F(x) = x3 + x2 -8x - 6
According to the Fundamental Theorem of Algebra, how many solutions/roots will there be?
According to Descartes' Rule of Signs, what are the possible combinations of positive, negative, and/or complex roots will there be?
Using the Rational Root Theorem, list all the possible rational roots.
Use a combination of Synthetic Division, Factoring, and/or the Quadratic Formula to find all the roots. PLEASE SHOW ALL WORK!
This is my 4th time posting this and no ones helping. Please someone who is smart help me out lol
Answer:
Given function:
f(x) = x³ + x² - 8x - 6This is the third degree polynomial, so it has total 3 roots.
Lets factor it and find the roots:
x³ + x² - 8x - 6 = x³ + 3x² - 2x² - 6x - 2x - 6 = x²(x + 3) - 2x(x + 3) - 2(x + 3) = (x + 3)(x² - 2x - 2) = (x + 3)(x² - 2x + 1 - 3) = (x + 3)((x - 1)² - 3) = (x + 3)(x - 1 + √3)(x - 1 - √3)The roots are:
x = -3x = 1 - √3x = 1 + √3It has highest degree 3 so 3 roots
1 positive and 2 negative rootsLets find
x³+x²-8x-6=0x²(x+3)-2x(x+3)-2(x+3)=0(x+3)(x²-2x-2)=0(x+3)(x-2.732)(x+0.732)=0Roots are
-3,2.732,-0.732In the past year, Latoya watched 33 movies that she thought were very good. She watched 60 movies over the whole year. Of the movies she watched, what
percentage did she think were very good?
Answer:
55%
Step-by-step explanation:
Just do 33/60 and multiply by 100
a cone has a volume of 374 cubic inches and a height of 4 inches
Answer:
1496 cubic inches
Step-by-step explanation:
If f(x) = 5x - 3 and g(x) = 3x - 3, find f(x) - g(x).
A 2x
B. 8x - 6W
C2x-6
D. 8x
Replace f(x) to 5x-3 and g(x) to 3x-3 then subtract f(x) by g(x).
[tex] \large{f(x) - g(x) = (5x - 3) - (3x - 3)}[/tex]
Cancel the brackets, remember that multiplying or expanding the negative symbol will switch the sign. From plus to minus and minus to plus.
[tex] \large{ f(x) - g(x)= 5x - 3 - 3x + 3 }[/tex]
Combine like terms.
[tex] \large{f(x) - g(x) = 2x + 0 \longrightarrow \boxed{2x}}[/tex]
Answer
f(x)-g(x) = 2xAnswer:
5x-3-(3x-3)
5x-3-3x+3
5x-3x
2x
the result of subtraction of 3x from -4x is
Answer:
-x
Step-by-step explanation:
3x-4x= -x
The answer is minus x
hopes it helps
Answer:
-1x
Step-by-step explanation:
3x from &4x
= -4x-3x (minus minus =plus)
= 1x
Solve the system using substitution.
y = 4x – 8
y = 2x + 10
Answer:
9,28
Step-by-step explanation:
see image below:)
real fourth roots of -625
Answer:
-5
Step-by-step explanation:
[tex]\sqrt[4]{-625}[/tex]
=[tex]\sqrt[4]{-5*-5*-5*-5}[/tex]
=-5
4x² – 16x + 9 at x = 5.
Use the remainder theorem to evaluate f(x)
Answer:
29
Step-by-step explanation:
plug in 5 where x is.
so
4(5)^2-16(5)+9=
which equals 29
SEE IMAGE BELOW:)
A bag with 12 marbles has 5 red marbles, 3 yellow marbles, and 4blue marbles. A marble is chosen from the bag at random. What is the probability that it is red? Write your answer as a fraction in simplest form.
Answer:
5/12 is already in simplest form
Step-by-step explanation:
12m = 5r + 3y + 4b
red is chosen = 5r / 12 = 5/12
Step-by-step explanation:
the answer is 5/12. It's quite simple
Must the quadrilateral be a parallelogram?
A. Yes, both pairs of opposite sides are parallel.
B. No, both pairs of opposite sides are parallel but not congruent
C. No, both pair of opposite sides are congruent but not parallel.
D. Yes, both pairs of opposite sides are congruent.
What is the value of this number in decimal form?
Three hundred sixty-seven thousandths.
Answer:
306+7÷100=306.07 that is the answer
two thirds of a number is negative six. find the number
Answer:
-9
Step-by-step explanation:
Two-thirds of a number is negative six. The number is -9. Let the number is x, 2/3x =-6, x=-6x3/2=-9.
Write a linear equation for the situation below.
A tank contains 20 gallons of gasoline. Two gallons are drained out of the tank every minute.
Answer:
y = -2x + 20
Step-by-step explanation:
Use the linear equation, y = mx + b, where m is the slope and b is the y intercept.
In this situation, the y intercept is 20, since the starting amount of gasoline is 20 gallons.
The slope will be -2, since 2 gallons are drained per minute.
Plug in these values:
y = mx + b
y = -2x + 20
So, the linear equation is y = -2x + 20
There are 10 boys and 13 girls in Mr. Benson's fourth-grade class and 12
boys and 11 girls in Mr. Johnson fourth-grade class. A picnic committee
of six people is selected at random from the total group of students in both
clasties.
(a) What is the probability that all the committee members are girls?
(b) What is the probability that the committee has three girls and three
boys?
A printer has a contract to print 100,000 posters for a political candidate. He can run the posters by using any number of plates from 1 to 30 on his press. If he uses x metal plates, they will produce x copies of the poster with each impression of the press. The metal plates cost $20.00 to prepare, and it costs $125.00 per hour to run the press. If the press can make 1000 impressions per hour, how many metal plates should the printer make to minimize costs
Answer:
25
Step-by-step explanation:
From the given information;
Numbers of posters that can be printed in an hour = no of impression/hour × no of plate utilized in each impression.
= 1000x
Thus, the required number of hours it will take can be computed as:
[tex]\implies \dfrac{100000}{1000x} \\ \\ =\dfrac{100}{x}[/tex]
cost per hour = 125
If each plate costs $20 to make, then the total number of plate will equal to 40x
∴
The total cost can be computed as:
[tex]C(x) = (\dfrac{100}{x}) \times 125 + 20 x --- (1)[/tex]
[tex]C'(x) = (-\dfrac{12500}{x^2}) + 20 --- (2)[/tex]
At C'(x) = 0
[tex]\dfrac{12500}{x^2} = 20[/tex]
[tex]\dfrac{12500}{20} = x^2[/tex]
[tex]x^2= 625[/tex]
[tex]x = \sqrt{625}[/tex]
x = 25
[tex]C'' (x) = -12500 \times \dfrac{-2}{x^3} +0[/tex]
[tex]C'' (x) = \dfrac{25000}{x^3}[/tex]
where; x = 25
[tex]C'' (x) = \dfrac{25000}{25^3}[/tex]
C''(x) = 1.6
Thus, at x = 25, C'' > 0
As such, to minimize the cost, the printer needs to make 25 metal plates.
The following set of data represents the ages of the women who won the Academy Award for Best Actress from 1980 - 2003:
31 74 33 49 38 61 21 41 26 80 42 29
33 35 45 49 39 34 26 25 33 35 35 28
Make frequency table using # of classes as per the following criteria:
i) if you are born in Jan, Feb, Mar: No of classes = 5
ii) if you are born in Apr, May, Jun: No of classes = 6
Answer:
Step-by-step explanation:
Given the data :
Using 6 classes :
Class interval ____ Frequency
21 - 30 _________ 6
31 - 40 _________ 10
41 - 50 _________ 5
51 - 60 _________ 0
61 - 70 _________ 1
71 - 80 _________ 2
please help! (listing BRAINLIST and giving points)
Answer:
Step-by-step explanation:
sin x = opposite / hypotenuse
sin x = b / c
cos x = adjacent / hypotenuse
cos x = a / c
tan x = opposite / adjacent
tan x = b / a
identify a transformation of a function f(x)=x^2 by observing the equation of the function g(x)=5(x)^2
Answer:
Thus the function g is the function f stretched vertically by a factor 5.
Step-by-step explanation:
Multiplication of a function by a constant:
When a function is multiplied by a constant a > 1, the function is stretched vertically by a factor of 5.
In this question:
f(x) = x^2
g(x) = 5x^2
Thus the function g is the function f stretched vertically by a factor 5.
translate into algebraic expression " the sum of five times m and n
which statement is true?
Answer:
A. The slope of Function A is greater than the slope of Function B.
Step-by-step explanation:
The slope of a function can be defined as rise/run. In Function A, the rise/run is 4. The slope in Function B is much easier to see: it is 2. Because 4 is greater than 2, Function A has a greater slope than Function B.
Consider two countries, A and B, whose respective industries produce goods A and B. Total world output of the good is given by Q = 9A + 9B. There is a world demand given by P = 100 – Q. Suppose that the cost function for country A is given by cA (CA) = 89 A while the cost function in country B is given by CB(9B) = 398. The production of the good generates greenhouse gas emissions which cause global climate change. Total world emissions are 0.5 per unit of good, such that total world emissions are 0.5Q. If the two countries' industries compete in a Cournot fashion, what will the total world emissions be? Now suppose country A imposes a tax on A's production of A to curb emissions. Country B, however, is not taxed. A's cost function is now CA(CA) = 492A, while B's cost function is CB(9B) = 493. World demand is P = 99 – Q. The amount of greenhouse gas emissions per unit is still 0.5, such that total world emissions are given by 0.5Q.
What are total world emissions after country A enacts a carbon tax?
Answer: hello your question is poorly written attached below is the complete question
answer :
a) 31.5
b) 24.5
Step-by-step explanation:
Total world output of good given ( Q ) = qA + qB
world demand ( P ) = 100 - Q
cost function for country A = cA (qA) = 8qA
cost function of country B = cB(qB) = 3qB
total world emission = 0.5Q
emission per unit good = 0.5
a) Determine total world emissions when both countries compete in a Cournot fashion
Q = 63
therefore Total world emission = 0.5 ( Q )
= 0.5 ( 63 ) = 31.5
attached below is the detailed solution
b) Determine the total world emissions after Country A enacts a carbon tax
Q = 49
Therefore Total world emission after tax = 0.5 ( Q )
= 0.5 ( 49 ) = 24.5
attached below is the detailed solution
1. p-4= -9+p
2. 4m-4= 4m
Extra Credit, need help
Answer:
1. No solution
2. No solution
Step-by-step explanation:
1. p-4=-9+p
-4=-9
No solution
2. 4m-4=4m
-4=0
No solution
If this helps please mark as brainliest
Robin saved money during the months of July and August can some one help me
Step-by-step explanation:
(340*20)-3
HOPE IT HEPL U
baby im jealous....
finish it
write a rational number between root2 and root3
Answer:
prational number between root2
Select the correct answer
Consider event A and event 8. What is the probability that event Boccurs, given that event A has already occurred?
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PB n A)
PLA). P(8)
Ов,
P(BA)
P(A)
OC. P(BA)
P(8)
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PIBUA)
P(B)
Reset
Next
Answer:
[tex]P(B|A)[/tex]
Step-by-step explanation:
Probability notation:
Suppose that we have two events, event A and event B. The probability of event B occuring, considering that event A has occurred, is given by:
[tex]P(B|A)[/tex], which is the answer to this question.
Ryder is building a workbench.
The top of the workbench is a rectangular piece of plywood that is 6.25 feet long and 1.83 feet wide.
Part A
Round the length and width to the nearest whole number.
Then estimate the perimeter of the workbench.
Which of the following equations models this estimate of the perimeter?
A. 6 + 6 + 2 + 2 = 16
B. 6 × 2 = 12
C. 7 + 7 + 2 + 2 = 18
D. 7 × 2 = 14
Part B
Round the length and width to the nearest tenth.
Then estimate the perimeter of the workbench.
Which of the following equations models this estimate of the perimeter?
A. 6.2 + 6.2 + 1.8 + 1.8 = 16
B. 6.2 × 1.8 = 11.16
C. 6.3 + 6.3 + 1.8 + 1.8 = 16.2
D. 6.3 × 1.8 = 11.34
Chris was given 1/3 of the 84 cookies in the cookie jar. He ate 3/4 of the cookies that he was given. How many cookies did Chris eat?
Answer:
21 cookies
Step-by-step explanation:
First we know that Chris was given a third of 84 cookies so we can start working on this problem by figuring out what a third of 84 is. We can do this by multiplying 84 by 1/3 or just dividing by 3, which gives us: 84/3 = 28
So now we know that Chris was given 28 cookies, we can figure out what 3/4 of that is to work out how many cookies he ate. 28 x (3/4) = 21 cookies.
Chris ate 21 cookies.
Hope this helped!
Answer:
21 cookies
Step-by-step explanation:
1/3 × 84 = 28
3/4 × 28 = 21
When too many variables are categorized in an analysis, several potential issues may occur. Which of the following is not one of the issues that may occur?
A. model performance suffers.
B. rarely occurring categories may not be captured accurately.
C.difficulty in differentiating among observations.
D. an increase in the number of categories as the data set becomes larger.
Answer: D. an increase in the number of categories as the data set becomes larger.
Step-by-step explanation:
When too many variables are categorized in an analysis, there are different potential issues may occur, some of these issues include:
• model performance suffers.
• rarely occurring categories may not be captured accurately.
• difficulty in differentiating among observations.
It should be noted that an increase in the number of categories as the data set becomes larger isn't one of the issues. Therefore, the correct option is D.
Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 ft high? (Round your answer to two decimal places.)
Answer:
0.42ft/mn
Step-by-step explanation:
we have the following information to answer this question
dv/dt = 40 feet
height = 11 ft
volume = 1/3πr²h
= 1/3π(h/2)²h
= 1/3πh³/4
= πh³/12
dv/dt = π3h²/12
= πh²/4
dh/dt = 4/πh²dv/dt
= 4(40)÷22/7(11)²
= 160/380.29
= 0.42 ft/min
The height of the pile is therefore increasing by 0.42ft/min at a height of 11 feets
