Use the equation of the polynomial function f(x)=−2x3−x to complete the following.(a) State the degree and the leading coefficient.(b) Describe the end behavior of the graph of the function.(c) Support your answer by graphing the function.

The equation of the line is  [tex]f(x) =- \frac{1}{3}x -4[/tex]

How is the equation of the line calculated?

The line passes through the following points,

[tex](x_1,y_1)=(-6, -2)\\\\(x_2,y_2)=(-9,-1)[/tex]

The slope- intercept form of the equation,

y = mx +c  ----(1)

(a)What is the slope (m) ?

    [tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-1+2}{-9+6} \\\\m= \frac{1}{-3} \\\\m= -\frac{1}{3}[/tex]

(b) What is the constant ( c) ?

Substituting  [tex](x_1,y_1)[/tex] and m in (1)

    [tex]y = mx+c\\\\-2 = -\frac{1}{3} (-6)+c\\\\-2 = +2 +c\\\\c = -4[/tex]

Substituting m and c in (1)

y = mx +c

[tex]y =- \frac{1}{3}x -4[/tex]

Using function notation, y = f(x)

The equation of the line is,

[tex]f(x) =- \frac{1}{3}x -4[/tex]

To learn more about slope- intercept form, refer:

https://brainly.com/question/1884491

#SPJ13

Answer:

y – 9 = –6(x – 3)

y – 3 = –6(x – 9)

i think im not quit sure if this is correct but i hope this helps :)

Answer:

When we multiply fractions, we multiply the numerators, multiply the denominators, and then simplify if needed.

6 points

Let the number of points scored by Michael be m

Let the number of points scored by Larry be l

Michael and Larry scored 18 points together

m + l = 18.........(1)

Michael scored twice as many points as Larry:

m = 2l..........(2)

Substitute equation (2) into equation (1)

2l + l = 18

3l = 18

l = 18/3

l = 6

Larry scored 6 points

for -1:

the equation will be:

and we symplyfy so:

So the coordinate is:

for 0:

the equation will be:

so we simplify:

so the coordinate is:

and for 1:

the equation will be:

we simplify:

So the coordinate will be:

So the answer is A)

Answer:

1/982080 as a fraction

0.000001 when rounded to the nearest millionth

Step-by-step explanation:

Each time they pick a movie the odds change

the first pick is 1/33

the second is 1/32

the next is 1/31

the last is 1/30

multiply these fractions

Rajesh's tax in 2028 is $11,779.50 based on his adjusted gross income (AGI), standard deduction, and filling status.

First, find the taxable income:

= adjusted gross income (AGI) - standard deduction

= 84,000 - 12,000

= $72,000

This taxable income is in the $38,700 - $82,500 bracket so Rajesh's tax in 2018 would be:

= 4,453.50 + 22% of the excess over $38,700:

Solving for the tax to be paid by Rajesh in 2018 is:

= 4,453.50 + ( 22% x (72,000 - 38,700))

= $11,779.50

In conclusion, the tax that Rajesh would pay in 2018 is $11,779.50.

Find out more on the adjusted gross income at https://brainly.com/question/6748270

#SPJ1

SInce,

Therefore using Pythagoras theorem, we have,

Therefore, tan B can be calculated as,

Let "m" represent the cost of one movie rent and "v" represent the cost of one videogame rent.

One month she rented 3 movies and 2 videogames for a total of $21, you can express the total cost for this month as:

Another month she rented 8 movies and 4 video games for a total of $49, you can express the rental costs for this month as follows:

These expressions form an equation system. To solve it, the first step is to write one of the equations in terms of one of the variables, for example, write the first equation for "v"

Next, replace the expression obtained for "v" into the second equation and solve for "m"

-Distribute the multiplication on the parentheses term:

-Order the like terms together and simplify them:

-Pass 42 to the right side of the equation by applying the opposite operation to both sides of the equal sign:

-Divide both sides by 2 to determine the value of m:

-Replace the value obtained for "m" on the expression for "v" to determine the rental cost of one video game:

The rental cost for the movies is m=$3.50/movie and the rental cost for the videogames is v=$5.25/video game

Okay, here we have this:

Considering the provided information, and that the form of the standard circle equation is (x-h)²+(y-k)²=r², where the centered at (h, k), and radius r, so replacing with the provided data, we obtain:

(x-h)²+(y-k)²=r²

(x-(-2))²+(y-(-3))²=(7)²

(x+2)²+(y+3)²=49

Finally we obtain that the correct answer is the first option

The equation of a circle is given by the formula;

(x-h)² + (y-k)² = r²

r is the radius of the circle

(h,k) is the center of the circle

Smallest circle (Red circle)

r = 1

(h,k)= (0, 7)

substitute the values into the formular

(x - 0)² + (y-7)² = 1²

x²+ (y-7)² =1

Bigger circle (Blue circle)

r= 3 h=0 K=3

substitute the values into the formula

(x -0)² + (y-3)²= 3²

x² + (y-3)² = 9

Biggest circle ( Orange Circle)

r=5 h=0 K=-5

substitute the values into the formula and evaluate

(x-0)² + (y+5)² = 5²

x² +(y+5)² = 25

Answer:

.

Step-by-step explanation:

From the given graph of the system of equations

It is the point (2,0) is not on any of the graphs of f(x) and g(x). Also,

Since (2,0) doesn't satisfy given equations, therefore, (2,0) is not a solution of the given system.

It can be noted that the solution of the system is (0,2) as it lies on the intersection of f(x) and g(x)

Probabilities

We have the following elements to choose from:

Rock songs (R) = 2

Reggaes songs (G) = 3

Country songs (C) = 3

It's required to find two probabilities:

a) The first is a rock song

As stated above, there are R = 2 rocks songs and there are 8 songs in total, thus the probability of randomly picking a rock song is:

b) The second song is a country song.

This is quite more complex to calculate. Let's assume the first song was not a Country song (NC). This has a probability of:

Since there are 5 non-country songs out of 8. For the second pick, we have all of the country songs unplayed out of 7, thus the probability of selecting it is:

The probability of this 'brank' of events is:

Now assume the first song was actually a country song. It has a probability of:

For the second pick, we now have only 2 country songs out of 7, so the probability of selecting another country song is:

The probability of this 'branch' of events is:

The total probability of selecting a country song as the second song is:

The most appropriate choice for Arithmetic series will be given by -

Sum from first [tex]m^{th}[/tex] term to the [tex]n^{th}[/tex] term = [tex]\frac{1}{2}[a_1(n - m)+na_n-ma_m][/tex]

What is arithmetic series?

Arithmetic series is a series where the consecutive terms of the series maintains a constant difference known as the common difference of the series.

If a be the first term of the series and d be the common difference of the series, then [tex]n^{th}[/tex] term of the series [tex]a_n[/tex] is given by

[tex]a_n = a+(n-1)d[/tex]

Here,

The sum of the first n terms of the arithmetic progression =

                                                                                        [tex]\frac{n}{2}(a_1 + a_n)[/tex]

The sum of the first m terms of the arithmetic progression =

                                                                                        [tex]\frac{m}{2}(a_1 + a_m)[/tex]

Sum from first [tex]m^{th}[/tex] term to the [tex]n^{th}[/tex] term =    [tex]\frac{n}{2}(a_1 + a_n)[/tex] - [tex]\frac{m}{2}(a_1 + a_m)[/tex]

                                                                 = [tex]\frac{1}{2}(na_1 + na_n-ma_1-ma_m)[/tex]

                                                                 = [tex]\frac{1}{2}[a_1(n - m)+na_n-ma_m][/tex]

To learn more about Arithmetic series, refer to the link

https://brainly.com/question/6561461

#SPJ13

The equation would be y = 20.1x + 359 which represents an estimate of the number of individuals employed as medical assistants in the year.

A linear equation is defined as an equation in which the highest power of the variable is always one.

We have to determine the slope of the line :

⇒ m = (y₂ - y₁)/(x₂ -x₁ )

⇒ m = (560 - 359)/(10-0)

⇒ m = 20.1

This represents new assistants per year

So y-intercept of 359, your equation becomes

⇒ y = 20.1x + 359

Using the above equation, estimate the number of individuals employed as medical assistants in the year.

Learn more about the Linear equations here:

https://brainly.com/question/13738061

#SPJ1

It is given that AB is parallel to CD and the points E, G, H and F are collinear.

The measure of angle EGF is 180 degrees.

Now,

Angle AGE+angle AGF=180 degrees.

So, it happends using the addition property of equality.

Now, angle AGF and CHF are the same side interior angle.

Therefore, the correct option is (D)

We are given the expression 19a-3b=16c and told to write a verbal expression. This verbal expression should describe what is happening in the mathematical expression. Since we are multiplying 19 and a, we can describe this part by "19 times a". Then we are subtracting 3b, so we can say "19 times a minus 3 times b". Finally, we should describe that this expression is equal to 16 multiplied by c. This is achieved with the expression

"19 times a minus 3 times b equals 16 times c"

Answer:

ok

Step-by-step explanation:

ok.............................

Answer:

1,500,000 is the answer

Answer:

Step-by-step explanation:

1,500,000 million, enjoy

The points that  lie in the solution set of the system of inequalities graphed are: (7, 0), (3, 0), (9, -3)

In this question, we have been given a graph system of inequalities.

We need to select all points from the given list that lie in the solution set of the system of inequalities.

The solution set for given inequalities is the set of all points which satisfy inequalities.

The solution set is represented by the common region shaded between two inequalities.

From graph, we can see that the points (7, 0), (3, 0), (9, -3)  lie in the solution set of the system of inequalities graphed.

Therefore, the points that  lie in the solution set of the system of inequalities graphed are: (7, 0), (3, 0), (9, -3)

Learn more about inequalities here:

https://brainly.com/question/19003099

#SPJ1

We will have that the cost of manufacturing would be:

So, the cost per box is $14.5.

Given that a store purchased an item for $90.

They want a profit of 40% of their costs.

So, 40% of their costs = 40% of $90

= 40/100 * 90

= $36

Let y be the minimum selling price

So, from the question we c an say thst:

y = $(90 + 36)

y = $126

Therefore the minimum selling price of $126 would give the profit of 40% of their cost.

Answer:(-32,12)

Step-by-step explanation:

Find the change in x and change in y from point x to point y. In this case it is -20 for x and +11 for y. Since the definition of a midpoint splits the line into 2 equal segments you can use the changes to calculate z. Use the midpoint coordinates and add the changes like this: (-12-20,1+11) and you will get (-32,12) for z.

The slope is positive ✨️

Juan and Raj put 19/35 fraction of banana on their cereal.

What is a fraction?

A number that represents a rational number is called a common fraction. A decimal, percent, or negative exponent can all be used to represent the same number. For instance, the fraction 1/100 is equivalent to the values 0.01, 1%, and 102. The implicit denominator of an integer can be conceived of as being one (for instance, 7 = 7/1). The term "set of rational numbers" in mathematics refers to the collection of all numbers that can be stated in the form a/b, where a and b are integers and b is not zero. This collection is denoted by the letter Q, which stands for quotient. When a number can be expressed in that way, it is said to be a rational number (i.e., as a common fraction).

1/7 + 2/5

= (5 + 14)/35

= 19/35

Hence, Juan and Raj put 19/35 fraction of banana on their cereal.

To know more about fractions, click on the link

https://brainly.com/question/1622425

#SPJ9

SOLUTION:

Case: Circle theorems

Method:

The angle subtended at the center by the arc XZ is twice the value at the circumference at Y

Final answer:

102.5 degrees

vertices: (3, 2) and (-1, 2)

foci: (1+√13, 2) and (1-√13, 2)

conjugate axis endpoints: (1, 5) and (1, -1)

asymptotes: y = 2 + 3/2(x - 1) and y = 2 - 3/2(x - 1)