The final equation is a polynomial of primes [tex]2x^{4} + x^{3} - x + 2[/tex] It can't be factored. Variables are sometimes known as indeterminate in mathematics.
what is polynomial ?An essential component of the "language" of mathematics and algebra are polynomials. They are used to express numbers that are the result of mathematical operations in almost every area of mathematics. Other types of mathematical expressions, such as rational expressions, also use polynomials as "building blocks."
given
Is a base form of a polynomial in other words is a polynomial that can't be factored.
so we have
[tex]A ) x^{3} +3x^{2} - 2x - 6 = ( x +3 ) ( x^{2} - 2 )\\B) x^{3} -2x^{2} +3x - 6 = ( x- 2 ) (x^{2} + 3)\\C)4x^{4} +4x^{3} - 2x - 2 = 2( x +1 )(2x^{2} - 1)\\D) 2x^{4} +x^{3} -x + 2[/tex]
hence, the final equation is a polynomial of primes [tex]2x^{4} + x^{3} - x + 2[/tex] It can't be factored.
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Josiah bought a new car for $25,000. He did some research and found that the value of his car would depreciate at an average rate of $3,750 per year. The table shows data about the value of his car over the next 4 years.
Number of Years Owned 1 2 3 4
Car Value $ 25000 21250 13750 10000
Express the relation as a set of ordered pairs.
Identify the domain and range of this relation.
Is this relation a function?
The domain is the set of years, which is {1, 2, 3, 4}, and the range is the set of values, which is {25000, 21250, 13750, 10000}. The ordered pairs of this function are (1, 25000), (2, 21250), (3, 13750), (4, 10000).
The relation described above can be expressed as a set of ordered pairs by calculating the value of the car for each year based on the depreciation rate. Let's calculate the value of the car for each year:
Year 1: 25000
Year 2: 25000 - 3,750
= 21250
Year 3: 21250 - 3,750
= 13750
Year 4: 13750 - 3,750
= 10000
Therefore, the ordered pairs of this relation are
: (1, 25000), (2, 21250), (3, 13750), (4, 10000).
The domain of this relation is the set of years, which is {1, 2, 3, 4}, and the range is the set of values, which is
{25000, 21250, 13750, 10000}.
This relation is a function because each input (year) is associated with one output (value).
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Pls help me to do this
Answer:
1. 2 more children
2. 13 centimeters
3. Can't determine without ruler
Step-by-step explanation:
1. 5-3 = 2
2. 22-9 = 13
Please help me answer this math question !
Answer:
y=-3x+6
Step-by-step explanation:
Please help I have a learning disability and this is due today
Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why.
0 + 32 and 0
yes, it uses the Commutative Property
No they are not equivalent. The first expression is equal to 32, not 0.
yes, it uses the Associative Property
yes, it uses the Identity Property
Answer:
yes, it uses the Commutative Property
Step-by-step explanation:
does leave as the whole percentage mean if it was 5.4% you would have it as 5%
Answer:
It is about rounding.
You would round up or down depending on the number after decimal.
If it is < 5 you drop it, if equal or greater than 5 then round up to the next whole number.
5.4% is rounded down to 5% since 4 < 5.
Mark got a loan of $77000 which he will complete repayment in
3 years. If the loan is compounded Sem- Annually at 7% per annum, what amount will he repay? (work out?)
Answer:
A = $94652.66
Step-by-step explanation:
Use the compound amount formula A = P(1 + r/n)^(nt), where r is the annual interest rate and n is the number of compounding periods per year.
Here, A = ($77000)(1 + 0.07/2)^(2*3), or
A = $77000(1.035)^6, or
A = $77000(1.229), or
A = $94652.66
What is the value of (-1-¹) ÷ (-4)?
A. -1/
T
B. -21
C.
D. 1/1/12
Answer:
D. 1 5/16
Step-by-step explanation:
mark brainliest
Find the ordered triplet (x,y,z) for the following system of equations: x+3y + 2z = 1, 03x+y+5z=10, -2x-3y+z=7
The ordered triplet (x, y, z) or the following system of equations: x+3y + 2z = 1, 03x+y+5z=10, -2x-3y+z=7 is (-170/127, -89/127, 282/127).
Start with the first equation:
x + 3y + 2z = 1
Isolate x by subtracting 3y and 2z from both sides:
x = 1 - 3y - 2z
Substitute this expression of x into the second equation:
0.3x + y + 5z = 10
Substitute the value of x found in step 2 into this equation:
0.3(1 - 3y - 2z) + y + 5z = 10
0.3 -0.9y -0.6z + y + 5z = 10
0.1y + 4.4z = 9.7
y + 44z = 97
Solve for y by isolating it:
y = 97 - 44z
Substitute this expression of y into the first equation:
x + 3(97 - 44z) + 2z = 1
x + 291 - 132z + 2z = 1
Solve for x:
x = 130z - 290
Substitute this expression of x into the third equation:
-2(130z - 290) - 3(97 - 44z) + z = 7
-260z + 580 - 291 + 132z + z = 7
Solve for z:
127z = 282
z = 282/127
Substitute this value of z into the expression of y:
y = 97 - 44(282/127)
= -89/ 127
Substitute the values of z into the expression of x:
x = 130(282/127) - 290
= - 170/ 127
So the solution of the system of equations is: x = -170/127, y = -89/127, z = 282/127.
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You are given that $x$ is directly proportional to $y^3$, and $y$ is inversely proportional to $\sqrt{z}$. If the value of $x$ is 3 when $z$ is $12$, what is the value of $x$ when $z$ is equal to $75$
The value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex]
To calculate the value of $x$ when $z$ is equal to $75$, first rewrite the given proportionality as equations.
When x is directly proportional to [tex]$y^3$[/tex], the equation is given by:
[tex]$x = ky^3$[/tex]
where k is the constant of proportionality.
Similarly, when y is inversely proportional to [tex]$\sqrt{z}$[/tex], the equation is given by:
[tex]$y = \frac{m}{\sqrt{z}}$[/tex]
where m is the constant of proportionality.
Substituting the second equation into the first equation gives:
[tex]$x = k\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]
Since the value of x is 3 when z is 12, the equation can be written as:
[tex]$3 = k\left(\frac{m}{\sqrt{12}}\right)^3$[/tex]
Rearranging gives:
[tex]$k = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}$[/tex]
Substituting this value of k into the original equation gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]
Substituting z as 75 gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{75}}\right)^3$[/tex]
Simplifying gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{\sqrt{12}}{\sqrt{75}}\right)^3m^3$$x = \frac{3m^3}{\left(\frac{m}{\sqrt{75}}\right)^3}$$x = \frac{3m^3\sqrt{75}}{m^3}$$x = 3\sqrt{75}$[/tex]
Therefore, the value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex].
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Mr. McDonald has $500.00 to spend at a bicycle store. All prices listed below include tax. He buys a new bicycle for $273. 98. He buys 3 bicycle reflectors for $7. 23 each and 1 bicycle helmet for 42.36. he plans to use the remaining money to buy new cycling outfits for $78.12 each. Write and solve an inequality to determine the greatest number of cycling outfits that Mr. Mc Donald can buy with the remaining money?
Answer:
(500-338.03)-78.12x
Step-by-step explanation:
so we know that he has 500 dollars on him. he bought a bike for 273.98. then we add that to 7.23 for each bike reflector. he bought 3 so we do 7.23*3, which is 21.69. he also bought a helmet which cost 42.36. now we add the numbers together. 273.98+21.69+42.36=338.03
he has 500 dollars on him. we need to find out how much money he has left. 500-338.03 is 161.97. he has that much money left.
the bike suits 78.12 each. the easy way to solve this is by doing 161.97/78.12.
this comes up as 2.073. rounded is 2. he can only buy 2 suits
the inequality you are looking for is: (500-338.03)-78.12x
Please tell me and tell me the correct answer. No link will acceptable. Check out the image. Need the correct answer.
Answer:
3(a+2) = 3a+6
Step-by-step explanation:
In the expression 3(a+2), 3 distributes into "a" and 2. Therefore, 3(a+2) = 3(a)+3(2) = 3a+6
Factor the algebraic expression 24a + 20
Answer:
Step-by-step explanation:
Take the GCF of 24 and 20.
4 (6a+5)
The simplified expression is 4(6a+5).
What is meant by expression?An expression is a sentence with a minimum of two numbers or variables and at least one math operation.
The given algebraic expression is 24a + 20.
By taking 4 as common factor, the expression become like 4(6a + 5).
Hence, 4(a+5) is the simplified expression.
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Help please!!
Thank you!! :)
Answer:
m∠R= 130
Step-by-step explanation:
[tex]6x-22+8x+34=180[/tex]
[tex]14x+12=180[/tex]
[tex]14x=180-12[/tex]
[tex]14x=168[/tex]
[tex]x=\frac{168}{14}[/tex]
[tex]x=12[/tex]
[tex]m[/tex]∠[tex]R= 8x+34[/tex]
[tex]= 8*12+34[/tex]
[tex]Answer:m[/tex]∠[tex]R= 130[/tex]
[tex]-----------[/tex]
hope it helps u, sis!!
have a great day!!
ILL GIVE BRAINLIEST
Answer:
I can't read the question it's too blurry
Given a prime $p$ and an integer $a$, we say that $a$ is a primitive root $\pmod p$ if the set $\{a,a^2,a^3,\ldots,a^{p-1}\}$ contains exactly one element congruent to each of $1,2,3,\ldots,p-1\pmod p$.For example, $2$ is a primitive root $\pmod 5$ because $\{2,2^2,2^3,2^4\}\equiv \{2,4,3,1\}\pmod 5$, and this list contains every residue from $1$ to $4$ exactly once.However, $4$ is not a primitive root $\pmod 5$ because $\{4,4^2,4^3,4^4\}\equiv\{4,1,4,1\}\pmod 5$, and this list does not contain every residue from $1$ to $4$ exactly once.What is the sum of all integers in the set $\{1,2,3,4,5,6\}$ that are primitive roots $\pmod 7$
Only 3 & 5 from the set {1,2,3,4,5,6} are primitive root (mod7), therefore, sum of integers is 3 + 5 = 8.
What is primitive root?A number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n in modular arithmetic. That is, g is a primitive root modulo n if for every integer a coprime to n, some integer k for which gk ≡ a (mod n).
The index or discrete logarithm of a to the base g modulo n is a value k like this. So, if and only if g is a generator of the multiplicative group of integers modulo n, g is a primitive root modulo n.
In Article 57 of his Disquisitiones Arithmeticae (1801), Gauss defined primitive roots and credited Euler with coining the term.
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PLS FIND X ASAP PLS PLS
Answer:
1- the figure doesn't provide enough information from what I'm aware of
2- x= 17.78
3- x=12
4- x=19
Step-by-step explanation:
Choose Yes or No to tell whether or not the symbol needs to flip when completing this inequality:
- 6w < 21
Answer:
yes ..................
(x - 7)2 + (y + 5)2 = 4
what’s the center and radius
Answer:
(7, - 5 ) and r = 2
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x - 7)² + (y + 5)² = 4 ← is in standard form
with centre = (h, k ) = (7, - 5 ) and r = [tex]\sqrt{4}[/tex] = 2
normally distributed with a mean of 5 days and a standard deviation of 4 days. What is the probability that the product has a shelf life of at least 1 week and at most 2 weeks
The probability that the product has a shelf life of at least 1 week and at most 2 weeks is 0.30.
Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability is a concept in mathematics that helps predict the likelihood of certain events. Probability generally refers to the degree to which something is likely to occur.
A standard normal variable with a mean of 0 and a variance of 1 can be created from a normally distributed random variable with a defined mean and variance.
Thus, The probability that the product has a shelf life of at least 1 week and at most 2 weeks is 0.30.
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Find the area of the figure
Answer:
the answer is 1,792
Step-by-step explanation:
times them all together
Answer:
112
Step-by-step explanation:
base times height
I NEED HELP THIS IS DUE TOMORROW!!!
The ratio of the new area to the old area is 16:1. The correct option is the second option
Calculating the area of a circleFrom the question, we are to determine the statement that is true about the area of the circle.
First, we will determine the old area
Using the formula for calculating the area of a circle
A = πr²
Where A is the area
and r is the radius
From the given diagram,
r = 6 ft
Thus,
Old area = π × 6²
Old area = 36π ft²
Now,
If the radius is quadrupled
That is,
r = 4 × 6 ft
r = 24 ft
The new area will be
A = π × 24²
A = 576π ft²
The ratio of the new area to the old area is
576π ft² / 36π ft²
16 /1
= 16 : 1
Hence, the ratio is 16:1
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which fraction is greater? a)3/18,2/6
Answer:
2/6
Step-by-step explanation:
The LCD of 18 and 6, so when you multiply 2/6, it will be 5/18. So 5/18 is greater than 3/18
Answer:
3/18 is smaller than 2/6
Step-by-step explanation:
A frictionless pendulum is pulled 3 feet to one side of its center resting point and then released. As
the pendulum swings back and forth, its horizontal position is given by s(t), where t is the number
of seconds since the pendulum was released. Note that s(t) measures the signed distance from the
center position in feet; it is positive when the pendulum is on one side of the center point and
negative when it is on the other side. The function s is sinusoidal.
Part A: If the pendulum were pulled further away from its resting point before it was released, how
would the amplitude of s be affected? Explain.
Part B: If the pendulum were pulled further away from its resting point before it was released, how
would the midline of s be affected? Explain.
No matter how far it is moved away, the midline of a function stays the same. because a sinusoidal function is involved.
What is amplitude ?A function's amplitude is the distance that the graph of the function moves above and below its midline. The value of the amplitude when graphing a sine function is comparable to the value of the sine coefficient. the greatest displacement or distance that a point on a wave or vibrating body can travel in relation to its equilibrium position A wave or vibration's amplitude or peak amplitude is a gauge of how far from the central value it deviates. All amplitudes are positive numbers.
given
( A)if pendulum were pulled away from its resting position, then Amplitude is the distance from its resting position to the end where it was released.
Amplitude is the same distance it was pulled away if more distance was pulled away then Amplitude is more.
(B). The midline of function s will not change, it will same irrespective of the distance pulled away. Because it's a sinusoidal function.
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5 t-shirts and a hat costs £17.00
2 t-shirts and a hat costs £8.00.
How much does a t-shirt cost?
How much does a hat cost?
Answer: A t-shirt costs £3.00x, while a hat costs £2.00
Sorry if it's wrong
Step-by-step explanation:
8. The price of a hoodie on sale increased from $25 to $45. By what percentage was the price of the hoodie increased?
Answer:
44.44%
Step-by-step explanation:
Question 4 OT 5
What is 39,040,000 expressed in scientific notation?
A. 3.904 x 107
B. 0.3904 x 108
O c. 0.39 x 10-8
O D. 3.904 x 108
Answer:
a. 3.904×10^7
Step-by-step explanation:
I hope this helps.
What are the 3 algorithms?
Sequencing, selection, and iteration are the three fundamental building blocks that make up an algorithm.
What is algorithm?An algorithm in mathematics is a process, a description of a series of steps that can be used to solve a mathematical computation, but they are now much more prevalent than that. The long division algorithm is perhaps the most well-known application of algorithms in science (and in daily life, for that matter).
Algorithms are all about figuring out the most effective ways to perform the math, despite the fact that the above explanation might sound a little fussy and detailed. Mathematicians are known for being lazy, so they frequently seek out shortcuts, as the anonymous mathematician puts it. For locating these short cuts, algorithms are used.
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how do i answer this question
The constant of variation for the given data is 1/4.
What is the constant of proportionality?If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
Given that the data in the table is,
x f(x)
-8 -2
-4 -1
0 0
4 1
8 2
The constant of proportionality will be calculated as,
F(x) = kx
-2 = k x -8
k = -2 / -8
k = 1 / 4
Here, the proportionality constant will be 1/4.
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state if the function is a growth or decay and the factor
y=2x
Answer:
the function shows growth of a factor of 2
Step-by-step explanation:
can you find the proportion pwease :)
Answer:
15 cookies, 10 brownies.
Step-by-step explanation:
I'm assuming that she is selling the same amount of cookies and brownies per hour. If that is the case...
Multiply it by 5. If 3 cookies were sold in one hour, and there's 5 hours, just multiply 3 by 5. Total number is 15 cookies.
Same goes for brownies. Multiple 2 brownies by 5. That makes 10 brownies.