Part A: polynomial in Standard form;-
bluef(x) = ax⁴ + bx³ + cx²+ dx + e
Part B: Closure property relates to polynomial;-
The polynomial's closer property for subtraction. When two polynomials of identical degrees with different leading coefficients are subtracted, a polynomial of the same degree is produced.
What is Polynomial?
A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.
A.
Any of the following can be the fourth degree polynomial with two terms:
f1(x) = ax⁴ + bx³
f2(x) = ax⁴ + cx²
f3(x) = ax⁴ + dx
f4(x) = ax⁴ + e
a ≠ 0 in all four instances.
Explanation. Because each of the aforementioned polynomials fi(x)-s can be written in the form of f(x) by setting blue0 equal to (c,d,e), (b,d,e), (b,c,e), and (b,c,d), respectively, each of the aforementioned polynomials is in standard form.
B.
The polynomial's closer property for subtraction. When two polynomials of identical degrees with different leading coefficients are subtracted, a polynomial of the same degree is produced.
Example.
Let r(x) be defined as a₁x³ + a₂x² + a₃x + a₄
s(x) is equal to b₁x³ + b₂x² + b₃x + b₄
where a ≠ 0 ≠ b and a ≠ b both belong to a set of real or complex numbers called ai and bi.
If this is how subtraction is defined, then
r(x) - s(x) = [a₁x³ + a₂x² + a₃x + a₄] - [b₁x³ + b₂x² + b₃x + b₄]
r(x) - s(x) = (a₁ - b₁)x³ + (a₂ - b₂)x² + (a₃ - b₃)x + (a₄ - b₄)
Given that (a₁ - b₁) ≠ 0, r(x) - s(x) is similarly a polynomial of fourth degree in this situation.
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A store owner bought dog bowls for $6 and sold them for $8.10. What is the mark-up, as a percentage?
Answer:I am not fully going to do it for you, but here is the best way i can explain, it if not i am sorry.
Step-by-step explanation: Simply take the sales price minus the unit cost, and divide that number by the unit cost. Then, multiply by 100 to determine the markup percentage. For example, if your product costs $50 to make and the selling price is $75, then the markup percentage would be 50%: ( $75 – $50) / $50 = . 50 x 100 = 50%.
Is 4 ÷ 3/2 the same as 4 ÷ 2/3. Explain
7. Write the equation of the line that is parallel to the line
represented by the table and passes through the point
(-3,-10).
X
0
4
8
12
Y
10
6
2
-2
The equation of the line that is parallel to the line y = -x + 10 is y = -x - 13.
Given table:
x y
0 10
4 6
8 2
12 -2
slope m = 6 - 10 / 4 - 0
= -4/4
m = -1
substitute in y=mx+c
y = -x+c passes through (0,10)
10 = -0 + c
c = 10.
y = -x + 10.
here m = -1 and passes through (-3,-10)
y = mx +c
-10 = -1(-3)+c
-10 = 3 + c
c = -13
y = -x + (-13)
y = -x - 13.
Therefore the equation of the line that is parallel to the line y = -x + 10 is y = -x - 13.
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4 - 3x = 8 - 4x please help
Step-by-step explanation:
we switch the like terms across the equation and when we do that we change the signs
PLEASE HELP ASAPPPPP ILL GIVE BRAINLIEST PLEASEEEEEE
Rewrite x³y + xy²
x³y +
xy(x² +5y)
xy² using a common factor.
xy(3x² +15y)
xy(x² +5y)
1x³y² (y + 5x)
Answer:
[tex] \frac{1}{6} {x}^{3} y + \frac{5}{6} x {y}^{2} \\ \frac{1}{6} xy( {x}^{2} + 5y)[/tex]
option 3 is correct
A train traveled at the same speed for 9 hours. It went 320.55 miles in all. To the nearest hundredth of a mile per hour, how fast was the train going?
The train's speed was= 56.7 miles per hour
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
Entire distance = 210 miles + 130 miles = 340 milesTotal time = 3.5 hours and 2.5 hours = 6 hoursAverage speed = distance/ time = 340 miles/ 6 hours= 56.66666666666 miles per hourRounding to the nearest tenth= 56.7 miles per hourHence, The train's speed was= 56.7 miles per hour
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-7.3, 7 3/4, 7.23, -7 2/3. Order the following rational numbers from least to greatest.
The order of the rational numbers from the least to greatest is [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 < [tex]7\frac{3}{4}[/tex] .
in the question ,
it is given that the rational numbers are -7.3, [tex]7\frac{3}{4}[/tex], 7.23, [tex]-7\frac{2}{3}[/tex] .
we have to arrange the rational numbers in order from least to greatest .
For arrangement we first convert all the rational numbers in decimal form .
the decimal form of the given rational numbers are as follows .
(i) -7.3 is already given in decimal form .
(ii) [tex]7\frac{3}{4}[/tex] = (7*4+3)/4 = (28+3)/4 = 31/4 = 7.75
(iii) 7.23 is already in decimal form .
(iv) [tex]-7\frac{2}{3}[/tex] = -(7*3+2)/3 = -23/3 = -7.666
the order is -7.666 < -7.3 < 7.23 < 7.75
which is [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 < [tex]7\frac{3}{4}[/tex]
Therefore , The order of the rational numbers from the least to greatest is [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 < [tex]7\frac{3}{4}[/tex] .
The given question is incomplete , the complete question is
Order the following rational numbers from least to greatest.
-7.3, [tex]7\frac{3}{4}[/tex], 7.23, [tex]-7\frac{2}{3}[/tex] .
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someone pls help this is the last question im begging you im gonna cry
Answer:
x = 10
Step-by-step explanation:
48 = x + 8 + 2x + x
48 = 4x + 8
-8 -8
40 = 4x
divide both sides by 4
10 = x or x =10
Please help me solve this
The value of a=2 and b= 4.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
a + 1 / b-1 = 5/1 and a-1/ b+ 1 = 1/1
So, a + 1 / b-1 = 5/1
now, cross multiplying
a+ 1 = 5b - 5
a- 5b = -6............(1)
Also, a-1/ b+ 1 = 1/1
a-1 = b + 1
a - b = 2 ..............(2)
solving Equation (1) and (2) , we get
2+ b - 5b= -6
-4b = -8
b= 2
and, a = 2 + 2 = 4
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Triangles geometry . I neeed help pls
The value of PQ is 43.
What is an isosceles triangle?
A triangle with at least two equal-length sides is known as an isosceles triangle in geometry.
From the figure,
PQ=3x+10, QR=5x-12
Given that, PQ=QR
So, 3x+10=5x-12
Find x:
3x+10=5x-12
Separate variable terms and constants
5x-3x=10+12
2x=22
x=22/2=11
we have PQ=3x+10=3(11)+10=33+10=43
So, PQ=43
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A factory produces 270000 000 sweets every
week. How many sweets does the factory
produce in a year? Give your answer in
standard form
The factory produced 1.404 x 10⁶ sweets in a year
How to calculate the number of sweets the factory produce in a year?
Standard form is a way of writing very large numbers or very small numbers in a simpler form. It is also called scientific notation
Given that: The factory produces 270000000 sweets every
week.
To know how many sweets the factory produces in a year, we will multiply the quantity produced in a week by 52 since there are 52 weeks in a year. Thus:
Number of sweet in a year = Weekly production x 52
= 270000000 x 52 = 14040000000 sweets
To express 140400000000 in standard form, we will move the position of the decimal point to the back of the first number(1) and take note of the number of steps we take to get there. The number of steps will then be used as the power of 10:
14040000000 = 1.404 x 10⁶
Therefore, the number of sweets produced by the factory in a year in standard form is 1.404 x 10⁶ sweets
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a random sample of size 36 is taken from a population with mean 50 and standard deviation 5. what is (the mean of the sample mean)?
With the help of standard deviation we can conclude our answer.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation. Standard deviation may be written as SD.acc to our question-
Calculate the z-score of 51.5 using the formula:We substitute From the standard normal distribution table, the area to the left of 1.80 is0.9641Therefore it is 0.9461learn more about standard deviation here:
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Please help, I'm struggling.
I think you would just add 8 + 5, because if NO is the same length as MN, then the length from MN is 5 and NP makes up the rest of the line.
Answer: MP = 13
a variable t follows a uniform probability distribution where t is between 0 and 8 what is the probability that the random variable has a value greater than 5?
There is a 1/3 chance that random variable will have a value higher than 5.
Define the term random variable?A random variable is called with an unknown value or a function that gives values to each of the results of an experiment. Random variables are similarly defined by letters and fall into one of two categories: continuous variables, which can take on any value within a continuous range, or discrete variables, which have specified values.For the variable t, which follows uniform probability distribution.
0 ≤ t ≤ 8
Total variables = 9.
For the probability of value greater than 5 for the random variable.
P(t > 5) = P(t = 6) + P(t = 7) + P(t = 8)
P(t > 5) = 1/9 + 1/9 + 1/9
P(t > 5) = 3/9
P(t > 5) = 1/3
Thus, there is a 1/3 chance that random variable will have a value higher than 5.
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The ordered pairs show the number of hours a student studied in a week, x, and that student’s exam score, y.
(1,70) (3,75) (5,80) (9,95) (12,98)
The equation y=2.7x+67 can be used to model the relationship between the number of hours a student studied in a week and their exam scores. Choose a number from each box to make the statement true.
The y-intercept shows that a student who studies____________
A: 0
B: 2.7
C: 67
D: 69.7
hours can expect to get a score of _______on the exam.
A: 0
B: 2.7
C: 67
D: 69.7
Answers:
1st box: 0
2nd box: 67
===============================================
Explanation:
The y intercept always occurs when x = 0. This is when the function curve either crosses or touches the vertical y axis. Therefore, the y intercept is when the student studies 0 hours
Plug x = 0 into the equation
y = 2.7x + 67
y = 2.7*0 + 67
y = 67
Or you can note that the equation is of the form y = mx+b
m = slope = 2.7b = 67 = y interceptThe y-intercept of 67 tells us that the person studying for 0 hours is estimated to get a score of 67
a haunted house claims that 80% of customers are scared speechless. if this is true, what is the probability that 60% or less out of a group of 50 customers will be scared speechless?
Answer: The probability of 60% or less scared speechless out of a group of 50 customers (i.e. 30 customers) is 0.0932% or 0.000932.
Step-by-step explanation: Given problem meets all criteria for application of a binomial distribution with the probability of success; p=0.8 or 80% (which makes probability of failure; q=0.2 or 20%) and the total number of trials; n=50.
Let probability of 30 or less people scared (30 is 60% of 50 people) be P(x≤30), where x≤30 encapsulates all possibilities from 0 to 30 people scared speechless.
Then, by binomial distribution,
P(x≤30) =r=030nCr*pr*q(n-r)
Now we can substitute given values and find the desired probability,
P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)(50-r)
P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)-r*(0.2)50
P(x≤30) =(0.2)50*r=03050!(50-r)!r!*(0.8)r*(0.2)-r
P(x≤30) =(0.2)50*r=03050!(50-r)!r!*4r
The first value on the right hand side of equation is a very small number while the summation factor on second is a relatively larger number.
P(x≤30) = 0.000932
Thus, there is a 0.09% chance of 30 or less people scared speechless out of a group of 50.
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Evaluate the expression:
6² x (16 +19) — 10³
36×(35)-1000=1260-1000=260
i just need the answers
Answer:
s is the price of each laptop that gives maximum profit
p is the maximum total profit that can be made.
Step-by-step explanation:
See the attached worksheet for additional explanation. The question asks for the meaning of s (selling price) and p (total profits) at the vertex of the curve. s is in units of price/laptop, while p is in units of total profits. Implicit in this graph is a demand curve (not shown) that illustrates how demand for laptops changes as the price changes. Also not shown, but assumed, is that if the laptops are sold at a low price, the declining profit margins resuce the overall total profits. This graph incorporates the cost and demand imformation in a manner that provides a condensed view of the more important variable: total profits.
The mean, median and mode of the numbers below are the same,
what is the value of a?
6, 2, a, 7, 4, 9,6
Answer:
8
Step-by-step explanation:
Put the numbers in order from lowest to highest. Add all the numbers together. We will ignore a for this step. You should get 34 when adding it all together. Then if you were to add 8 to that 34 you'd get 42. Divide 42 by the amount of numbers you have which is 7. Your answer is 6. Now to make sure 8 is our value. We want to make sure the median is also 6. to find the median you need to have the numbers in order for lowest to highest and find the number in the middle. Don't forget to add your new number 8 into that order. You should get 6 as the median. Therefore our answer is 8
Q1 Q2 Logic puzzles
Solve the problems.
3 paintings are for sale.
Painting A is three times the
price of painting B.
Painting B is half the price of
painting C.
Painting C costs £368.
What are the prices of paintings
A and B?
Painting A = £ I
Painting B = £
Step-by-step explanation:
so basically, because Painting C costs £368 and Painting B is half that cost, Painting B costs £184. And Painting A is three times that amount Painting A costs £552.
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What is the value of z where distance of between two point R(6, - 1, - 3) and S(3, 3, z) is 13?
Answer:
-15, 9
Step-by-step explanation:
Substituting into the distance formula,
[tex]\sqrt{(6-3)^2+(-1-3)^2+(-3-z)^2}=13 \\ \\ \sqrt{25+(3+z)^2}=13 \\ \\ 25+(3+z)^2=169 \\ \\ (3+z)^2=144 \\ \\ 3+z=\pm 12 \\ \\ z=-3 \pm 12 \\ \\ z=-15, 9[/tex]
-13x + x = 8x – 20x help me pls
The solution of the equation given as -13x + x = 8x - 20x is infinite many solutions
How to evaluate the equation?From the question, the equation is given as
-13x + x = 8x - 20x
To start with, we need to rewrite the expression
So, we have the following representation
x - 13x = 8x - 20x
Solving further, we need to evaluate the like terms
So, we have the following equation
-12x = 8x - 20x
Evaluate the like terms again
So, the equation becomes
-12x = -12x
Both sides of the above equation are the same
i.e. -12x is on both sides of the equation
When we have a solution that all sides of the equation have the same value, then the solution is that the equation has infinite many solutions
Hence, -13x + x = 8x - 20x has infinite solutions
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Betsie is going to buy 250 envelopes.
Here is some information about the cost of envelopes in two shops.
Value World
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Letters2go
Pack of 25 envelopes for £3.19
Betsie wants to buy the envelopes for the best possible price.
Which shop should Betsie buy the 250 envelopes from?
You must show how you get your answer.
Betsie should buy the 250 envelopes from the shop Letter2go.
As, 250 envelopes will cost £31.9 in Shop Letter2go whereas will cost £33.17 in Shop Value World.
Given, that Betsie is going to buy 250 envelopes.
the cost of envelopes in two shops:
Value World:
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Letters2go:
Pack of 25 envelopes for £3.19
Now, if we see the cost of envelopes in shop 1 i.e. Value World
Cost of Pack of 10 envelopes = £1.99
Also, 1 pack is free for 2 packs
1 pack = £1.99
2 packs = 2×£1.99 = £3.98
Also, with 2 packs Betsie get 1 pack free
so, Betsie gets 3 packs for £3.98.
1 pack = 10 envelopes
3 packs = 30 envelopes.
Hence, In shop Value World:
30 envelopes = £3.98
1 envelope = £3.98/30
250 envelopes = (3.98/30)×250
So, 250 envelopes will cost £33.17 in Shop Value World.
And in shop Letter2go:
25 envelopes = £3.19
1 envelope = £3.19/25
250 envelopes = (3.19/25)×250
So, 250 envelopes will cost £31.9 in Shop Letter2go.
Hence, 250 envelopes will cost £33.17 in Shop Value World and £31.9 in Shop Letter2go.
So, Betsie should buy the 250 envelopes from the shop Letter2go.
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What is the value of x in the equation 3/2 (4x – 1) – 3x = 54 –(x + 2)?
A. 1/16
B. 3/16
C. 19/16
D. 3
The solution for x in the equation given as 3/2 (4x – 1) – 3x = 54 –(x + 2) is 13.375
How to determine the solution to the variable k in the expression?From the question, the algebraic expression is given as
3/2 (4x – 1) – 3x = 54 –(x + 2)
There is no constant to multiply or divide in the expression
3/2 (4x – 1) – 3x = 54 –(x + 2)
Open the brackets
So, we have
6x – 3/2 - 3x = 54 - x - 2
Collect the like term in the above equation
This gives
6x - 3x + x = 54 - 2 + 3/2
Evaluate the like term in the above equation
So, we have the following representation
4x = 53.5
Divide through by 4
x = 13.375
The above equation cannot be solved further
Hence, the solution is x = 13.375
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Mr. Yi buys vegetables at a market. He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18. Onions cost twice as much as potatoes. To determine the unit price for each item, his daughter sets up and solves the system of equations shown.
6p + 3n = 18 and 2n = p
6(2n) + 3n = 18
12n + 3n = 18
15n = 18; n = $1.20
Onions cost $1.20 per pound.
Analyze the daughter’s solution. Which statements are true? Check all that apply.
The equation 2n = p should be 2p = n.
The equation 6p + 3n = 18 should be
6n + 3p = 18.
The actual cost of the onions is $3.00 per pound.
Potatoes cost $0.60 per pound.
Potatoes cost $1.50 per pound.
Potatoes cost $2.40 per pound.
The correct statements are,
(1) The equation 2n = p should be 2p = n.
(2) The actual cost of the onions is $3.00 per pound.
(3) Potatoes cost $1.50 per pound.
What is an expression?The mathematical expression combines 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 denote the logical syntax's operation order and other properties.
Given that Mr. Yi buys vegetables at a market. He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18. Onions cost twice as much as potatoes.
The equation will be formed as,
6p + 3n = 18
n = 2p
Substitute the value of n = 2p in the equation,
6p + 3(2p) = 18
6p + 6p = 18
12p = 18
p = $1.5
The cost of an onion is,
n = 2p
n = 1.5 x 2
n = $3
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If f(x)=4x^3+5, then what is the remainder when f(x) is divided by x−3?
Using Remainder theorem
Answer:
113
Step-by-step explanation:
Finding a remainder seems like you should be dividing. Remember everything is a shortcut for something else in math. So first you learn Long Division, but that's too much writing, so then you learn Synthetic Division, but there's an even shorter shortcut. It is called Remainder Theorem. If you just substitute 3 (because x-3 in the question) into the function, and you calculate it, you get the remainder.
f(x) = 4x^3 + 5
f(3) = 4(3)^3 + 5
f(3) = 4(27) + 5
= 108 + 5
= 113
See image.
10) Determine the value of 10 - t when t = 4.
11) Determine the value of 12 + m when m = 6.
12) Determine the value of a + 5.2 when a = 1.9.
13) Determine the value of 3.4 - b when b = 2.1.
Answer:
10) 6
11) 18
12) 7.1
13) 1.3
Step-by-step explanation:
all you have to do is substitute
10 - 4 = 6
12 + 6 = 18
1.9 + 5.2 = 7.1
3.4 - 2.1 = 1.3
which polynomial function has a leading coefficient of 1 and roots (7+i) and (5-i) with multiplicity 1?
The polynomial function which has a leading coefficient 1 is (x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i))
Given that a polynomial function has leading coefficient 1 and roots (7+i) and (5-i) with multiplicity 1.
We want to find the polynomial function.
As we know that the complex conjugate properties of the roots of a polynomial states that if a+bi is a root of a polynomial then their complex conjugate a-bi is also a root.
So, according to this property (7-i) and (5+i) with multiplicity 1 is also a root of polynomial.
Thus, all the roots are x=7+i, x=7-i, x=5+i and x=5-i
So, the polynomial is f(x)=(x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i))
Hence, the polynomial function which has a leading coefficient 1 and roots (7+i) and (5-i) is (x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i)).
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Kermit and Miss Piggy are a part of a close group of 10 Muppets. Four of the Muppets are randomly selected to
do press for their next movie. What is the probability Miss Piggy will do press but Kermit will not?
A.4/15
B.1/15
C.1/24
D.None of the above
Answer:
d
Step-by-step explanation:
Because answer would be 4/10 or 5/10
How many kilometres is 6.5cm
Answer:
0.000065 km
Step-by-step explanation:
To get from cm to km you need to divide 6.5 by 0.000001 which equals 0.000065km
