The remainder when polynomial function is divide by linear function is 773.
Given that the polynomial functon f(x)=3x⁴+5 and the linear function is x+4.
As it is given that we have to find the remainder the polynomial
f(x)=3x⁴+5 is divided by the linear expression g(x)=x+4.
f(x)=3x⁴+5 .......(1)
g(x)=x+4 .......(2)
We know the remainder theorem that when a polynomial f(x) is divided by a linear expression (x−a), the remainder will be f(a).
From equation (2), we have a linear expression.
Now, on simplifying equation (2) to obtain the zero of g(x), we get
g(x)=x+4=0
x+4=0
Now, on comparing (x+4) and (x−a), we get
a=-4 ......(3)
Here, we have to get the value of f(a).
Now, using the remainder theorem, we can say that to get the remainder when the polynomial f(x)=3x⁴+5 is divided by g(x)=x+4, we have to replace x by -4 in the polynomial f(x)=3x⁴+5, we get
f(-4)=3(-4)⁴+5
f(-4)=3(256)+5
f(-4)=768+5
f(-4)=773
Therefore, the remainder when the polynomial f(x)=3x⁴+5 is divided by the linear expression g(x)=x+4 is 773.
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Solve for the value of x in the diagram below.
MP Reason Abstractly If y varies directly with x-
direct variation. Then find each value.
9. If y = 14 when x = 8, find y when x = 12.
The cost of one pound of grapes, g, is 15 cents more than one pound of apples, a. The cost of one pound of
bananas, b, is twice as much as one pound of grapes. Write an equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples
An equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples is,
⇒ b = 2a + 30
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Cost of one pound of grapes = g
Cost of one pound of apples = a
Cost of one pound of banana = b
Since, The cost of one pound of grapes is 15 cents more than one pound of apples.
It can be written as;
g = a + 15 .... (i)
And, The cost of one pound of bananas is twice as much as one pound of grapes.
It can be written as;
b = 2g ..... (ii)
To find an equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples as,
Put the value of g from (i) in (ii) we get,
b = 2 ( a + 15 )
b = 2a + 30
Hence, An equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples is,
⇒ b = 2a + 30
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A leather recliner with a regular price of $795.00 is on sale for 15% off. What is the sale price of the recliner?
Answer:
$675.75
Step-by-step explanation:
To find the sale price of the recliner, we can multiply 15% by the regular price.
15% = 0.15
(0.15)(795.00) = $119.25
This gives us the amount that the sale takes off from the regular price. We can subtract that from the regular price to find the sale price.
795.00 - 119.25 = $675.75
A bonus shortcut way to get our answer would be to subtract 15% from 100%.
100% = 1.00
1.00 - 0.15 = 0.85
This tells us that the sale price is 85% of the regular price. Using this information, we can multiply 85% by the regular price to also get our sale price.
85% = 0.85
(0.85)(795.00) = $675.75
(-125) power -1/3
Evaluate this with step by step
water main construction a water main is to be constructed with a 20% grade in the north direction and a 10% grade in the east direction. determine the angle θ required in the water main for the turn from north to east.
The value of the angle θ required in the water main for the turn from north to east is 87.40°.
According to the statement
We have to find that the value of the angle.
So, For this purpose, we know that the
An angle is created when two straight lines or rays meet at a standard endpoint.
From the given information:
a main is to be constructed with a 20% grade within the north direction and a tenth grade within the east direction.
Then
Let n = North
and e = east
Then
using vectors,
n = j + 0.20 k
e = i + 0.25 k
And the
n · e = 1x0 + 0x1 + 0.20×0.25 = 0.05
Now take magnitude then
|n|·|e| = i(1² + 0.20²)·i(1²+0.25²) = 1.105
Now,
E° = arccos((n · e)/|n|·|e|)
E° = arccos(0.05/1.105)
E° = arccos (0.0452)
E° = 87.40°
So, The value of the angle θ required in the water main for the turn from north to east is 87.40°.
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y = -4.2x + 7.9 in standard form
The equation of the line y = -4.2x + 7.9 expressed in standard form is 42x + 10y = 79.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is written as axe + by = c, where a and b are the coefficients of the variables x and y, respectively, and c is a constant. On the other hand, we can write the equation in point-slope form, (y - y1) = m, if we know the slope m and a point on the line (x, y).
Given the equation of a line, multiply both sides by 10 to turn the decimals into integers.
y = -4.2x + 7.9
10y = 10(-4.2x + 7.9)
10y = -42x + 79
Rewriting it in standard form ax + by = c,
10y = -42x + 79
42x + 10y = 79
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the domain of consists of numbers x for which not equals equals not equals 0 that are in the domains of both f and g. both f and g. either f or g.
The statement is true that the domain of f(x)/g(x) consists of numbers "x" that are in the domains of both f(x) and g(x) for which g(x) is not equal to 0.
A function's area is the set of its available inputs, or the set of enter values for which the characteristic is described. The area is the collection of objects that the system will take delivery of as inputs within the characteristic machine paradigm.For the function f(x)/g(x) to be defined, g(x) must now not be equal to 0.hence, the domain of the characteristic f(x)/g(x) consists of all of the numbers "x" which can be inside the domain names of each the functions f(x) and g(x) for which g(x) is not 0.To learn more about functions, visit :
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5) 2(n + 5) = 20
what is the answer need immediately
What is 7+7?
Easy Brainly and points if 2 ppl answer :)
The answer to this question is 14
50 points mathamatics please help
Answer:
Option B: 6342
Step-by-step explanation:
Answer: 6342
Step-by-step explanation:
906 x 7 = 6342
Hello I will AWard Brainlist !!! Help its A Math Question Please Help I will AWard Brainlist thanls so much !!!
The lengths 9, 9 / 2 and 9√3 are not part of a 30 - 60 - 90 right triangles. (Correct choice: A)
What set of measures are associated with a 30 - 60 - 90 right triangles?
Herein we must find what set of lengths are part of a 30 - 60 - 90 right triangle. In accordance with the Euclidean geometry, there are the following relationships for the sides of the 30 - 60 - 90 right triangle:
The longest leg is √3 times the length of the shortest leg.The hypotenuse is 2 times the length of the shortest leg.The hypotenuse is 2√3 / 3 times the length of the longest leg.Now we proceed to check if each set of sides belongs to a 30 - 60 - 90 right triangle:
Case 1
The length of the shortest leg of the triangle is 9 / 2, then the lengths of the longest leg and the hypotenuse are 9√3 / 2 and 9, respectively. (False)
Case 2
The length of the shortest leg of the triangle is 4, then the lengths of the longest leg and the hypotenuse are 4√3 and 8, respectively. (True)
Case 3
The length of the shortest leg of the triangle is 7, then the lengths of the longest leg and the hypotenuse are 7√3 and 14, respectively. (True)
Case 4
The length of the shortest leg of the triangle is 5 / 3, then the lengths of the longest leg and the hypotenuse are 5√3 / 3 and 10 / 3, respectively. (True)
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Which expression is equivalent to (9^-2x3^5)-2?
Answer:
1
Step-by-step explanation:
3^-4 x 3^5
3 - 2
=1
PLSS HELP :((
will mark brianlist if its the correct answer ty
Use the Distributive Property to rewrite each expression.
4(x + 2y - 3)
Answer:4x + 8 y -12
Step-by-step explanation:
What is the value of the digit 7 in the population of Memphis? What is the value of the digit 1 in the population of Denver? How many times as great as the value of the digit 1 in the population of Cleveland in this value?
PLSS HELP IT WILL MAKE ME FAIL
The number of times that the value of the digit 1 in the population of Cleveland in this value is 10.
How to illustrate the information?Based on the information, it should be noted 7 is in ten thousand place for Memphis. This means that it represents 70000.
It should be noted the 1 in Denver is in the same place. It represents 10000. On Cleveland, this is 1000.
Therefore, the number of times will be:
= 10000 / 1000
= 10
Therefore, the correct option is 10.
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Cleveland population 431,369 Denver population 610,345
Memphis population 676,640 What is the value of the digit 7 in the population of Memphis? What is the value of the digit 1 in the population of Denve?How many times as great the value of the digit 1 in the population of Cleveland is this value?
(-7,10) perpendicular to 2x - 3y= -3 using slope-intercept form
y = -3/2x - 20.5 is the line crossing through (-7,10) perpendicular to 2x - 3y= -3
In an equation, parallel lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.
Here given that 2x - 3y= -3
can also be written as
y = 2/3x + 1
Here 2/3 is the slope and 1 is the y-intercept
To find a parallel line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.
y - y₁ = m(x - x₁)
We have, m = -3/2, x₁ = -7 and y₁ = 10
y - 10 = -3/2(x - (-7))
y - 10 = -3/2(x + 7)
y - 10 = -3/2x - 21/2
y = -3/2x - 21/2 + 10
y = -3/2x - 20.5
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At the end of 1994 Walters Was half as old as his grandmother. The sum of the years in which they were born in 3838. How old will Walter be at the end of 1999?
The age of Walter at the end of year 1999 will be equal to 55 years.
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.
Let's assume respective age of Walter and Walter's grandmother is x and y years respectively.
In 1994 , age of Walter was :
x = y / 2
or y = 2x
It is also given that the sum of years they were born is 3838.
The year Walter was born = (1994 - x)
The year Walter's grandmother was born :
= (1994 - y)
= 1994 - 2x (∵ y = 2x)
So , we can write an equation to find out Walter's age which is :
1994 - x + 1994 - 2x = 3838
3988 - 3x = 3838
3x = 3988 - 3838
x = 150 / 3
x = 50 years
or the age of Walter in 1994 is 50 years.
At end of 1999 Walter's age will be:
= 50 + 5.
= 55 years
Therefore , the age of Walter at the end of year 1999 will be equal to 55 years.
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place these number from least to greatest
-3
6
3.1
-2.5
1/4 -3/4
Given L is between N and M, NL = 6x - 5, LM = 2x + 3, and NM = 4x + 9. Determine if L is the midpoint of segment MN. Justify your answer using sound mathematical reasoning.
Answer: L isn't the midpoint of segment MN.
Step-by-step explanation:
NL+LM=NM
6x-5+2x+3=4x+9
8x-2=4x+9
8x-2+2=4x+9+2
8x=4x+11
8x-4x=4x+11-4x
4x=11
Divide both parts of the equation by 2:
2x=5.5
NL=6x-5
NL=(2x)(3)-5
NL=(5,5)(3)-5
NL=16.5-5
NL=11.5
LM=2x+3
LM=5.5+3
LM=8.5
NL≠LM
Hence, L isn't the midpoint of segment MN.
In summary, based on the given lengths and mathematical reasoning, we have determined that point L is the midpoint of segment MN because the lengths of NL and LM are equal when x = 2.
We must compare the lengths of the two segments NL and LM and see if they are identical in order to establish whether point L is the midpoint of segment MN.
NL = 6x - 5
LM = 2x + 3
The lengths of NL and LM ought to be equal if L is the middle of segment MN. To put it another way, NL and LM ought to be equal.
Constructing the equation
6x - 5 = 2x + 3
Now, solve for x:
6x - 2x = 3 + 5
4x = 8
x = 2
As soon as we know the value of x, we can put it back into the NL and LM formulas to get their lengths at x = 2:
NL = 6x - 5 = 6 * 2 - 5 = 12 - 5 = 7
LM = 2x + 3 = 2 * 2 + 3 = 4 + 3 = 7
The lengths of NL and LM are both 7 units.
Point L is in fact the middle of segment MN because both segments NL and LM have similar lengths.
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the price of a tv is £950 plus VAT at 20% .what is the total cost of the TV?
1140 is the final price.
Step-by-step explanation: 20% of 950 is 190, so add that to 950 and you get 1140
to determine whether or not number of complaints influences accidents occurring in an area, charles has designed a survey. what is the explanatory variable?
In the survey study, the explanatory variable is: number of complaints .
What is an Explanatory Variable?An explanatory variable can be described as a type of independent variable that is manipulated by the researcher which explains the or predict the differences that occurs in a response variable.
For example, number of complaints is the independent variable that the dependent variable, "accidents that occurs in an area" depends on. That is, it explains or predicts the accidents that occurs in an area.
Therefore, we can conclude that, in the survey study, the explanatory variable is: number of complaints .
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how can i solve literal equations?
Literal equations are equations containing two or more variables. Our goal is to solve for just one variable with respect to others. If it is known to us that how to solve regular equations, then literal equations are very easy to solve.
Literal equation is also termed as simultaneous equation ,
where more than 1 variable is present and can be solved by inputting value entirely into 1 variable form
For example,
x+ y=6
x-y=2
now putting x=y+2 from the second equation,
y+2+y=6
2y+2=6
y+1=3
y=2
x=y+2=2+2=4
To solve a literal equation means to express one variable with respect to the other variables in the equation.
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Equations that have two or more variables are considered literal equations. Our aim is to solve for a single variable in relation to other variables. Literal equations are fairly simple to solve if we know how to solve regular equations.
Simultaneous equation is another name for a literal equation.
where a problem with more than one variable can be handled by entering all of the values into a single variable form.
For Example :
x + y = 6
x - y = 2
Now putting x = y + 2 from the equation
y + 2 +y = 6
2y + 2 = 6
2y = 6-2
2y = 4
y = 2
Hence,
x = y + 2 = 2 + 2 = 4
To express one variable in relation to the other variables in an equation is to solve it literally.
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an equilateral triangle has three congruent sides that measure 1.5 inches on each side. what is the perimeter of the triangle?
The perimeter of the triangle is 4.5inches.
Equilateral Triangle : can be defined as a triangle having all three sides equal.
Perimeter of triangle is defined as the sum of the lengths of the three side.
Perimeter of triangle is denoted by 3x(side).
Given that the side of the triangle is 1.5 inches
Perimeter = 3x(1.5)
Perimeter=4.5 inches
Therefore , The Perimeter of the triangle is 4.5 inches .
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a rectangle has perimeter 24 m. express the area a of the rectangle as a function of the length, l, of one of its sides.
The Expression for the Area a of the rectangle as a function of length L is given by A(L) = 12L - L^2 .
Let,
length, L, and the width, W, are components that help determine the area, A, and the perimeter, P of the rectangle. These are given by the following equations
A=LW
P=2L+2W
Given,
Perimeter of the Rectangle = 24m.
We are asked to express the perimeter of the rectangle as a function of the length, L, of one of its sides.
We will first set up the equation of the Perimeter of the rectangle. We can let the width of the rectangle be W.
P = 2L+2W
24 = 2L+2W
12 = L+W
W = 12-L
Since we want to express the Area as a function of L, we have to find the value of W in terms of L. This is so we can eliminate the width in the equation for the Area. The Area as a function of L is as follows.
A(L, W) = LW
A(L) = L(12-L)
A(L) = 12L-L^2
Therefore, the Area as a function of L is given by A(L) = 12L-L^2.
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The altitude a (in feet) of a plain t minutes after liftoff is given by a= 3400t + 600. How many minutes after liftoff is the plane at an altitude of 21,000 feet?
The number of minutes after liftoff of the plane at an altitude of 21,000 feet is 6 minutes
What is a function?A function can be defined as an expression or law that shows the relationship between a dependent and independent variable.
Given the function;
a= 3400 t + 600
Where;
a is the altitude in feett is the time in minutesIf the altitude is 21000 feet, let's determine the time
Substitute the value into the function
21000 = 3400t + 600
collect like terms
21000 - 600 = 3400t
20400 = 3400t
Make 't' the subject
t = 20400/ 3400
t = 6 minutes
Thus, the number of minutes after liftoff of the plane at an altitude of 21,000 feet is 6 minutes
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There were approximately 3.3 * 10 8 people in the united states of america in 2010 the average person ate 1.5 * 10 2 lb of sugar that year approximately how many pounds of sugar were eaten in the us in 2010
Amount of sugar eaten in the US in 2010 = 4.95 x 10¹⁰ lb
Approximate number of people in the United States of America in 2010 = 3.3 x 10⁸
Amount of sugar ate by an average person in US = 1.5 x 10² lb
We have to find an approximate amount of sugar eaten in US in 2010.
It will be the product of the number of people in US and the sugar ate by a person in US.
So, Amount of sugar eaten in the US in 2010 approximately = 3.3 x 10⁸ x1.5 x 10²
= 4.95 x 10¹⁰ lb
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Describe in words where cube root of 70 would be plotted on a number line.
A Between 3 and 4, but closer to 3
B Between 3 and 4, but closer to 4
C Between 4 and 5, but closer to 4
D Between 4 and 5, but closer to 5
Answer:
C Between 4 and 5, but closer to 4
Step-by-step explanation:
cube root of 70 is 4.1212
HELP PLEASE I DON'T UNDERSTAND :[
Answer: the first option i believe
Step-by-step explanation:
based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least how many miles per gallon? 15
The number if miles per gallon is 35 miles.
How to solve the box plot.
From the information, it was stated that the box plot shows a gas mileage for twenty cars.
Therefore, based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least 35 miles per gallon.
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20796