Use synthetic division to find the quotient and remainder of (3[tex]x^{4}[/tex]-8[tex]x^{3}[/tex]+9x+5)+(x-2)
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How to get answer:
[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=3x^4-8x^3+9x+5+x-2\\Group\:like\:terms\\=3x^4-8x^3+9x+x+5-2\\\mathrm{Add\:similar\:elements:}\:9x+x=10x\\=3x^4-8x^3+10x+5-2\\\mathrm{Add/Subtract\:the\:numbers:}\:5-2=3\\=3x^4-8x^3+10x+3[/tex]
For this case we have a polynomial division.
A term of the quotient must be found step by step to eliminate the terms of the dividend.
The final result must comply with:
[tex]P (x) = Q (x) * D (x) + R (x)\\[/tex]
Where:
P (x) is the dividend
Q (x) is the quotient
D (x) is the divisor
R (x) is the remainder
Answer:
See attached image
![Use Synthetic Division To Find The Quotient And Remainder Of (3[tex]x^{4}[/tex]-8[tex]x^{3}[/tex]+9x+5)+(x-2)](https://i5t5.c14.e2-1.dev/c-qa-images/answers/attachments/7YyCSeARmBcwRAfMhjTfsMcnHBphNNRg.jpeg)
Related Questions
The question is in the attached. Thank yo
Answers
C Is your awnser! have a good day Pretty sure its C because theres only 1 line
Which conversions from scientific notation to standard notation are true? Check all that apply.
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For this case we have the following expressions:
a) [tex]1.71 * 10 ^ 3[/tex], in this case we have a positive exponent, therefore we move the decimal point as many times to the right as indicated by the exponent, that is, 3 times. So, we have:
[tex]1.71 * 10 ^ 3 = 1,710[/tex]
b) [tex]8.05 * 10 ^ 5[/tex], in this case we have a positive exponent, therefore we move the decimal point as many times to the right as indicated by the exponent, that is, 5 times. So, we have:
[tex]8.05 * 10 ^ 5 = 805,000[/tex]
c)[tex]2.4 * 10 ^ 4[/tex], in this case we have a positive exponent, therefore we move the decimal point as many times to the right as indicated by the exponent, that is, 4 times. So, we have:
[tex]2.4 * 10 ^ 4 = 24,000[/tex]
d) [tex]8.25 * 10^{-3}[/tex], in this case we have a negative exponent, therefore we move the decimal point as many times to the left as indicated by the exponent, that is, 3 times. So, we have:
[tex]8.25 * 10^{-3} =0.00825[/tex]
e) [tex]7.09 * 10^{-6}[/tex], in this case we have a negative exponent, therefore we move the decimal point as many times to the left as indicated by the exponent, that is, 6 times. So, we have:
[tex]7.09 * 10^{-6} = 0.00000709[/tex]
f) [tex]3.99 * 10 ^ 5[/tex], in this case we have a positive exponent, therefore we move the decimal point as many times to the right as indicated by the exponent, that is, 5 times. So, we have:
[tex]3.99 * 10 ^ 5 = 399,000[/tex]
g) [tex]8 * 10 ^ 7[/tex], in this case we have a positive exponent, therefore we move the decimal point as many times to the right as indicated by the exponent, that is, 7 times. So, we have:
[tex]8 * 10 ^ 7 = 80,000,000[/tex]
h) [tex]1.03 * 10^{-4}[/tex], in this case we have a negative exponent, therefore we move the decimal point as many times to the left as indicated by the exponent, that is, 4 times. So, we have:
[tex]1.03 * 10^{-4}= 0.000103[/tex]
Answer:
The correct options are: b, e, g and h
|-67.05 – 42.98| – (29.80 + 45.83)
A.
30.04
B.
34.04
C.
34.40
D.
44.04
Answers
Answer:
its d 44.04
Step-by-step explanation:
PLZ help 20pts
Which graph represents the equation y=2/3x−2 ?
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The slope-intercept form:
y = mx + b
m - slope
b - y-intercept
We have y = 2/3 x - 2
y-intercept = -2
Only the one graph has that y-intercept (look at the picture).
y = [tex]\frac{2}{3}x[/tex] - 2 means the line will intercept the y-axis at -2 and have a slope (rise over run) of 2 over 3.
Answer: C
Last year there were 1,435 8th grade students enrolled at your sc hool. This year there are 1,220. What is the percent change in the number of 8th grade students?
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1.2% of 8th grade students is the percentage change.
If EF = 5w + 20, FG = 7w + 28, and EG = 72, find the value of w. Find EF and FG
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Answer:
w = 2, EF = 30 , FG = 42
Explanation:
We have EF = 5w + 20 and FG = 7w + 28
Since these points E, F and G are col-linear points we have.
EG = EF + FG
And given that EG = 72
So, EF+EG = 72
5w + 20 + 7w + 28 = 72
12w + 48 = 72
12 w = 24
w = 2
So EF = 5w + 20 = 5x2 + 20 = 30
FG = 7w + 28 = 7x2 + 28 = 42
In triangle ABC, m∠BAC = 50°. If m∠ACB = 30°, then the triangle is triangle. If m∠ABC = 40°, then the triangle is triangle. If triangle ABC is isosceles, and AB = 6 and BC = 4, then AC =
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Abc is a RIGHT triangle.
Then AC= 4 or 6
these are the right answers for edquity
The angles in the triangle ABC total 120 degrees, verifying it as a correct triangle. Given it is an isosceles triangle with AB and AC being the equal sides of length 6, and by applying the law of cosines, the length of side AC can be calculated.
Explanation:Given the angles of the triangle ABC as m
We can use the Law of Cosines to find the length of the side AC. The Law of Cosines states that c² = a² + b² - 2ab * cos(y). By substituting the given values into this formula, we find AC = sqrt[4² + 6² - 2*4*6*cos(50°)] which gives us the length of side AC.
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please try to answer quickly :) thanks
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For the 1 and 2/5, go four little lines past the 1.
-1/2, go five little lines in between 0 and -1.
and for -2 1/10, go to -2 and then one little line towards the 3, so it is one little line to the left of -2.
A football team won 9 out of 12 games what percentage of games has the football team won
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Janelle buys 4 cases of water. Each case of water contains 12 bottles. Janelle drinks 3 bottles of water. Veronica writes a numerical expression to represent the situation. Her expression (12 - 3) x 4 has a mistake.
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4 cases of 12 bottled waters is 48 total amount of bottled waters since Veronica drank 3 she has 45 bottled waters left
help please? .....................
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[tex]2x^2+6x-10=x^2+6\qquad\text{subtract}\ x^2\ \text{and 6 from both sides}\\\\x^2+6x-16=0\\\\x^2+8x-2x-16=0\\\\x(x+8)-2(x+8)=0\\\\(x+8)(x-2)=0\iff x+8=0\ \vee\ x-2=0\\\\x+8=0\qquad\text{subtract 8 from both sides}\\\boxed{x=-8}\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}\\\\Answer:\ \boxed{B.\ -8\ and\ C.\ 2}[/tex]
What is the value of x in the equation 3(2x + 4) = –6? (4 points)
–3
1
12
19
3.
The steps below show the incomplete solution to find the value of x for the equation
5x –2x –3 = –2 + 15:
Step 1: 5x –2x –3 = –2 + 15
Step 2: 5x –2x –3 = 13
Step 3: 3x –3 = 13
Which of these is most likely the next step? (4 points)
3x = 16
3x = 10
3x = 39
3x = 3
Answers
[tex]3(2x + 4) = - 6[/tex]
First you would distribute the 3 into the ( )
so 2 would become 6 and 4 would become 12
[tex]6x + 12 = - 6[/tex]
next you subtract 12 from -6
[tex]6 x = - 18[/tex]
now you divide -18/6
[tex] \frac{ - 18}{6} = - 3[/tex]
then for #3.
[tex]3x - 3 = 13[/tex]
the next step would be to add 3 to 13
[tex]3x = 16[/tex]
then divide 3 from 16 to get
[tex] \frac{16}{3} = 5.333333333[/tex]
so around 5.3
Which of the following is equivalent to 17g – 2g?
A.) (17 – 2) + g
B.) (17 – 2)g²
C.) (17 – 2) + g²
D.) (17 – 2)g
Answers
Hey there!!
Given equation :
17g - 2g
Let;s first look at something which is common in both the terms.
Yes, the alphabet which is common is the ' g '.
Now, let's apply distributive property.
... 17g - 2g
... g ( 17 - 2 )
Hence, the appropriate answer would be ' D '.
Hope my answer helps!
A spider ate 2 5 % 25%25, percent more bugs this month than last month. The spider ate 8 88 bugs last month. How many bugs did the spider eat this month? Bugs
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bugs eaten this month = bugs eaten last month plus 25% of last month
x = 88 + .25 x 88
x = 88 + 88(.25)
= 88 + 22
= 110
Answer: 110 bugs
Solve the equation. Check your answer.
-11=5+8x
x=?
Answers
Answer:
x=-2
Step-by-step explanation:
Consider equation -11=5+8x
Collecting the like terms
-8x=11+5, -8x=16
Dividing through by -8 ob both sides of the equation
(-8x)-/8=16/-8
x=-2
If a movie starts at 7:10 and ended at 9:05 how long was it
Answers
1 hour 55 minutes
break the time down into hours and minutes
7 : 10 → 8 : 00 = 50 minutes
8 : 00 → 9 : 00 = 1 hour
9 : 00 → 9 : 05 = 5 minutes
adding 1 hour + 50 minutes + 5 minutes = 1 hour 55 minutes
The movie lasted for a total of 115 minutes, which is calculated by adding the one hour between 7:10 and 8:10 to the additional 55 minutes between 8:10 and 9:05.
To calculate the duration of a movie that starts at 7:10 and ends at 9:05, you would subtract the start time from the end time. Starting at 7:10 and going up to 8:10 is one hour. From 8:10 to 9:05 is an additional 55 minutes. Therefore, adding these two parts together, the movie lasted for 1 hour plus 55 minutes, which is a total of 115 minutes.
Step-by-step, the calculation is as follows:
Calculate elapsed time from 7:10 to 8:10 (1 hour).Add the additional minutes from 8:10 to 9:05 (55 minutes).Combine both to find the total duration (1 hour + 55 minutes = 115 minutes).
solve the world problem. the formula d = rt gives the distance traveled in time t at rate r. if a bicyclist rides for 2.3 hours and travels 41 miles, what was her average speed.
A.9.43 miles per hour
B.38.7 miles per hour
C.5.6 miles per hour
D.17.83 miles per hour
Answers
The answer to your question is D. 17.83 because 41 divided by 2.3 is equal to the answer and you are trying to solve for r.
Nick works two jobs to pay for college. He tutors for $15 per hour and also works as a bag boy for $8 per hour. Due to his class and study schedule, Nick is only able to work up to 20 hours per week but must earn at least $150 per week. If t represents the number of hours Nick tutors and b represents the number of hours he works as a bag boy, which system of inequalities represents this scenario?
A.) t + b greater than or equal to 20 15t + 8b = 150
B.) t + b less than or equal to 20 15t + 8b greater than or equal to 150
C.) t + b less than or equal to 20 15t + 8b less than or equal to 150
D.) None of the systems shown represent this scenario.
Answers
He can't work more than 20 hours so t+b must be less than or equal to 20.
He has to earn $150 so it cannot be less than 150. Theoretically he could earn more, e.g doing 10 hours of each job which equals $230
Therefore t + b less than or equal to 20 15t + 8b greater than or equal to 150
Answer:
Option B is the correct answer.
Step-by-step explanation:
Earning for tutoring per hour = 15$
Earning for bag boy per hour = 8$
We have Nick is only able to work up to 20 hours per week but must earn at least $150 per week and t represents the number of hours Nick tutors and b represents the number of hours he works as a bag boy.
Nick is only able to work up to 20 hours per week
t + b ≤ 20
But must earn at least $150 per week
15 t + 8 b ≥ 150
Option B is the correct answer.
helpppppppp? please thank you
Answers
The x values are the same for both green dots, so you are looking at a simplified version of the distance formula.
d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
Since x1 = x2 = 5, the first set of brackets = (5 - 5) = 0
d = sqrt( y2 - y1)^2 )
d = y2 - y1
y2 = 5
y1 = - 1
d = 5 - - 1
d = 6 Answer
Lucia knows the fourth term in a sequence is 52 and the ninth term in the same sequence is 82. Complete the explanation of how she can find the common difference for the sequence. Then use the common difference to find the second term of the sequence
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well, I really can't really understand the way you asked the question, But, If it helps I can give you the entire sequence all the way to 82.
The sequence is,
2, 12, 22, 32, 42, 52, 62, 72 , 82, ect...,
(9 – 23) + |47 – 16|
A.
15
B.
17
C.
19
D.
25
Answers
You answer is: 17
Or otherwise B. is your correct answer.
(9 - 23) = -(14)
| 47 - 16| = 31
31 + (-14) = 17
Answer:
B: 17
Step-by-step explanation:
A team of scientists estimate the current number of butterflies in a park to be 20 thousand. The butterfly population is expected to increase at a rate of 4% per year. Which equation models the number of butterflies, in thousands, in the park after n years? A. 0.04(20)n B. 20(1.04)n C. 1.04(20)n D. 20(0.04)n
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Answer:
Option B is the correct answer.
Explanation:
Current number of butterflies in the park = 20 thousand.
Rate of increase of butterfly population = 4% = 0.04
The population of butterfly after 1 year = 20+0.04*20 = 20*1.04
The population of butterfly after 2 years = 20*1.04 + 20*1.04*0.04 = 20*1.04*1.04
The population of butterfly after 3 years = 20*1.04*1.04 + 20*1.04*1.04*0.04 = 20*1.04*1.04*1.04
So, population of butterfly after n years = 20*(1.04*1.04*1.04* .... n times)
[tex]= 20*1.04^n[/tex]
Option B is the correct answer.
Answer:
The answer is C
Step-by-step explanation:
Graph the function with the given description. A linear function h models a relationship in which the dependent variable increases 1 unit for every 5 units the independent variable decreases. The value of the function at 0 is 3.
Answers
The function is an illustration of a linear function.
See attachment for the graph of [tex]\mathbf{h(x) =-\frac{1}{5}x + 3}[/tex]
Let the independent variable be x
The highlights are given as:
The value of the function at 0 is 3. i.e. h(0) = 3When the independent variable decreases by 5 (i.e. -5), the independent variable increases by 1. So, the slope (m) is -1/5From the above highlights, we have:
[tex]\mathbf{m = -\frac{1}{5}}[/tex] --- the slope
[tex]\mathbf{b = 3}[/tex] --- the y-intercept
A linear equation is represented as:
[tex]\mathbf{h(x) =mx + b}[/tex]
So, we have:
[tex]\mathbf{h(x) =-\frac{1}{5}x + 3}[/tex]
See attachment for the graph of [tex]\mathbf{h(x) =-\frac{1}{5}x + 3}[/tex]
Read more about linear functions at:
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You and your friend are having a race, but since you are faster than him, you decide to give him a head start. He starts 10m in front of the starting line while you start on the starting line. You run at 6 meters/second, while your friend runs at 5.5 meters/second. After how many seconds will you and your friend be same distance from the starting line? seconds months
Answers
Answer:
20 seconds
Step-by-step explanation:
Your friend starts 10 meters in front of the starting line.
You start from the starting line.
You run at 6 meters/ second.
Your friend runs at 5.5 meters/second.
You and your friend will be at the same distance from the starting line only when you are able to catch your friend.
The relative speed between you two is the difference in your speed and your friend's speed that is:
[tex]6-5.5=0.5m/s[/tex]
So to cover 10 meters of separation at the speed of 0.5 meter/second it will take:
[tex]t=\frac{10}{0.5}= \frac{100}{5}=20s[/tex]
So it will take 20 seconds for you and your friend to be at the same distance from the starting line.
Answer:
20 seconds is correct.
Step-by-step explanation:
Please Help!!!
Which statement represents the biconditional statement of the conditional statements?
If the measures of two angles have a sum of 180º, then the angles are supplements.
If two angles are supplements, then their measures have a sum of 180º.
A. The measures of two angles have a sum of 180º if and only if the angles are supplements.
B. The measures of two angles do not have a sum of 180º if and only if the angles are supplements.
C. The measures of two angles do not have a sum of 180º if and only if the angles are not supplements.
D. The measures of two angles have a sum of 180º if and only if the angles are not supplements.
Answers
A. The measures of two angles have a sum of 180º if and only if the angles are supplements.
the angles must be supplementary to equal 180
a person who is entitled to social security benefits but is not receiving them would take his or her case to...
A: administrative court
B: Civil court
C: criminal on the state
D: It depends on the state
Answers
Answer:
A: administrative court.Step-by-step explanation:
An administrative court is specialize in administrative laws, its concern is mainly about public powers. Basically, the role of these type of courts is to ensure that officials are doing their job according to the law. Some of the issues that matters to an administrative courts are: taxation, dispensation of monetary benefits, environmental licenses, building inspection, child custody, immigration decisions, and more.
So, in this case we are talking about social security, someone is not receiving the benefits from it, so this means that a public institution is not working well, that's an administrative court jurisdiction, because it's in the public sector.
Sarah received a gift in a rectangular box with a volume of 240 in3. If the base of the box was 20 in2, how tall was the box? A) 2 inches B) 10 inches C) 12 inches D) 15 inches
Answers
Answer:
12 inches
Step-by-step explanation:
volume = length * width * height
volume = (length * width) * height
volume = (area of base) * height
height = volume/(area of base)
height = (240 in^3)/(20 in^2) = 12 in
Answer the box was 12 in bc 20x240divided by 4 =12
As a farmer, one of your responsibilities is to plow the field to prepare it for planting. On day 1, you plowed of the field. On day 2, you plowed of the field. How much more of the field did you plow on day 1 than on day 2?
Answers
Answer:
1/2 more then day 2.
Step-by-step explanation:
The difference in the amount of field plowed on day 1 compared to day 2 is 1/4, assuming day 1 was ½ and day 2 was ¼ of the field.
Explanation:To calculate how much more of the field was plowed on day 1 than on day 2, we need to subtract the fractions that represent the part of the field plowed on each day. However, you did not specify the fractions, so I will assume you meant to say ½ of the field was plowed on day 1 and ¼ of the field on day 2. Thus, the difference can be calculated as follows:
Calculate the difference in fractions: ½ - ¼.Find a common denominator for the two fractions, which is 4 in this case.Convert both fractions to have the common denominator: ½ = 2/4 and ¼ remains the same.Subtract the numerators: 2 - 1 = 1.Write the result as a fraction with the common denominator: 1/4.Therefore, you plowed 1/4 more of the field on day 1 than you did on day 2.
: student council is selling tickets to the fall ball dance. Tickets cost $6.00 per person , or $10 per couple. To cover the expenses required, they need to make at least $1,450. Let x represent the number of individual ticket sold, and y represent the number of couple tickets sold. Write a linear inequality to model the situation
Answers
[tex]6x + 10y \geqslant 1450[/tex]
This basically says that the total money made from tickets will be gretarr than or equal to $1450.
To model the situation with a linear inequality, represent the number of individual tickets sold as x and the number of couple tickets as y. The inequality is 6x + 10y >= 1450, signifying that the revenue from individual and couple ticket sales needs to be at least $1,450.
Explanation:To write a linear inequality to model the student council ticket sales, let x represent the number of individual tickets sold, and y represent the number of couple tickets sold. The tickets cost $6.00 per individual and $10.00 per couple. The council needs to make at least $1,450 to cover the expenses of the fall ball dance.
To derive the inequality, we consider the revenue generated from selling individual tickets (x tickets × $6.00 per ticket) plus the revenue generated from selling couple tickets (y tickets × $10.00 per ticket) should be at least $1,450:
6x + 10y ≥ 1450
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Using synthetic division what is the quotient of (2x^3-3x-10) divided by (x-2)