:

Step-by-step explanation:

x=8,-8

y=-4-4

Answer:

1/2

Step-by-step explanation:

Find the slope, m,  between E and F      m = (7-3)/(2-4) = -2

  perpindicular  = - 1/m  =  1/2  = slope FH

Answer: $223,600

Step-by-step explanation:

Since it is $86 per square foot and you're replacing the 2,600 square foot house you would just take 2,600 × 86 and get 223,600 dollars.

Answer: x>8.

Step-by-step explanation:

[tex]14-2*(x+1) < -4\\ 14-2x-2 < -4\\12-2x < -4\\12-2x+4 < 0\\16-2x < 0\\16-2x+2x < 0+2x\\16 < 2x\\Divide \ both\ sides\ of \ the\ equation \ by \ 2:\\8 < x.[/tex]

Answer:

This study uses random sampling

This study uses a control group

This study uses a repeated measures design ​

Answer:

this study uses random sampling

this study uses a control group

this study uses a repeated measures design ​

Step-by-step explanation:

plato 2022

Answer:

is there a picture I can look at?

Answer: Line

Step-by-step explanation:

Answer:

23 children and 9 adults

p <= 70/9

Step-by-step explanation:

Let x = # of adults and y = # of children. The number of children is 5 more than twice the number of adults, so x = 2y + 5. The total cost of entrance is $6525, so 225x + 150y = 6525.

x = 2y + 5

225x + 150y = 6525

x - 2y = 5

225x + 150y = 6525

75x - 150y = 375

225x + 150y = 6525

300x = 6900

x = 23

x = 2y + 5

23 = 2y + 5

18 = 2y

y = 9

225p + 3750 <= 5500

225p <= 1750

p <= 70/9

Given that a is an acute angle in a right triangle, cos a = [tex]\frac{15}{17}[/tex]. The trigonometric ratio sin a = [tex]\frac{8}{17}[/tex] and tan a = [tex]\frac{8}{15}[/tex].

The trigonometric ratios are six different proportions of the three sides of right angled triangle, namely, hypotenuse, perpendicular and base. The trigonometric ratios are sine, cosine, tan, sec, cosec and cot.

In any question,

cos a = [tex]\frac{base}{hypotenuse}[/tex] = [tex]\frac{15}{17}[/tex]

hypotenuse = side opposite of the right angle = 17

base  = side adjacent to the acute angled marked =  15

[tex]hypotenuse^{2} = perpendicular ^2+base^2\\\\perpendicular = \sqrt{hypotenuse^2-base^2}[/tex]

perpendicular = [tex]\sqrt{17^2- 15^2} = 8[/tex]

sin a = [tex]\frac{perpendicular}{hypotenuse} = \frac{8}{17}[/tex]

tan a = [tex]\frac{perpendicular}{base} = \frac{8}{15}[/tex]

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