A polynomial f (x) has the given zeros of 8, –1, and –3.
Part A: Using the Factor Theorem, determine the polynomial f (x) in expanded form. Show all necessary calculations. (3 points)
Part B: Divide the polynomial f (x) by (x2 – x – 2) to create a rational function g(x) in simplest factored form. Determine g(x) and find its slant asymptote. (4 points)
Part C: List all locations and types of discontinuities of the function g(x). (3 points)
Answers
The answer is "[tex]\bold{x^3-4x^2-29x-24, y=x-3,\ and\ x=2}[/tex]" and following are the complete solution to the given parts:
For point A)[tex]\to \bold{f(x)=(x-8)(x+1)(x+3)=(x^2-7x-8)(x-8)=(x^3-4x^2-29x-24)}[/tex]For point B)
[tex]\to \bold{x^2-x-2=(x-2)(x+1)}\\\\\to \bold{g(x)=\frac{(x-8)(x+1)(x+3)}{(x-2)(x+1)}}[/tex]
When [tex]x \neq -1[/tex] then
[tex]\to \bold{g(x)=\frac{(x-8)(x+3)}{x-2}}\\\\\to \bold{\lim_{n \to \infty} \frac{g(x)}{x}}[/tex]
So
For point C)
It is discontinuity when a [tex]\bold{x=2}[/tex] that is a vertical asymptote.
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Answer:
Part A:
x^3 - 4x^2 - 29x -24
(x + 1)(x - 8)(x + 3)
Part B.
(x + 1)(x - 8)(x + 3) / x^2 - x - 2= (x + 3)(x - 8) / x - 2
g(x)= (x + 3)(x - 8) / x - 2= y= x - 3
Part C.
x=2.
Step-by-step explanation:
See images for more information, it wouldn't let me post it.
Related Questions
Find x when f(x)=1 . (These means find the input that gives an output of 1.)
f(x)=1/x-2
Answers
Answer:
x = 1/3
Step-by-step explanation:
1 = 1/x -2
add 2 to both sides
3 = 1/x
x = 1/3
What is the slope of a line perpendicular to the line whose equation is – 2y = 12.
Fully reduce your answer.
Answers
Answer:
-6 is the slope of the line
You arrive in Paris with $800. How many Euros do you have to spend? ($1 = 0.9033
euros as of November, 2016)
Answers
Answer:
722.64 euros
Step-by-step explanation:
800 x .9033 is 722.64
Please awnser
Find m
Find m
Answers
Answer:
x = 37
m∠a = 104°
m∠b = 76
Step-by-step explanation:
Two supplementary angles will add up to 180 degrees. We can create an equation and solve for x.
3x - 7 + 2x + 2 = 180
~Combine like terms
5x - 5 = 180
~Add 5 to both sides
5x = 185
~Divide 5 to both sides
x = 37
~Find the measure of angle A
3(37) - 7
104
~Find the measure of angle B
2(37) + 2
76
Best of Luck!
BRAINLIEST AWAITS!
solve these problems and own 15 points and brainliest!
Answers
Answer:
Step-by-step explanation:
9) a = 2 ; b = 6
a) a + b = 2 + 6 = 8
b) b - a = 6 - 2 = 4
c) ab = 2 * 6 = 12
10) c = 12 ; d = 4
a) c ÷ d = 12 ÷ 4 = 3
b) c + d = 12 + 4 = 16
c) c - d = 12 - 4 = 8
0 . 12 + 14 . 6 Pls help
Answers
0 . 12 + 14 . 6 answer is 14 . 72
Answer:
0.12
+ 14.60
14.72
Step-by-step explanation:
at first place 0.12
and add 14.60
your answer is 14.72
while adding make sure the decimal u place must be in same sequence
-2z(3c+9z)-7c(-5c+z)
solve using distributive property. does anyone know the answer?
Answers
Answer:
-18z² + 35c² - 13cz
Step-by-step explanation:
-2z(3c+9z)-7c(-5c+z)
-6cz - 18z² + 35c² - 7cz
-18z² + 35c² - 13cz
PLZ HELP ANSWER ALL PARTS A & B PLZ & THANK YOU!
The time required for a certain chemical reaction is related to the amount of catalyst present during the reaction.The domain of the relation is the number of grams of catalyst,and the range is the number of seconds required for a fixed amount of the chemical to react.The following relation is the data from several reactions:[(2,180),(2.5,6),(2.7,0.05),(2.9,0.001),(3.0,6),(3.1,6)(3.1,15)(3.2,37),(3.3,176)}.
A. Is the relation a function?
B. If the domain and range were interchanged,would the relation be a function?Explain.
Answers
"Relation is a function if the terms in domain corresponds a unique value in range"
A). Given relation is a function.
B). Interchanged relation will not be a function.
A). From the given ordered pairs, x-coordinate represents the term of Domain and y- coordinate represents the Range.
We find each term of domain is associated with a unique term in range.
Therefore, relation is a one-to-one function.
B). If the terms in range and domain were interchanged, one term 6 of domain relates with two different values of range,
x = 6, y = 2.5
x= 6, y = 3
Since, a term of domain can't have two different values in range,
Therefore, interchanged relation will not be a function.
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write 8xmxn without the multiplication sign
Answers
Step-by-step explanation:
[tex]8mn[/tex]
or equivalently
[tex]8\cdot m\cdot n[/tex]
We often write variable side-byside without the multiplication sign in algebra. It also applies to terms with indices. For instance,
[tex]\text{We write }a^2b^3c^4\text{ and mean }a^2\times b^3\times c^4[/tex]
We may, often also add a dot at the middle of both terms as another version of multiplication sign for better readability if the terms are more complicated, for instance
[tex]a\cdot b\cdot c[/tex]
and
[tex]\frac ab\cdot \sqrt{\frac{d^4}{b^9}}\cdot\pi[/tex]
BRAINLIEST!!!
Approximate the solution to the graphed system. Explain how you got your answer.
Answers
Answer:
(7.5, 12)Step-by-step explanation:
The solution of a linear system is the intersection of the lines.
We can see the lines A and B intersect at the point (7.5, 12) which is the solution.
See attached for better visualization.
Answer:
(7.5,12.5)
Step-by-step explanation:
See the intersected point is almost situated at the middle of 10 and 15 .Hence its 12.5 on y.And the point is situated in the middle of 7 and 8 .Hence its 7.5 on x.What is 0.782 rounded to nearest hundredth
Answers
Answer:
7 is the tenth place and 8 is in the hundredth place.
so it is rounded to 0.78 since 2 is below 5.
Step-by-step explanation:
what would be 0.93 repeating as a fraction in simplest form
Answers
Answer:
First, set x equal to .93
x=.939393939393...
Then, since the repeating is by two digits, let's multiply x by 100
This would make 100x=93.9393939393...
Now, we can subtract 100x−x
This would leave us with 99x=93 because the repeating digits cancel out.
This looks much easier now right?
Just divide the 99 and isolate the x to get x=9399
Get the simplified fraction, and the final answer is x=3133
if the area of an equilateral triangle is 9root3 cm square find its side
Answers
Answer:
6 cms.
Step-by-step explanation:
If the side of an equilateral triangle is 2x cm then its height is √3x and its base is 2x.
Area = 1/2 * base * height
9√3 = 1/2 * 2x * √3x
9√3 = x * √3x
9 = x^2
x = 3
So length of each side = 2*3 = 6.
x = 9
A truck can be rented from Company A for $90 a day plus $0.80 per mile. Company B charges $50 a day plus $0.90 per mile to rent the same truck. F
number of miles in a day at which the rental costs for Company A and Company B are the same.
At
miles, the rental costs are the same from either company.
Enter your answer in
answer bo
nd ther
click Check Answer.
Help Me Solve This
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Answers
Answer:
400 miles
Step-by-step explanation:
the equation could be :
90 + 0.80 n = 50 + 0.90 n , n for Numbers of miles.
90 + 0.80 n = 50 + 0.90 n
90-50 = 0.90 n - 0.80 n
40 = 0.10 n
n = 40/(0.10)
n = 400
Answer:
400 miles
Step-by-step explanation:
Define the variables:
Let x = number of miles driven
Let y = total cost of rental
Company A
Given:
Charge to rent the truck is $90 a day plus $0.80 per mile.⇒ y = 90 + 0.8x
Company B
Given:
Charge to rent the truck is $50 a day plus $0.90 per mile.⇒ y = 50 + 0.9x
To find the number of miles for which Company A and Company B charge the same amount, substitute the equation for Company A into the equation for Company B and solve for x:
⇒ 90 + 0.8x = 50 + 0.9x
⇒ 90 + 0.8x - 50 = 50 + 0.9x - 50
⇒ 40 + 0.8x = 0.9x
⇒ 40 + 0.8x - 0.8x = 0.9x - 0.8x
⇒ 40 = 0.1x
⇒ 40 ÷ 0.1 = 0.1x ÷ 0.1
⇒ 400 = x
Therefore, the number of miles for which the rental costs are the same from either company is 400 miles.
To find the cost, substitute x = 400 into one of the equations:
⇒ y = 90 + 0.8(400)
⇒ y = 90 + 320
⇒ y = 410
Therefore, the daily cost from both companies for 400 miles would be $410.
1.The null set is represented by
a) { }
b) {0}
c)
d) None of these
Answers
Answer:
A
Step-by-step explanation:
( ) The null set is always empty.
Answer:
a
Step-by-step explanation:
The null set will always be empty
6(-3m+1) = 5(-2m-2)
I need help lol
Answers
Answer:
2
Step-by-step explanation:
you multiply the 6 and 5 to the parethinsis and simplify
2x – 5 +3x ≤ 15
ayudenme plss
Answers
x≤4
One garden had 5 times as many raspberry bushes as a second garden. After 22 bushes are transplanted from the first garden to the second garden, the number of raspberry bushes in the gardens are the same. How many bushes did each garden have originally?
Please show work and no links or files! :)
Answers
To solve this problem form the system of equations as per statements given in the question then get the answer by solving them.
Number of bushes in garden one were 55 and in second garden 11 originally.
Let the number of raspberry bushes in one garden = x
And the number of raspberry bushes in second garden = y
Garden one has 5 times as many raspberry bushes as second garden,So the equation for the given statement will be,
x = 5y -------(1)
22 bushes were transplanted from garden one to the second, number of bushes in both the garden becomes same,Therefore, equation for this statement will be,
(x - 22) = (y + 22)
x - y = 22 + 22
x - y = 44 ------(2)
Substitute the value of x from equation (1) to equation (2)
5y - y = 44
4y = 44
y = 11
Substitute the value of 'y' in equation (1),
x = 5(11)
x = 55
Therefore, Number of bushes in garden one were 55 and in second garden 11 originally.
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https://brainly.com/question/12422372
Calculate the slope of the line containing the points (6,-4) and (-1,-4).
Answers
Answer:
Step-by-step explanation:
(x₁ , y₁) = (6, -4) & (x₂ , y₂) =(-1 , -4)
In these two points, there is no change in y-coordinates. So, the line is parallel to x-axis.
Slope of line parallel to x-axis = 0
The digit 4 in which number represents a value of 4 hundredths?
a 8.34 its a see the 4 the four is in the hundredths place
b0.994
c405..6 cant figure it out here's the answer
Answers
Answer:
A
Step-by-step explanation:
Because 8's place value is the ones , 3's place value is the tenths and 4's place value is the hundredths.
Example > 0.1 = tenths slot. 0.01 = hundredths slot. 0.001 = thousandths slot. 0.0001 = ten thousandths slot.
Your welcome pooh.
simplify this exponential expression
[tex]( \frac{1}{3} )^{2} [/tex]
Answers
Answer:
Answer: 3^-2
Step-by-step explanation:
[tex]( \frac{1}{3} ) {}^{2} \\ \\ = \frac{ {1}^{2} }{ {3}^{2} } \\ \\ = {3}^{ - 2} [/tex]
Answer:
[tex]\frac{1}{9}[/tex]
Step-by-step explanation:
Evaluate the power
[tex]\frac{1^2}{3^2}[/tex]
Divide
[tex]\frac{1}{9}[/tex]
helppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
answer:
A is your answer...
explanation:
I just divided each number by 4 to get the results..
hope it helps and plz mark brainliest
given the function evaluate the function at the following points d and e
Answers
Answer:
d).
g(x) = x² +3
g(2t) = (2t)² +3 = 4t²+3
e).
g(x) = x² +3
g(t+1)= (t+1)²+ 3 = t² +2t+1 +3 = t²+2t +4
I hope I helped you^_^
Nolan reads 14 pages per hour .After a total of 3 hours of reading this week,how many pages will Nolan have read in all
Answers
A student council group is preparing flower arrangements for a nursing home. There are 162 roses, 108 dahlias, and 180
tulips to be used in the arrangements. The arrangements are identical and there are no leftover flowers.
How many roses, tulips, and dahlias are in each arrangement?
Answers
Answer:
Step-by-step explanation:
since GCF(162,108,180)=18
and you have not mentionned it was the maximum of arrangements you want:
[tex]\begin{array}{c|c|c|c}\#arrangement&\#Roses&\#Dahlias&\#Tulips\\-------&-------&-------&-------\\1&162&108&180\\2&81&54&90\\3&54&36&60\\6&27&18&30\\9&18&12&30\\18&9&6&10\\-------&-------&-------&-------\\\end {array}[/tex]
Please help!!!!! 25 POINTS
How do you find the solutions to a system of equations involving quadratic functions and other functions?
How do quadratic functions compare to linear and exponential functions?
Answers
Answer:
1. How to Solve using Algebra
Make both equations into "y =" format.
Set them equal to each other.
Simplify into "= 0" format (like a standard Quadratic Equation)
Solve the Quadratic Equation!
Use the linear equation to calculate matching "y" values, so we get (x,y) points as answers.
Algebraic method is more easy to do
2. linear functions have constant first differences. quadratic functions have constant second differences. exponential functions have a constant ratio.
What is the perimeter of triangle Q(3,-3) R(-4,5) P(3,5)
Answers
Answer:
QR = ( -7, 8) = √113
QP= ( 0, 8) = 8
PR= ( -7, 0) = 7
=> √113 + 8+ 7 = 15+√113
D
Question 1
5 pts
What number should be added to -28 to make the sum 0? (5 points)
28
-28
27
0
Answers
PLEASE HELP!! What is the standard deviation of a data set whose values are all the same?
A. −1
B. 0
C. 1
D. −2
Answers
Answer:
zero
Step-by-step explanation:
Answer:
I got this same question on my quiz, so I added the other two questions as well, with their answers.
Step-by-step explanation:
1. What is the standard deviation of the data set? Round to the nearest tenth if needed.
2, 4, 7, 8, 9
Answer: 2.9
2. Data Set A has a mean of 215 and a standard deviation of 35. Data Set B has a mean of 400 and a standard deviation of 12. Which data set is more spread out?
Answer: Data Set A
3. What is the standard deviation of a data set whose values are all the same?
Answer: 0
x - 11 = 1 what is the value of x
Please help, thank you.
Answers
Answer:
x = 12
Step-by-step explanation:
1 + 11 = 12, so x = 12. hope this helps
