dividing polynomials simplify (p^3-6) ÷ (p-1)
Answers
To divide
(p³ - 6) by (p-1)
set the division symbol and insert the numbers.
Divide p³ by p, the result is p²
write the result on top of the root sign
Multiply p² by (p-1)
write the result below (p³ ) inside the root sign
subtract
Divide p² by p, the reust is p
write the p on top of the root sign
multiply p by (p-1) and write the result inside the root sign
subtract
Take down 6
Divide p by p
The result is 1
write the result at the top of the root sign
Multiply p-1 by 1
write the result inside the root sign
subtract
write
The reuslt when you divide (p³ - 6) by (p-1) is;
[tex](p^2+p-1)+\frac{5}{(p-1)}[/tex]
Related Questions
need some help pleaseSolve the next equation3x^2+x-6=0
Answers
We have the next equation
[tex]3x^2+x-6=0[/tex]In order to solve this equation, we will use the next formula
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where
a=3
b=1
c=-6
we substitute the values and reduce
[tex]\begin{gathered} x_{1,2}=\frac{-1\pm\sqrt[]{1^2-4(3)(-6)}}{2(3)} \\ x_{1,2}=\frac{-1\pm\sqrt[]{73}}{6} \\ \end{gathered}[/tex]if we have a second-degree equation we will have two solutions
first solution
[tex]x_1=\frac{-1+\sqrt[]{73}}{6}=1.257[/tex]the second solution is
[tex]x_1=\frac{-1-\sqrt[]{73}}{6}=1.59[/tex]the two solutions of the equation are
[tex]x_1=1.257,_{}x_2=1.59[/tex]Type the correct answer in the box. Consider functions f and g. f(x) = (1 + 1) g(t) = 3 + 1 Evaluate the function composition. (g)(-64) =
Answers
We are given the following functions
Answer:
its -8
Step-by-step explanation:
that other dude has schitzophrenia he thinks he put an answer
Antwaan uses a large paper cone to hold popcorn as shown below. 12 cm POP CORN 22 cm Which equation can Antwaan use to find the volume of this cone in cubic centimeters? V = (6)? (22) V=376)-(22) O V = +(12)(22) 1 11012/on
Answers
Volume of a cone : 1/3 π r^2 h
Where:
r= radius = Diameter /2 = 12/2 = 6 cm
h = height = 22 cm
Replacing
V = 1/3 π (6)^2 (22)
The half-life of gold-194 is approximately 1.6 days.How much of a 7gram sample of gold-194 would remain after 3days? Round to three decimal places.
Answers
Given that the half-life of gold-194 is approximately 1.6 days.
We can find how much of a 7-gram sample of gold-194 would remain after 3days using the formula below;
[tex]\begin{gathered} A=A_0(\frac{1}{2})^{\frac{T}{h_{}}} \\ \text{Where A = final amount}=\text{?} \\ A_0=initial\text{ amout}=7\text{ grams} \\ T\text{ =Time}=3\text{days} \\ h=\text{ half life}=1.6\text{days} \end{gathered}[/tex]We would then substitute the parameters into the formula above.
[tex]\begin{gathered} A=7(0.5)^{\frac{3}{1.6}} \\ A=7(0.5)^{1.875} \\ A=1.908 \end{gathered}[/tex]Therefore, the amount of a 7gram sample of gold-194 would remain after 3days is;
Answer: 1.908 gram
Giving that f(x)=19x and g(x)= -3x-4 what is (fg)(x)
Answers
Solution:
Given the functions below
[tex]f\mleft(x\mright)=19x\text{ }and\text{ }g\left(x\right)=-3x-4[/tex]To find the composite function (fg)(x),
[tex](fg)(x)=(19x)(-3x-4)[/tex]Expand the brackets
[tex](fg)(x)=-57x^2-76x[/tex]Hence, the answer is
[tex]-57x^2-76x[/tex]graph on the coordinate plane 4.5, 2
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The given points are, (-5, 5) and (4.5, 2).
To ordered pairs are noted as (x, y), that is first value corresponds to the value on the x axis and the second one corresponds to the value on the y aixs. Therefore we have,
mary question word problem please can u show work on the picture for me to understand it get confusing when it's not marked what question
Answers
a. The company produces 52 boxes per hour. Then, after 3 hours they produce 52*3 = 156 boxes. If they had 404 boxes after 3 hours, then they started with 404 - 156 = 248 boxes.
Given that they produce 52 boxes per hour, then after h hours, they produce 52h boxes. Therefore, the number of boxes, b, as a function of the number of hours, h, is:
b = 248 + 52h
b. Replacing with h = 8, we get:
b = 248 + 52(8)
b = 248 + 416
b = 664
There will be 664 boxes after an 8-hour shift
Given AGHJ - AXYZ, find each missing measure.H18 ftzXa) GJ =d) mZH =27 fte) m =38b) XY=c) ZY =f) mZJE
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Sally invested some money at15 % interest. Sally also invested$203 more than4 times that amount at8 % . How much is invested at each rate if Sally receives$2017.03 in interest after one year? (Round to two decimal places if necessary.)
Answers
Sally has two investments:
x at 15% of interest
4x+$203 at 8% of interest
Each month she is receiving
0.15x+0.08(4x+$203)=0.15x+0.32x+$16.24
=0.47x+$16.24
Then, the whole year she received
=12(0.47x+$16.24)
since we know that after onw year she received $2017.03
then
$2017.03 = 12(0.47x+$16.24)
Now we just must find x
0.47x+$16.24 = $2017.03/12
= $168.085
0,47x = $168,085-$16,24
= $152,085
Therefore x = $323,58 is the amount of money of her first investment
Since the second investment's is given by 4x+$203
then the amount of money of her second investment is $1 310,56
VE FULL CREDIT The formula te convert Fahrenheit to Celsius is C = (F - 32). a) Solve the formula for F. b) How would you dress for outdoor weather if the temperature is 30°C7 Show work to support your answer
Answers
solve for C:
Multiply both sides by 9/5:
[tex]\frac{9}{5}C=F-32[/tex]Add 32 to both sides:
[tex]F=\frac{9}{5}C+32[/tex]---------------------------------------------------------
for C = 30:
[tex]\begin{gathered} F=\frac{9}{5}(30)+32 \\ F=54+32 \\ F=86 \end{gathered}[/tex]Answers:
a)
[tex]F=\frac{9}{5}C+32[/tex]b)
[tex]F=86[/tex]( algebra )solve for the equation below for the indicated variable f=ma (solve the equation for m )
Answers
Given the equation,
[tex]f=ma[/tex][tex]\begin{gathered} f=m\times a \\ \frac{f}{a}=m \end{gathered}[/tex]Therefore,
[tex]m=\frac{f}{a}[/tex]Write the English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. A number decreased by the sum of the number and one.
Answers
Given: x represent the number. A number decreased by the sum of the number and one.
Required: The algebraic expression for the english phrase and its simplification.
Explanation:
Given that x is the number.
Sum of the number and one = (x + 1)
Now, the number is decreased by the sum of the number and one.
So, the algebraic expression is
[tex]x-(x+1)[/tex]Simplifyung further,
[tex]x-x-1=-1[/tex]Final Answer: The algebraic expression is x-(x+1) and after simplification, it is -1.
Which of the following ratios is equivalent to1/2?1:21:12:1
Answers
The correct equivalent expression for 1/2 is:
1 : 2
identify the number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions may apply.) Square root -81
Answers
√-81 = -9i Pure imaginary - complex
The _______ number in a. ordered pair is the y-coordinate and corresponds to a number on the __________.
Answers
The given statement is,
The _______ number in an ordered pair is the y-coordinate and corresponds to a number on the __________.
To fill the blanks:
As we know, the first number in an ordered pair is the x- coordinate and the second number in an ordered pair is the y- coordinate.
Added that the first number in an ordered pair corresponds to a number on the x-axis and the second number in an ordered pair corresponds to a number on the y-axis.
So, the answer is,
The second number in an ordered pair is the y-coordinate and corresponds to a number on the y-axis.
The probability that Jacqueline will be elected to the students' council is o.6, and the probability that she will be selected to represent her school in a public-speaking contest is 0.75. The probability of Jacqueline achieving both of these goals is 0.5. Answer the questions below:1. The two evens are mutually exclusive. True or False2. The events are not independent. True or False3. What is the probability that Jacqueline is either elected to the student' council or picked for the public-speaking contest? Round you answer to two decimal place
Answers
Recall that two events are mutually exclusive if they cannot happen at the same time. In the given problem we are given that the probability of both events occurring is 0.5 therefore, the events are not mutually exclusive.
Now, two events are independent if one event happening does not affect the probability of the other, in the given problem the events don't affect each other, therefore, the events are independent.
Finally, to determine the probability of either event happening, we will use the following formula for not mutually exclusive events:
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B).[/tex]We know that:
[tex]\begin{gathered} P(A)=0.6, \\ P(B)=0.75, \\ P(A\cap B)=0.5. \end{gathered}[/tex]Therefore:
[tex]P(A\cup B)=0.6+0.75-0.5=0.85.[/tex]Answer:
1) False.
2) False.
3) 0.85.
What is the solution to the system of linear equations graphed below? a) (0,1) b) (7,0) c) Infinitely Many Solutions d) No Solution y у 11- 3 3 2 1 2 3 4 5 6 8 9 10 D
Answers
As shown in the figure:
The graphed lines are parallel, because the difference of y-coordinates are constant.
So, there is no intersection between the lines
So, The answer is option d) No solution
The area of the rectangle shown is 34 square inches.4 inchesWhat is the length of the base of the rectangle in inches?
Answers
The formula for any give rectangle is just that you multiply it's lenght by it's width, or as expressed by the equation;
[tex]\text{Area}=length\text{ x width}[/tex]Since in the picture we are given a side of the rectangle measuring 4 inches, with it's length as unkown, we can only assume that the 4 inches there is the width therefore for a sqaure with an area of 34 square inches, we can express it as;
[tex]\begin{gathered} \text{Area = lenght x width , where Area = 34, and width = 4} \\ 34\text{ = lenght x 4 , then divide both sides by 4} \\ \frac{34}{4}=\frac{4}{4}(lenght)\text{ , and remember that }\frac{4}{4}\text{ = 1} \\ \text{lenght = }\frac{34}{4} \\ \text{lenght = 8.5} \end{gathered}[/tex]Therefore the lenght of the rectangle in our question is 8.5 inches.
Movie Theater Admission Adults: $8Children (under 13): $5Matinee (before 6 P.M.): $31. Janelle (age 12) and her cousin, Marquita (age 14), go to a 7:00 P.M.show. Write an expression for the totalcost of admission. What is the total cost?2. Jan takes her three children and two neighbor's children to a matinee. All of the children are under age 13. Write an expression for the total cost of admission. How much in all did Jan pay for admission?
Answers
1. The total cost is $13
2. The total cost is $15
Explanation:1. Janelle (age 12) and her cousin,
Marquita (age 14), go to a 7:00 P.M.
Total cost of admission is:
$(5C + 8A)
Where C represents the number of children, and A the number of adults.
The cost is:
$[5(1) + 8(1)] = $13
The above is if Marquita who got to a 7:00 PM show is paying adult fee of $8.
2. Jan takes her three children and two neighbour's children to a matinee
Total number of children is 3 + 2 = 5
Total cost of admission is:
3M
Where M represents the number of people who going to a martinee.
The cost is:
3(5) = $15
What do you know to be true about the values of a and b?bº775aA. abD. Can't be determined
Answers
The answer is D. can't be determined
we need more details t
Solve the system of equations. Enter the x-value and y-value of the solution separately, as indicated.x + 4y=39- 4x - 4y=0
Answers
Given:
The system of equations is
[tex]\begin{gathered} x+4y=39 \\ -4x-4y=0 \end{gathered}[/tex]Required:
We want to find x-values and y-values
Explanation:
First add both equations
[tex]\begin{gathered} x+4y-4x-4y=39 \\ -3x=39 \\ x=-13 \end{gathered}[/tex]put value of x in any of equation
[tex]\begin{gathered} -4x-4y=0 \\ x+y=0 \\ -13+y=0 \\ y=13 \end{gathered}[/tex]Final answer:
x-value is -13
y-value is 13
Learn with an example Last year, the city of Kingwood experienced a budget deficit of $843,130. In comparison, the expected deficit for this year is 40% more. What is this year's expected deficit?
Answers
the budget deficit is,D = 843,130 $
the 40 % of the deficit is,
[tex]=843130\times\frac{40}{100}[/tex][tex]\begin{gathered} =84313\times4 \\ =337252\text{ \$} \end{gathered}[/tex]so, this year deficit is,
= D + 337252
= 843130 + 337252
= 1180382 $
thus, the total deficit of this year is 1180382 $
Hello, can you please help me solve this question a, b and c !
Answers
Given:
We need to solve
[tex]\cos ^4x-\sin ^4x[/tex]Solution;
Now,
[tex]\begin{gathered} \cos ^4x-\sin ^4x=(\cos ^2x)^2-(\sin ^2x)^2 \\ =(\cos ^2x-\sin ^2x)(\cos ^2x+\sin ^2x) \\ =(\cos 2x)(1) \\ =\cos 2x \end{gathered}[/tex]So,the simpler form is
[tex]\cos 2x[/tex]
(a)What is the domain of the relation ? Enter a value on the same line , separated by commas (b)What is the range of the relation ? Enter a value on the same line , separated by commas
Answers
Answer:
• Domain: {1,2,3,7,9}
,• Range: {1,4,6,7,8}
Explanation:
Given the relation in the table, we are required to find the domain.
Domain
The domain is defined as the set of all the values of x that satisfies the relation.
From the table, the domain is:
[tex]\{1,2,3,7,9\}[/tex]Range
The range is defined as the set of all the values of y that satisfies the relation.
From the table, the range is:
[tex]\{1,4,6,7,8\}[/tex]Which of the following expressions are equivalent to…I will take a screenshot of the expression I need help with.
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Given:
[tex]-\frac{2}{-13}[/tex]You can move the negative anywhere or in front of the fraction.
[tex]-\frac{2}{-13}=\frac{-2}{-13}=-\frac{-2}{13}[/tex]
Answer:
A. and B.
how to draw this venn diagram please and also explain ur steps how u got the numbers
Answers
Answer
See the diagram at the end of the explanation
Step-by-step explanation
Given that the total number of surveyed people is 30 and 2 people don't like chocolate or vanilla ice creams, then 28 (= 30 - 2) people like at least one of these flavors.
Considering only the people who at least like one of the flavors, the next Venn diagram can be drawn:
where:
[tex]\begin{gathered} x+y+z=28\text{ \lparen number of people who like at least one flavor\rparen} \\ x+y=22\text{ \lparen number of people who like chocolate\rparen} \\ y+z=18\text{ \lparen number of people who like vanilla\rparen} \end{gathered}[/tex]Combining the first and second equations, we get:
[tex]\begin{gathered} 22+z=28 \\ z=28-22 \\ z=6 \end{gathered}[/tex]Combining the first and third equations, we get:
[tex]\begin{gathered} x+18=28 \\ x=28-18 \\ x=10 \end{gathered}[/tex]Substituting these results into the first equation:
[tex]\begin{gathered} 10+y+6=28 \\ 16+y=28 \\ y=28-16 \\ y=12 \end{gathered}[/tex]Now, with these results we can draw the Venn diagram as follows (where the "2" outside the circles indicates the number of people who don't like chocolate or vanilla):
Solve the equation 6+(c+8)=136-(c+8)-131+7(t+2)=854(A+4)-9(A-4)=3711=7-(1-y)3+7(p-10)= -38-(5-3p)20+5(3-5A)=-5(A-6)+5
Answers
Let's solve the next equation:
[tex]6+(c+8)=13[/tex]We need to find the value for c, this value is correct when we replaced it with a number and the equality equation becomes true.
First, subtract both sides by 6
[tex]6-6+(c+8)=13-6[/tex][tex]c+8=7[/tex]Now, subtract both sides by 8
[tex]c+8-8=7-8[/tex][tex]c=-1[/tex]Replacing the c value to verify:
[tex]6+(-1+8)=13[/tex][tex]6+7=13[/tex]The c value is correct.
A feedlot in Adams County has developed its own blend of grains for horses. The blendincludes oats, which cost $9.80 per kilogram, and feed corn, which costs $4.30 per kilogram.Overall, the mixture costs $8.15 per kilogram. If a worker at the feedlot is mixing up a batchand starts with 270 kilograms of oats, how many kilograms of corn should he add to makethe blend?Write your answer as a whole number or as a decimal rounded to the nearest tenth.
Answers
EXPLANATION
Let's call x to the oats and y to the corns.
Let's see the facts:
x= oats ----> $9.80/Kg
y= corns ---> $4.30/Kg
If the mixture cost is $8.15/ Kg, and the workers starts with 270 kilograms of oats, the kilograms of corn would be given by the following relationship:
The total cost of the oats is:
9.8*270 = 279.8 dollars
The total mixing amount is:
270 + y = z
The total cost equation is as follows:
8.15.z= 9.8*270 + 4.3*y
Replacing z= y + 270:
8.15(270+y) = 9.8*270 + 4.3y
Applying the distributive property:
2200.5 + 8.15y = 2646 + 4.3y
Subtracting 2200.5 to both sides:
8.15y = 2646 - 2200.5 + 4.3y
Subtracting 4.3y to both sides:
8.15y - 4.3y = 2646 - 2200.5
Simplifying like terms:
3.85y = 445.5
Dividing both sides by 3.85:
y= 445.5/3.85
Simplifying:
y = 115.71
The worker should add 116 kilograms of corns.
Nancy has 8 pieces of string that are exactly the same length. Which equation the total length of string she has
Answers
Nancy has 8 pieces of strings that are exactly the same length each. That means each of the piece of strings have the same length.
Let
This table shows the rainfall (in centimeters) for a city in different months. The quadratic regression equation that models these data is y=-0.77x^2+6.06x - 5.9Using this model, the predicted rainfall for month 11 is about -32.4 centimeters. Does this prediction make sense? Why or why not?A. No, because you can’t have a negative amount of rainfall.B. Yes, because the rainfall is declining.C. Yes, because it is the result of substituting x=11D. No, because you can’t measure rainfall in centimeters
Answers
The quadratic regression equation model given is;
[tex]\begin{gathered} y=-0.77x^2+6.06x-5.9 \\ \text{where y is the rainfall measure in cm} \\ x\text{ is the month} \end{gathered}[/tex]For month 11, substituting x = 11 in the equation,
[tex]\begin{gathered} y=-0.77x^2+6.06x-5.9 \\ y=-0.77(11)^2+6.06(11)-5.9 \\ y=-93.17+66.66-5.9 \\ y=-32.41\operatorname{cm} \end{gathered}[/tex]The predicted rainfall in month 11 is -32.4cm
From the options given, the correct answer is option A because the prediction does not make sense because there can not be a negative amount of rainfall.
Therefore, option A is the right answer.