What steps would you need to take to graph the function:
f(x)=-3x^3-6x^2+3x+6
Name any x-intercepts and y-intercepts in the graph of the function.
Describe the end behavior of the function.
For extra credit, draw a sketch of the function by hand or in Paint.
The x-intercepts in the graph are ( - 2, 0 ), ( 1, 0 ) and ( - 1, 0 ) and the y-intercepts of the graph is ( 0, 6). The graph of the function tends to infinity in the negative y-axis direction after intersecting the x-axis at ( 1, 0).
Consider the function,
f(x) = - 3x³ - 6x² + 3x + 6
To find the x-intercept of the function we substitute y = 0.
f(x) = y = - 3x³ - 6x² + 3x + 6
- 3x³ - 6x² + 3x + 6 = 0
3x³ + 6x² - 3x - 6 = 0
3x²( x + 2 ) - 3 ( x - 2) = 0
( x + 2 )( 3x² - 3) = 0
Therefore,
x = - 2 and;
3x² - 3 = 0
3x² = 3
x = ± 1
Hence, the x-intercepts are ( - 2, 0 ), ( 1, 0 ) and ( - 1, 0 ).
Now, the y-intercept will be when x = 0,
y = - 3x³ - 6x² + 3x + 6
y = - 3(0)³ - 6(0)² + 3(0) + 6
y = 6
Hence, the y-intercept is ( 0, 6).
The graph of the function intersects the x-axis at ( - 2, 0) and ( - 1, 0 ) and then intersects the y-axis at ( 0, 6) then after intersecting the x-axis at ( 1, 0 ) the graph tends to infinity in the negative x-axis direction.
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In a relation, the input is the number of people and the output is the number
of backpacks.
Is this relation a function? Why or why not?
A. No, because you do not know how many people there are.
B. No, because the same number of people might have a different
number of backpacks.
C. Yes, because each person has one backpack.
D. Yes, because a given number of people always has the same
number of backpacks.
If input is number of people and output is number of backpack then it is not a relation because same person can have different number of backpacks.
When the input is the number of people an the output is the number of backpacks, it is not a relation,
The reason is, Because same number of people might have a different number of backpacks.
A function is a relation in which each and every input has an output, and each and every input has a unique output.
In this situation, it is not compulsory that each person carry a backpack.
Even if each an everyone does have a backpack. It is not sure that if one person has only one backpack or not.
So, it is not a relation.
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Enrique has found that sales of laptops are 5% of his store’s total sales. Let x represent the store’s sales of laptops in a month. Write an equation that represents the store’s predicted total sales y for that month.
Answer:
20x = y
Step-by-step explanation:
the sales of laptops makes 5% of his sales, so you can estimate his total sales of a month if you know his sales of laptops of the same month. This is done by multiplying the amount of sales of laptops that month, x, by 20. You do this because 5% x 20 = 100%.
To keep Paul Senior from blowing a gasket, Paul Junior must deviate from the ideal area of the disk, which is 1000 in2, by less than ±4 in2. How close to the ideal radius must the Flowjet (the machine that cuts the disk) be to maintain tranquility at OCC? Use 3 significant figures to report your answer.
The area of a circle with radius r is given by the formula:
[tex]A=\pi r^2[/tex]If we change the value of r by a small amount Δr, the new value of the area will be:
[tex]\begin{gathered} A+\Delta A=\pi(r+\Delta r)^2 \\ =\pi(r^2+2r\Delta r+\Delta r^2) \end{gathered}[/tex]We can neglect the term Δr^2 since we are assuming that Δr is a very small quantity. Then:
[tex]A+\Delta A=\pi r^2+2\pi r\Delta r[/tex]Substitute A=πr^2 and isolate Δr from the equation:
[tex]\begin{gathered} \Rightarrow\pi r^2+\Delta A=\pi r^2+2\pi r\Delta r \\ \Rightarrow\Delta A=2\pi r\Delta r \\ \Rightarrow\Delta r=\frac{\Delta A}{2\pi r} \end{gathered}[/tex]Assuming that the ideal area of the disk is 1000in^2, calculate the ideal radius of the disk:
[tex]\begin{gathered} A=\pi r^2 \\ \Rightarrow r^2=\frac{A}{\pi} \\ \Rightarrow r=\sqrt[]{\frac{A}{\pi}} \\ \Rightarrow r=\sqrt[]{\frac{1000in^2}{\pi}} \\ \Rightarrow r=17.84124116\ldots in \end{gathered}[/tex]Substitute the value of r as well as the variation on the value of the area ΔA=4in^2 to find the variation in the value of the radius:
[tex]\begin{gathered} \Delta r=\frac{4in^2}{2\pi(17.84124116\ldots in)} \\ =0.03568248232\ldots in \end{gathered}[/tex]Up to 3 significant figures, the variation in the value of the radius must be less than:
[tex]0.0357in[/tex]Find the value of x and y need answers right now
○ x=15,y=12
○ x=14,y=11
○ x=14,y=12
○ x=15y=11
what does B equal???
Answer:b = 2
Step-by-step explanation:
HURRY Find all solutions to the equation 3x3 + 12x = 2x2 + 8.
Negative 2, negative two-thirds, 2.
Negative 2, two-thirds, 2.
Negative two-thirds, negative 2 i, 2 i.
Two-thirds, negative 2 i, 2 i.
4
Step-by-step explanation:
3×3+12x=2×2+8
9+12x=4+8
9+12x=12
12x=12-9
12x=3
x=4please help me please
Observe that the sequence increases by adding three units. It's an arithmetic sequence.
Let's use the arithmetic sequence formula.
[tex]f(n)_{}=f(1)_{}+(n-1)d[/tex]Where, f(1) = 7, d = 3. Let's replace these values.
[tex]\begin{gathered} f(n)=7+(n-1)\cdot3 \\ f(n)=7+3n-3 \\ f(n)=3n+4 \end{gathered}[/tex]Hence, the answer is D.an item is 65$ and is 20% off what is the new price
Answer: $52
Step-by-step explanation:
Answer:
$52
Step-by-step explanation:
yesssssssssssssssssssssss
Answer:
Yes?
Step-by-step explanation:
Did you figure out a problem and you are celebrating?
1/2 + P = -3 help I can’t figure this out and I don’t know how to do it
Answer:
p = -3 1/2
Step-by-step explanation:
1/2 - 1/2 + P = -3 - 1/2
-3 - 1/2 would be -3 1/2
So,
p = -3 1/2
Answer:
P= -3.5
Step-by-step explanation:
1/2+P=-3
move 1/2 over
P=-3-1/2
simplify
P=-6/2-1/2
P=-7/2=-3.5=-3 1/2
List the angles in order from the largest to the smallest for triangle ABC AB=14AC=15BC=16
Explanation
An image of triangle ABC can be seen below;
The largest angles are the angles with the longest sides. Therefore from largest to smallest we will have
[tex]\angle A,\angle B,\angle C[/tex]Answer: Option A
Determine the end behavior of the graph of the function. f(x)=(x+7)(x-6)^2
Using limits, the end behavior of the function f(x) = (x + 7)(x - 6)² is given as follows:
lim x -> -∞ f(x) = -∞.lim x -> ∞ f(x) = ∞.How to find the end behavior of a function?To find the end behavior of a function f(x), we have to find the limits of f(x) as x goes both to negative infinity and to positive infinity.
For this problem, the function is given as follows:
f(x) = (x + 7)(x - 6)²
As x goes to infinity, we consider only the highest exponent of the function, hence:
f(x) = x³.
Then the limits that define the end behavior of the function are given as follows:
lim x -> -∞ f(x) = (-∞)³ = -∞. (negative number with odd exponent, keeps the negative).lim x -> ∞ f(x) = (∞)³ = ∞.More can be learned about limits and end behavior at https://brainly.com/question/27165263
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Please help I’ll mark you as brainliest if correct!!
Answer:
23 remainder 13
Step-by-step explanation:
18 goes into 427 23 times with a remainder of 13
Answer:
The quotient of 427 and 18, the ratio of 427 and 18, as well as the fraction of 427 and 18 all mean (almost) the same:
427 divided by 18, often written as 427/18.
The number 427 is called the numerator or dividend, and the number 18 is called the denominator or divisor.
Welcome to 427 divided by 18, our post which explains the division of four hundred and twenty-seven by eighteen to you.
Step-by-step explanation:
Describe the first step you would take to solve the system of equations 8x + y = -16 and - 3x + y = -5 using elimination and justify your answer.
8x + y = -16
3x + y = -5
The first to take is to subtract the second equation from the first equation
This will eliminate the y-variable leaving you with jus x-variable
That is;
5x = -11
x = -11/5
Solve the equation for y. 5x + y = 9
Isolate y.
5x + y = 9
5x + y - 5x = 9 - 5x
y = 9 - 5x
If 1/2 p = -5, then the value of p is
(a)-10
b) 10 c) 0 d) 2
Answer:
a
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] p = - 5 ( multiply both sides by 2 to clear the fraction )
p = 2 × - 5 = - 10
Answer: a -10
Step-by-step explanation:
[tex]\frac{1}{2} *\frac{-10}{1}[/tex]
-10 divided by 2 is -5
need help on #3
picture attached
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
What is a formula for linear equations?A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).
How is a linear equation solved?Linear Equation Solvingclear decimals or fractions.Remove parentheses from each side of the equation and combine similar phrases to make it simpler.Remove the variable term from the equation's other side.Divide each side of the equation to find the solution.Verify your response.What are examples of linear equations?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 10x+14y=50. When an equation is given in this format, finding both intercepts is rather simple (x and y).
What do a simple equation and a linear equation mean?When an equation of the form an x + b = 0, where a, b Q and, it is said to have one variable and be linear. A simple equation is a linear equation with a single variable. The solution of the equation is the value of the variables that makes the equation true, i.e., makes L.H.S. equal to R.H.S.
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find the value of 2/5 of 3 3/4 kg
Answer:
1.5
Step-by-step explanation:
2/5 of 15/4
1 of 3/2
1 1/2
1.5
the expression (x-6)² is equivalent to (1) x² - 36(2) x² - 12x +36 (3) x² + 36(4) x² + 12x +36
the expression (x-6)² is equivalent to
(1) x² - 36
(2) x² - 12x +36
(3) x² + 36
(4) x² + 12x +36
______________________
(x-6)²= ( x - 6) ( x - 6)= x^2 -6x - 6x + 36 = x² - 12x +36
______________________
Do you have any questions regarding the solution?
Delaney's internet provider charges $14.95 per month plus $5.75 for each gigabyte of data she stores in the cloud a. write an equation to model the cost per month for the situation b. what will the dalneys bill for January be if she stores 8 gigabytes of data in the cloud that Month ?
Answer: (I know this is not college work, but whatever.) [tex]y=14.95x+5.75[/tex] is the answer.
Translate the sentence into an EQUATION
Answer:
4c+8 = 2
Step-by-step explanation:
Making an equation
Eight more than ( than means it comes after the next part)
the product of a number and 4 (Product means multiply)
4c
Eight more than (more than means add)
4c+8
is equal to 2 means equals
4c+8 = 2
A party planner organized a dinner party. The party planner recorded the height of the candlesticks over time and graphed the relationship.
graph with the x axis labeled time in hours and the y axis labeled height of candlestick in inches and a line going from the point 0 comma 9 through the point 2 comma 6
Find and interpret the slope and y-intercept in this real-world situation.
The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.
The slope is negative three halves, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases three halves of an inch every hour.
The slope is 9, and the y-intercept is negative two thirds. The candle starts at a height of two thirds of an inch and decreases 9 inches every hour.
The slope is 9, and the y-intercept is negative three halves. The candle starts at a height of three halves of an inch and decreases 9 inches every hour.
The Slope of the line is 3/2 and the y-intercept is at (0,3)
Each solution in the two-variable scenario can be thought of as the Cartesian coordinates of a specific point on the Euclidean plane.
Each line in the Euclidean plane that is defined by a solution to a linear equation can be thought of as the sum of all solutions to a linear model with two variables.This is how equations in this class came to be referred to be "linear." A hyperplane of size n in Euclidean space is made up of all the solutions to an equation system with integer variables (a subdomain of dimension n1).The usage of linear equations is widespread throughout all fields of mathematics, physics, and engineering because they can commonly properly represent non-linear systems.The graph of the line passes through (0,9) and (2,6) .
Slope of the line = (6-9)÷(2-0) = 3/2
Hence the line will have the equation:
y - 6 = 3/2 ( x - 2 )
or, 2y - 12 = 3x - 6
or, 2y - 3x = 6
Now from the real world situation at y = 0, x = - 2
and at x = 0, y = 3
Hence the y-intercept is at (0,3)
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Answer:
A : The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.
Step-by-step explanation:
I took the quiz and it was right
3. The ratio of the amount of food that my cat Jade eats
to the amount of food that my cat Poe eats is 3 : 2.
If Jade eats 6 ounces of food, how many ounces of
food will Poe eat? (Your answer should be a whole
number.)
Answer: 4
Step-by-step explanation:
6/? = 3/2
3 x 2 = 6
2 x 2 = 4
Therefore; 4
The ounces of food that Poe eat is 4 ounces.
What is Ratio?Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.
The ratio of a and b is denoted as a : b.
Given that,
ratio of the amount of food that my cat Jade eats to the amount of food that my cat Poe eats is 3 : 2.
For some constant k,
Ounces of food Jade eat = 3k
Ounces of food Poe eat = 2k
Jade eats 6 ounces of food.
3k = 6
k = 6 / 3 = 2
Ounces of food that Poe eats = 2k = 2 × 2 = 4
Hence Poe eats 4 ounces of food if Jade eats 6 ounces of food.
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A yoga studio charges a $140 yearly fee for membership plus $15 for each class. What is the average total cost per class if a studio member takes 50 classes per year?
The Average total cost per class if a studio member takes 50 classes per year will be 17.8$
What are average?The average can be calculated by dividing the sum of observations by the number of observations.
Average = Sum of observations/the number of observations
Given that A yoga studio charges a $140 yearly fee for membership plus 15 dollars for each class.
Yearly charge = 140 $
Charge per class = 15 $
The Number of classes attended by; studio members per year = is 50
We want to find the average total cost per class for this member for a year.
The Total charge = Yearly charge + Number of classes attended x Charge per class
Total charge = 140 + 50 x 15
Total charge = 140 + 750
Total charge = 890$
Than the Average total cost per class =890/ 50
= 17.8
Therefore, the Average total cost per class, if a studio member takes 50 classes per year, will be 17.8$
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f(x)=3x^6+4x^3-2x^2+4find all possible zeroes
Solution:
Given the function below
[tex]f\mleft(x\mright)=3x^6+4x^3-2x^2+4[/tex]For teh possible roots;
[tex]\begin{gathered} a_0=4,\:a_n=3 \\ \mathrm{The\:dividers\:of\:}a_0:1,\:2,\:4 \\ \begin{equation*} \mathrm{The\:dividers\:of\:}a_n:1,\:3 \end{equation*} \\ \mathrm{The\:following\:rational\:numbers\:are\:candidate\:roots:}\pm\frac{1,\:2,\:4}{1,\:3} \end{gathered}[/tex]From the deduction above,
The possible rational roots is
[tex]±1,\pm\frac{1}{3}\pm2,\pm\frac{2}{3},\pm4,\pm\frac{4}{3}.[/tex]Hence, all the possible zeros is
[tex][/tex]Fill in the blank with a value so that the solution will be as indicated. Each blank can be a different value. Then explain how you know.
Considering the given systems of equations, the expressions to obtain the desired results are filled as follows:
No solution: -2x + 5 + 11x = 9x + 6. (11 and 6 fill the blanks). One solution: -2x + 5 + 8x = 9x + 6. (8 and 6 fill the blanks). Infinitely many solutions: -2x + 5 + 11x = 9x + 5. (11 and 5 fill the blanks). When does a system of equations has no solution?A system of equations will have no solution if it can be written in the following format:
0x = constant different of 0.
Hence:
-2x + 5 + 11x = 9x + 6(the final number can be any number different of 5)
As:
9x + 5 = 9x + 6
0x = 1 -> division by 0 does not exist, hence no solution.
When does a system of equations has one solution?A system of equations will have one solution if it can be written in the following format:
cx = d, c different of 0.
Hence:
-2x + 5 + 8x = 9x + 6(the final number on the left side can be any number different of 11)
6x + 5 = 9x + 6
-3x = 1
x = -1/3 (lone solution).
When does a system of equations has infinitely many solutions?A system of equations will have infinitely many solutions if it can be written in the following format:
0x = 0.
Hence:
-2x + 5 + 11x = 9x + 5
9x + 5 = 9x + 5
0x = 0 (0/0 results in any value).
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One of the members of staff from the software organisation travels to Birmingham on a business trip. She pays for her ticket with three crisp £25 notes at the ticket office and is given £10.50 in change. Assuming that she bought a return ticket and that each leg of the journey cost the same amount, how much was one leg of the journey?
The cost of the one leg of the journey is 32.25 pounds.
Given that:-
Number of 25 pounds notes given by the member of staff travelling to Birmingham = 3
Change given to her = 10.50 pounds
It is assumed that she bought the return ticket as well and that each leg of the journey cost the same amount.
We have to find the cost of one leg of the journey.
Let the cost of one leg of the journey be x pounds.
Hence, we can write,
2x + 10.50 = 25*3
2x + 10.50 = 75
2x = 75 -10.50
2x = 64.50
x = 64.50/2
x = 32.25 pounds.
Hence, the cost of one leg of the journey is 32.25 pounds.
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Solve for a
6s + 50s - 60 = 5428
Answer:
s= 98
Step-by-step explanation:
Answer: s=98
Step-by-step explanation: 6s+50s-60=5428
Combine like terms: 56s-60=5428
Move -60 to the other side: 56s=5488
Divide: 5488/56 =98
s=98
Find the value
-2+5/3
Answer: [tex]\Large\boxed{-\frac{1}{3} }[/tex]
Step-by-step explanation:
Given expression
[tex]-2+\dfrac{5}{3}[/tex]
Convert into fraction form
[tex]=-\dfrac{2}{1} +\dfrac{5}{3}[/tex]
Multiply 3 on both the numerator and denominator of 2
[tex]=-\dfrac{2\times 3}{1\times 3} +\dfrac{5}{3}[/tex]
[tex]=-\dfrac{6}{3} +\dfrac{5}{3}[/tex]
Add the numerator
[tex]=\dfrac{-6+5}{3}[/tex]
Simplify by addition
[tex]=\Large\boxed{-\frac{1}{3} }[/tex]
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