The remainder and factor of the given algebraic expression [tex]\frac{5x^{5} -4x^{3} -11x^{2} +12}{x+1}[/tex] is [tex](5x^{4} -5x^{3} +x^{2} -12x+12)(x+1)[/tex] and [tex]0[/tex]
As per the given question, we are supposed to find out the factor and remainder of the given algebraic expression [tex]\frac{5x^{5} -4x^{3} -11x^{2} +12}{x+1}[/tex] using remainder theorem concept.
Before solving this, we need to know the concept of remainder theorem.
According to which "When a polynomial is divided by a linear polynomial, the remainder theorem is used to get the remaining. We are aware that long division of polynomials can be used to find the remainder after dividing one polynomial by another. The remainder can instead be discovered using the remainder theorem."
Hence using the same concept we can conclude that the factors are [tex](5x^{4} -5x^{3} +x^{2} -12x+12)(x+1)[/tex] and remainder is [tex]0[/tex]
Algebraic Expression: An algebraic symbol or set of symbols that includes one or more integers, variables, and arithmetic operations.Remainder Theorem: When a polynomial is divided by a linear polynomial, the remainder theorem is used to get the remaining. We are aware that long division of polynomials can be used to find the remainder after dividing one polynomial by another. The remainder can instead be discovered using the remainder theorem.To learn more about Remainder Theorem, click on the link given below:
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I really need help from someone please
Answer:
b
Step-by-step explanation:
I need to find the missing angles
Answer:
g=93 h=87 k=122 m=58
Step-by-step explanation:
IM SURE THIS IS EASY FOR ANYONE WHO KNOWS MATH AND I NEED HELP ASAP LOL
•Answer the question and write out an equation that will go with the problem:
Lance is an air-fighter pilot. He has to log 20 hours in the air during the work week and 10 hours over the weekend in order to keep his license. Over the last week, he logged 5 hours on each of the following days: Monday, Thursday, and Friday. The other two days he logged 5 hours together. Did me make his quota for the work week?
Answer:
Nope. 5x3=15 +5=20 20+10=30 so no he didn't.
Step-by-step explanation:
Bye bye license
The recipe for beef stew calls for 1/4 teaspoon of pepper for every 3 potatoes. If 9 potatoes are used, how much pepper is needed?
Solve the proportion StartFraction one-fourth over 3 EndFraction = StartFraction p over 9 EndFraction to answer the question. Explain your steps.
Answer:3/4 teaspoons Trust me it is correct
The number of teaspoons of pepper required for beef is ( 3 / 4).
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that the recipe for beef stew calls for 1/4 teaspoon of pepper for every 3 potatoes the number of teaspoons required for 9 potatoes will be calculated as below:-
3 potatoes = ( 1 / 4 ) teaspoon
1 potato = ( 1 / 12 ) teaspoon
9 potatoes = 9 / 12 teaspoon
9 potatoes = 3 / 4 teaspoon
Therefore, the number of teaspoons of pepper required for beef is ( 3 / 4).
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find an expression in terms of n for the nth term of this sequence, 15,19,25,33,43
Answer:
Hello,
Step-by-step explanation:
P(n)=ax²+bx+c (quadratic sequence)
with a=1,b=1,c=13
[tex]\\\boxed{u_n=n^2+n+13}\\[/tex]
Answer:
tₙ = n² + n + 13=============================
Given sequence:
15, 19, 25, 33, 43, ...We can see this not AP or GP as the difference or ratio of consecutive terms is not common.
But we can see the difference between terms has common difference of 2:
19 - 15 = 425 - 19 = 633 - 25 = 843 - 33 = 10and
10 - 8 = 28 - 6 = 26 - 4 = 2It means the sequence is of the second degree, in other words it is quadratic.
In general it is of the form:
tₙ = an² + bn + c, where a, b, c are coefficients, n - is the number of the terms.Use the terms of the given sequence to work out unknown coefficients.
t₀ = 15 - (4 - 2) = 15 - 2 = 13
a(0)² + b(0) + c = 13c = 13It gave us the value of c.
t₁ = 15
a(1)² + b(1) + c = 15a + b + c = 15a + b + 13 = 15a + b = 2t₂ = 19
a(2)² + b(2) + c = 194a + 2b + c = 194a + 2b + 13 = 194a + 2b = 6Compare the last two equations and solve for a and b:
a = 2 - b4(2 - b) + 2b = 68 - 4b + 2b = 62b = 8 - 62b = 2b = 1Then
a = 2 - 1 a = 1So we know the coefficients:
a = 1, b = 1, c = 13The nth term equation is:
tₙ = n² + n + 139-3-3-3 = 0 written as a division problem
The value of 9-3-3-3=0 written as division problem is the value of 0.333
According to the Honor algebra:
The symbols for variables used in algebra, which may be found in Greek and Latin literature, can be used to date the creation of algebra to the height of Greek or Latin culture.
9-3-3-3=0 as written as division
⇒ 9÷3÷3÷3 =0
⇒ 9÷3 =3÷3
⇒ 3=1
⇒ x=1/3
⇒ x=0.333
so, the value of 9 divide by 3 and divided by 3 equals to 3 divvied by 3 is the value of 0.333.
When things are more realistic, algebra becomes much more intriguing. With a two-pan balance, some mystery bags, and a ton of jelly beans, solving linear equations is much more enjoyable.
Therefore, the 9-3-3-3=0 written as division is the value of 0.333.
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Ellen's living room is 5 meters wide and 7 meters long. She wants to install indigo carpet that costs $10.00 per square meter. How much will it cost to buy enough carpet for the living room?
It will cost $350.00 to buy enough carpet for the living room.
What is an area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of the three-dimensional object.
Now it is given that,
Length of room,l =
Width of room, w =
So, area of the room = l*w = 7*5
⇒ area of the room = 35 square meter
Since, indigo carpet costs $10.00 per square meter
Thus, total cost to install the carpet = area of the room*carpet costs
⇒ total cost to install the carpet = 35*10
⇒ total cost to install the carpet = $350
Thus, It will cost $350.00 to buy enough carpet for the living room.
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Which of the following is not an example of an experiment? Multiple choice question.
Picking a team that will win the World Series.
Selecting a card from a deck of cards.
Pick the team that won last year's World Series.
Buying a computer based on repair history.
The answer option which is not an example of an experiment is to: C. pick the team that won last year's World Series.
What is an experiment?An experiment can be defined as a scientific investigation which typically involves the process of manipulating an independent variable (the cause), so as to determine or measure the dependent variable (the effect).
In this scenario, some examples of an experiment include the following:
"Picking a team that will win the World Series.""Selecting a card from a deck of cards.""Buying a computer based on repair history."In conclusion, "picking the team that won last year's World Series" is not an example of an experiment because it does not connote a scientific investigation or observation
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Which expression is the completely factored form of x³ + 8y6 ?
O (x+2y²) (x² - 2xy² + 4y¹)
○ (x+2y²) (x² + 4yª)
○ (x+2y²)³
(x − 2y²) (x² + 2xy² + 4y¹)
-
Attached is the Correct Answer Please verify yours.
[tex](x + 2 {y}^{2} )( {x}^{2} - 2x {y}^{2} + 4 {y}^{4} )[/tex]
What are the roots of the function f(x) = (log(3^x
) − 2 log(3)) - (x^
2 − 1) with x ∈ R
(-4c³d)²
someone answer this asap i’ll make it the brainiest please
1.
Solve the Decimal Division Application. Round to the nearest tenth if needed.
There is approximately 0.16 square inches in 1 square centimeter. Determine
how many square centimeters are in 64 square inches.
40,000 square centimeters
10.2 square centimeters
400 square centimeters
4,000 square centimeters
Answer:
c, 400
Step-by-step explanation:
64 square in. = 412.902 square cm
412.902 rounded equals 400
hope that helps <3
5. Which value is an integer but not a whole
number?
A. 75%
B. 5¹.10
C. √20
D. -4³/16
Answer: √20
Step-by-step explanation:
The square root of 20 is 4.47213595 which is a decimal and not a whole number.
Employees in 2012 paid 4.2% of their gross wages towards social security (FICA tax), while employers paid another 6.2%. How much will someone earning $39,000 a year pay towards social security out of their gross wages?
Someone who is earning $39,000 a year, would pay $1,638 towards social security out of their gross wages
Employees in 2012 paid 4.2% of their gross wages towards social security tax.
As the gross yearly wages of an employee is $39,000 and he have to pay the 4.2% of his gross wages towards social security or FICA tax.
Percentage means division by 100 and to know the contribution of the employee we need to multiply the percentage with the gross wages of the employee
He paid towards social security = 4.2% of 39000
= 4.2/100×39000
= 0.042 × 39000
= $1,638.00
He would pay $1,638 towards social security tax out of their wages.
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Angle Z and Angle X on intersecting lines are vertical angles. If Angle Z is 63°, what is Angle X?
The measure of angles X if Angle Z and Angle X on intersecting lines are vertical angles is 63 degrees
Vertical anglesVertical angles are a pair of opposite angles formed by intersecting lines. In vertical angles, the angles meet at point X.
Given the following parameters
angle Z = 63degrees
If the angleZ and angle X are vertical angles, hence <X = <Z
Therefore;
<X = 63 degrees
Hence the measure of angles X if Angle Z and Angle X on intersecting lines are vertical angles is 63 degrees
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Please help describe each transformation in order 1-3
Answer:
A translation 4 units right and 5 units down followed by a rotation of 90 degrees clockwise about the top left vertex of triangle 2
Please help fast thanks
Step-by-step explanation:
try this option, all the details are in the attachment.
What is the area of the composite figure whose vertices have the following coordinates? (2,-2), (2,1), (4,2), (6,2), (4,-1)
Enter your answer in the box.
__Units Sqared
The area of the composite figure whose vertices have the (2,-2), (2,1), (4,2), (6,2), (4,-1) coordinates is 6 square units
We first need to plot all the given points A (2,-2), B (2,1), C (4,2), D (6,2)and E (4,-1) which is coordinate geometry
After joining the Points which is a pentagon and it can be divided in two shapes one is triangle CDE and a quadrilateral ABCE
Using the distance formula
BC = [tex]\sqrt{(y2-y1)^{2}+(x2-x1)^{2} }[/tex] = [tex]\sqrt{(2-1)^{2} + (4-2^{2} }[/tex] = √5
Since BC = AE and BC ll AE , we can say ABCE is a parallelogram
area of a parallelogram = base × Altitude
= 2 × 2= 4
Area of triangle CDE where CD is perpendicular and CE is the base
= 1/2 ( 2×2)
= 1/2 (4)
= 2 square units
So the area of ABCDE = Area of ABCE + area of CDE
= 4 square units + 2 square units
= 6 square units
Hence, the area of the composite figure whose vertices have the (2,-2), (2,1), (4,2), (6,2), (4,-1)coordinates is 6 square units
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Solve for x: −7 < x − 1 < 8 (1 point)
6 < x < 9
−6 > x > 9
6 > x > −9
−6 < x < 9
The value of x in the inequality is: D. -6 < x < 9
How to Solve an Inequality?Given the inequality, −7 < x − 1 < 8, solve for the possible values of x as shown below:
−7 < x − 1
Add 1 to both sides
-7 + 1 < x - 1 + 1
-6 < x
or
x − 1 < 8
Add 1 to both sides
x - 1 + 1 < 8 + 1
x < 9
Combining both inequalities together, the value of x is: D. -6 < x < 9
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Answer:
98 Glass pitchers.
Step-by-step explanation:
You can determine this is the answer due to multiplying the sum and the product together, making the final answer 98 Glass pitchers. Hope this helped! :D
(X₁ + X₂)²
Find the square.
Show your work
Step-by-step explanation:
[tex]{ \purple{ \tt{(X₁ + X₂)²}}}[/tex]
This above problem is in the form of
[tex]{ \blue{ \tt{ {(a + b)}^{2}}}}[/tex]
where the expanded form of
[tex]{ \blue{ \tt {(a + b)}^{2}}} = { \green{ \bold{ {a}^{2} + {b}^{2} + 2ab}}} [/tex]
then the (X₁ + X₂)² answer will be
[tex]{ \purple{ \tt{(X₁ + X₂)²}}} = { \purple{ \tt{ {X₁}^{2} + {X₂}^{2} + 2X₁X₂}}}[/tex]
During an experiment, the temperature of a mixture changes from 12 1/4°F to 15 3/5°F. What is the percent of the increase in the temperature of the mixture? I need an answer to the as a percent rounded to the nearest hundredth.
During the experiment the temperature changes slightly. Hence
the percentage increase in the temperature of the mixture is 27.35%.
Given, the temperature of the mixture changes from 12 1/4°F to 15 3/5°F
we are asked to determine the percentage of increase in the temperature of the mixture.
Initial temperature = 12 1/4°F
convert it into proper fraction.
= 48+1/4
= 49/4°F
Final temperature = 15 3/5°F
convert it into proper fraction.
= 75+3/5
= 78/5
Therefore, percentage increase:
= Final temp - Initial temp/Initial temp × 100
% Increase = (78/5 - 49/4)/49/4 × 100
% Increase = (78×4 - 49×5/5×4)/49/4 × 100
% Increase = 312-245/5×49 × 100
as 4 gets cancelled from numerator and denominator.
% Increase = 67×100/249
% Increase = 6700/249
% Increase = 27.346%
we need to round it off to the nearest hundredth.
% Increase = 27.35%
Hence the percentage increase in the temperature is 27.35%.
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Which of the following represents an INEFFICIENT point of production?
a. Point A
b. Point B
c. Point D
d. None
e. Point C
The point that represents an INEFFICIENT point of production is point A.
The correct answer is an option (a)
In this question we have been given a graph of Skateboards vs. Bikes.
We need to find the point that represents an INEFFICIENT point of production.
Inefficient production means the economy can be producing more goods without using any additional resources.
In given production possibility curve, an INEFFICIENT point of production is point A.
Therefore, the point that represents an INEFFICIENT point of production is point A.
The correct answer is an option (a)
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The function F(x) = −0.005x 2 + 0.8x + 12 models the relationship between a certain vehicle’s speed and the fuel economy, where F(x) is the fuel economy in kilometres per litre and x is the speed of the vehicle in kilometre per hour.
a) Determine the average rate of change in the fuel economy in the interval of speed [60,80].
b) b) Interpret your result.
The average rate of change in the fuel economy in the interval of speed [60,80] is 0.1
The given function F(x) = −0.005x 2 + 0.8x + 12 models the relationship between a certain vehicle’s speed and the fuel economy
where F(x)= fuel economy in kmpl
x =speed of the vehicle in km/h
we need to find the average rate of change in the fuel economy in the interval of speed [60,80].
At speed 60 km/h
the fuel economy = - 0.005(60²) + 0.8(60) +12
= - 18 + 48 + 12
= 42 kmpl
At speed 80 km/h
the fuel economy = - 0.005(80²) + 0.8(80) +12
= - 32 + 64 + 12
= 44 kmpl
the average rate of change is given by the formula = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
By substituting the values we get= [tex]\frac{44- 42}{80-60}[/tex]
= 2/ 20
= 0.1
Hence, The average rate of change in the fuel economy in the interval of speed [60,80] is 0.1 which reflects that for increase in every one kilometer there is increase in fuel economy by 0.1
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Convert the following expression to scientific notation.
0.000000000001 =
Choice 'A'
Choice 'B'
Choice 'C'
Choice 'D'
1.0 × 10-12
10.0 × 10-12
10.0 × 10-10
1.0 x 1010
Answer:
none of them
Step-by-step explanation:
2) Use three functions above to evaluate the following: input f(x)=x-3_soupat f(3) = -3 p(0) = p(x)=0, x= function p(-4)= x/g(x) p(x)=5, x= 5 2 -3 f(x)=12, x=-4 f-3 = 12 -3 36207 g(-3)= p(1)= | p(3)= g(x)= -3, x = 95 = -3 p(x)=1, x= p(x)=2, x=
Answer:
f(3) = 3 - 3 --> f(3) = 0
f(x) = 12, x = 15 (because 15 - 3 would equal 12)
g(-3) = 2 (because in the chart for g(x), an x of -3 is 2)
g(x) = -3, x = 5 (because in the chart for g(x), a g(x) of -3 is an x of 5)
For the graph questions, p(0)= means that the 0 is the x integer and you must find the y when x=0
p(0) = 3
p(-4) = 5
p(1) = 3
p(x) = 1, x = 2
For the graph questions, p(x)=0 means that the 0 is the y integer and you must find the x when y=0
p(x) = 0, x = 2.5
p(x) = 5, x = -4
p(3) = -1
p(x) = 2, x = 1.5
A garden store Sells bags of potting soil in flats. There are 7 Bags in each flat . each palette has 7 flats the garden store sold 17 pallets on Saturday and 23 How many bags of potting soil did the gardner sell in all ?
The garden store was able to sell a total of 1,960 bags of potting soil on Saturday and Sunday.
What is distributive property of multiplication over addition ?
If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.
In order to find the number of bags of potting soil sold over those two days, the first step is find out the number of pallets store sold there potting soil :
= 17( on Saturday) + 23 (Sunday)
= 40 palettes
Each palettes has 7 flats so the total number of flats sold is:
= 40 x 7
= 280 flats
Each flat then contains 7 bags so the total number of bags sold is:
= Number of flats sold x 7
= 280 x 7
= 1960 bags
In conclusion 1,960 bags of potting soil were sold.
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*100 POINTS ANSWER ASAP*
Complementary Angles- When the sum of two angles is equal to 90 degrees, they are called complementary angles. (For example, 30 degrees and 60 degrees are complementary angles)
Supplementary Angles-Supplementary angles are those angles that sum up to 180 degrees. (For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°.)
Congruence Postulate- to be congruent if two angles and the side between these two angles of one triangle are congruent to corresponding angles and the included side (side between two angles) of the other triangle
Linear Pairs of Angles-A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
PLS HELLP!!
Which expression is equivalent to sum of quantity negative three and one third times n plus one sixth end quantity plus quantity one and three sixths times n minus three twelfths end quantity?
negative twenty nine sixths times n minus one twelfth
negative twenty nine sixths times n plus one twelfth
negative eleven sixths times n minus one twelfth
negative eleven sixths times n plus five twelfths
The equivalent expression is negative eleven sixths times n minus one twelfth. Option C
What are algebraic expressions?Algebraic expressions are expressions that comprises of variables, terms, constants, coefficients and factors.
They are also made up of arithmetic operations such as division, multiplication, addition, subtraction, bracket, etc.
Equivalent expressions are expressions with the same solution but different arrangement of elements.
Given the expression
{ -3 1/3n + 1/6} + { 1 3/6n - 3/12 }
expand the bracket
-3 1/3n + 1/6 + 1 3/6n - 3/12
collect like terms
-10/3n + 1/6 + 9/6n - 3/12
-10/3n + 9/6n + 1/6 - 3/12
find the lowest common multiple
-20n + 9n/6 + 2 - 3 /12
-11n/6 - 1/12
Thus, the equivalent expression is negative eleven sixths times n minus one twelfth. Option C
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what is the linear equation that has a y-intercept of -4 and a x-intercept of -5
The linear equation that has a y-intercept of -4 and a x-intercept of -5 s y = -4/5x - 4
Equation of a lineThe equation of a line in slope intercept form is expressed y = mx + b
where
m is the slope
b is the y-intercept
Given the coordinate points (0, -4) and (-5, 0), the slope is calculated as:
Slope = y₂-y₁/x₂-x₁
Slope = 4/-5
Slope = -4/5
Determine the equation
y = -4/5x + (-4)
y = -4/5x - 4
Hence the linear equation that has a y-intercept of -4 and a x-intercept of -5 s y = -4/5x - 4
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Difference between the two sets
[tex] \\ \\ [/tex]
Let A = {1, 2, 3, 4, 5, 6, 7} B = {1, 3, 5, 7, 9} C = {0, 2, 4, 6, 10} Find the difference of the given pair of sets.
1.) A - B
2.) B - A
3.) (A ∪ B) - C
Answer:
1) A - B = {2, 4, 6}
2) B - A = {9}
3) (A ∪ B) - C = {1, 3, 5, 7, 9}
Step-by-step explanation:
Set Notation
[tex]\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}[/tex]
Given sets:
A = {1, 2, 3, 4, 5, 6, 7}B = {1, 3, 5, 7, 9}C = {0, 2, 4, 6, 10}Question 1
[tex]\begin{aligned}\sf A-B & =\sf \{ 1, 2, 3, 4, 5, 6, 7 \} - \{1, 3, 5, 7, 9 \}\\& =\sf \{ 2, 4, 6 \}\end{aligned}[/tex]
Question 2
[tex]\begin{aligned}\sf B-A & =\sf \{1, 3, 5, 7, 9 \} - \{ 1, 2, 3, 4, 5, 6, 7 \}\\& =\sf \{9 \}\end{aligned}[/tex]
Question 3
[tex]\begin{aligned}\sf (A \cup B)-C & =\sf \left(\{ 1, 2, 3, 4, 5, 6, 7 \} \cup \{1, 3, 5, 7, 9 \} \right) - \{0, 2, 4, 6, 10 \}\\& =\sf \{ 1, 2, 3, 4, 5, 6, 7, 9 \} - \{0, 2, 4, 6, 10 \}\\& = \sf \{ 1, 3, 5, 7, 9 \}\end{aligned}[/tex]
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