So, the polynomial with the require properties is x⁵ + x⁴ - 3x³ - 5x² - 2x
What is a polynomial?A polynomial is an expression of the form aₙxⁿ + aₙ₋₁xⁿ⁻¹ + aₙ₋₂xⁿ⁻² + ... + a₂x² + a₁x + a₀ where aₙ are coefficients and n ≥ 2.
How to construct the given polynomail?Since we are given a polynomial with the following properties: fifth degree, −1 is a zero of multiplicity 3, 2 is the only other zero.
We have that it has zero at
x = -1 and x = 2⇒ x + 1 = 0 and x - 2 = 0
⇒ (x + 1) and (x - 2) are factors of the polynomial
We are told that the polynomial has a zero of -1 with multiplicity of 3. This implies that the factor (x + 1) is repeated 3 times. That is (x + 1)(x + 1)(x + 1)
So, multiplying all four factors we have a polynomial of fourth degree as p(x) = (x + 1)(x + 1)(x + 1)(x - 2)
= (x² + 2x + 1)(x + 1)(x - 2)
= (x³ + 3x² + 3x + 1)(x - 2)
= x⁴ + x³ - 3x² - 5x - 2
To obtain a polynomial of degree 5, we multiply through by x, so we have
g(x) =xp(x)
= x(x⁴ + x³ - 3x² - 5x - 2)
= x⁵ + x⁴ - 3x³ - 5x² - 2x
So, the required polynomial is x⁵ + x⁴ - 3x³ - 5x² - 2x
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Select the correct answer.
What is the SI unit of time?
A second
B minute
C hour
D day
What is the number in scientific notation? 0.000000000093
Check the picture below.
PLS HELP ASAP
(50 POINTS)
Using the image, how will oxygen complete its valence shell?
Answer:b B
Step-by-step explanation:or a
hello can someone please explain?
ill give brainly and 10 points
|3.7−(−1.5)|
The initially reported temperature was 3.7 however the temperature changed to -1.5.
Suppose you go shopping for a new futon bed for your room. The model you really like happens to be on sale for $525. It's original price is $700. What percent of the original price will you save if you purchase it?
Round your percentage to one decimal place.
Do not include
%
sign with your answer.
25 percent of the original price was saved during the purchase of the futon bed
The percent of the original price that is saved can be calculated as follows
The original price is $700
The new price is $525
The first step is to calculate the percentage change
= 700-525
= 175
Therefore the percent saved can be calculated as follows
= 175/700 × 100
= 0.25 × 100
= 25
Hence 25 percent of the original price was saved
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[2^3x(152 divided by 8)]-52
Answer:
152x-52
Step-by-step explanation:
The value of the expression after division is A = 100
What is an 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.
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 data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 2³ ( 152 / 8 ) - 52 be equation (1)
On dividing the equation by 8 in the expression , we get
On simplifying the equation , we get
A = 8 ( 19 ) - 52
On further simplification , we get
A = 152 - 52
A = 100
Therefore , the value of A is after the division is 100
Hence , the equation is A = 100
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The table shows the linear relationship between the playing time in minutes of high-definition videos and the file size of these videos in megabytes (MB) What is the rate of change of this function?
180
60
120
30
The rate of change of the linear function for the given table is determined as: C. 120.
What is a Linear Relationship Function?A linear relationship function is represented as a straight line graph which can be expressed as a linear equation in slope-intercept form as, y = mx + b.
The rate of change of the function is represented as m, which is also the slope of the graph, and the y-intercept is b.
How to Find the Rate of Change of a Function?A linear function has a rate of change/slope which can be found using the formula:
m = y2 - y1/x2 - x1.
Given the set of table values that represents a linear function below, we can use two pairs of values to find the rate of change as follows:
(0.5, 60) = (x1, y1)
(1.5, 180) = (x2, y2)
Plug in the values
Rate of change (m) = (180 - 60)/(1.5 - 0.5)
Rate of change (m) = (120)/(1)
Rate of change (m) = 120
Therefore, the rate of change of the linear function for the given table is determined as: C. 120.
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explain how you would round 25.691 to the greatest place
Answer:
In order to round 25.691 to the greatest place or the nearest whole number, first start at the last digit behind the decimal, in the case, being the 1. When it comes to things like this, if the digit is 4&under meaning its the number 4,3,2,1 or 0. If it is 5&up, that means it could be 5-9, making the digit go up (but if its 2, then the digit just goes away, you wont have to worry about that one specific number).
Next step is to round the 9 which makes the 6 go up one digit (meaning it turns into a 7). Now, when you round the seven, it will make the whole number go up one digit, but if you want to round that as well, to start, it's first rounding equaled up to 26. If you're rounding it to a whole tens number, it would be 30. I hope that this helps you understand this subject or topic much better! :3
Step-by-step explanation:
What are the solutions to the system of equations?
{y=2x2−5x−7y=2x+2
The solutions to the system of equations are (x₁, y₁) = (9 / 2, 11) and (x₂, y₂) = (- 1, 0).
How to resolve a system of equation by algebra methods
Herein we find a system formed by one linear equation and one nonlinear equation (quadratic equation). First, we equalize the two equations to eliminate the variable y:
2 · x² - 5 · x - 7 = 2 · x + 2
2 · x² - 7 · x - 9 = 0
2 · [x² - (7 / 2) · x - 9 / 2] = 0
2 · (x - 9 / 2) · (x + 1)
There are two solutions to x: x₁ = 9 / 2, x₂ = - 1. And the solutions for y are:
x₁ = 9 / 2y₁ = 2 · (9 / 2) + 2
y₁ = 11
x₂ = - 1y₂ = 2 · (- 1) + 2
y₂ = 0
Then, the solutions to the system of equations are (x₁, y₁) = (9 / 2, 11) and (x₂, y₂) = (- 1, 0).
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Solve for the value of r.
(9r+2)°
70°
90°
Answer:
If they all had to equal 360 when put together then the answer would be 22. If they All had to equal 180 when put together, then the answer would be 2.
Step-by-step explanation:
The directions are not quite clear but I have two answers just in case.
An elevator in a tall building goes up 7 floors then down 9 floors down 4 floors up 8 floors and down 2 floors now it it in floor 14 on what floor did the elevator start
Answer: I'm pretty sure its 14.
Step-by-step explanation: 14 + 7 - 9 - 4 + 8 - 2 = 14
Write a compound inequality for the graph shown below.
Use x for your variable.
Answer:
-7 ≤ x ≤ -4
Step-by-step explanation:
You want a compound inequality that expresses the same relation as a number line graph with solid dots at -7 and -4, and shading between.
Meaning of the graphThe graph shown is indicating values of x lie between -7 and -4, including those values. As an inequality, this is written ...
-7 ≤ x ≤ -4
I really need help I need to turn this in tmr can someone pls help I beg y a lot pósese
fraction numerator 6 y plus 2 x over denominator 5 end fraction equals 18
The given statement fraction numerator 6 y plus 2 x over denominator 5 end fraction in numerical form 18 is 6y + 2x = 90.
What is a linear equation in two variable?A linear equation in two variables has the highest degree of 1 and contains two variables generally in x and y.
Given in numerator we have 6y + 2 and in the denominator, we have 5 and this fraction equals to 18, This can be numerically represented as
(6y + 2x)/5 = 18.
6y + 2x = 90.
This is a linear equation in two variables x and y and for every value of x we get a corresponding value of y or vice-versa and all (x,y) ∈ R.
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i need help pleaseeeeee
A coefficient in the algebraic expression is: 5
The constant is: 12
A variable is: x
A term in the algebraic expression can be: 5x or 12.
What are the Parts of an Algebraic Expression?An algebraic expression consist of terms, which can be:
A variable in form of alphabetsA variable multiplied by a coefficientA constant, which is just a number.Thus, given the algebraic expression, 5x + 12, the following parts of the algebraic expression can be identified as shown below:
A coefficient in the algebraic expression is: 5 (tis is the number multiplied by the variable x)
The constant is: 12 (this is the number standing alone)
A variable is: x (this is the alphabet in the algebraic expression)
A term in the algebraic expression can be: 5x or 12.
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What value represents the vertical translation from the graph of the parent function f(x)=x2 to the graph of the function g(x)=(x+5)2+3?
Answer:
3
Step-by-step explanation:
See the attached image.
A sample of 156 runners is taken from a population of 5300 runners who complete a major marathon.
8. How many runners' times are used to calculate u for the finishing times for this event? Answer choice
5300
34
156
26
Answer:
4736 because count add them together or do it your way
2x−3y=−5 4x−4y=−4 Is (2,3)(2,3)left parenthesis, 2, comma, 3, right parenthesis a solution of the system?
(2,3) is a solution to the system of equations.
A collection of one or more linear equations containing the same variables is known as a system of linear equations (or linear system).
Consider the system of equations,
2x - 3y = - 5 --------(1)
4x - 4y = - 4 --------(2)
Multiplying equation (1) with 2.
4x - 6y = - 10
4x - 4y = - 4
Now, subtracting the above equations:
4x - 6y - ( 4x - 4y) = - 10 + 4
4x - 6y - 4x + 4y = - 6
- 2y = - 6
2y = 6
y = 3
Then,
4x - 4y = - 4
4x - 4 × 3 = - 4
4x - 12 = - 4
Adding 12 on both sides of the equation,
4x - 12 + 12 = - 4 + 12
4x = 8
x = ( 8/4 )
x = 2
Therefore, (x, y) = ( 2, 3) is a solution to the system of equations.
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Answer:
Yes
Step-by-step explanation:
Find the value of x and y.
Answer:
x = 36
y = 15
Step-by-step explanation:
127 - 52 = 75
75 / 5 = 15
2x + 3 = 5(15)
2x + 3 = 75
2x = 72
x = 36
Solve showing all work and simplify completely:
7/15 + 1/3
Answer: 4/5
Step-by-step explanation:
7/15 + 1/3
(7/15 x 1/1) (1/3 x 5/5) = ?
7/15 + 5/15 = ?
7+5/15 = 12/15
12/15 both sides divided by 3 = 4/5
therefore
7/15 + 1/3 = 4/5
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{7}{15} + \dfrac{1}{3}}[/tex]
[tex]\mathsf{= \dfrac{7}{15} + \dfrac{1\times5}{3\times5}}[/tex]
[tex]\mathsf{= \dfrac{7}{15} + \dfrac{5}{15}}[/tex]
[tex]\mathsf{= \dfrac{7 + 5}{15 - 0}}[/tex]
[tex]\mathsf{= \dfrac{12}{15}}[/tex]
[tex]\mathsf{= \dfrac{12\div3}{15\div 3}}[/tex]
[tex]\mathsf{= \dfrac{4}{5}}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{4}{5}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Tell whether each equation is true, false, or open. Explain.
2.) 5x+7 = 17
1.) 85+ (-10) = 95
3.) -8(-2) - 7 = 14 – 5
Answer:
1.) 85+ (-10) = 95 is false.
2.) 5x+7 = 17 is false.
3.) -8(-2) - 7 = 14 – 5 is false.
Step-by-step explanation:
1. is false because since 85 ≠ 95, then 85 + ( - 10) = 95 is false.
2. is false because since 12 ≠ 17, then 5x + 7 = 17 is false.
3. is false because since -15 ≠ 14, then -8( - 2) - 7 = 14–5 is false.
x is less than or equal to 1.
0x<1
01sx
Ox21
Ox≤ 1
Answer:
the correct answer is O. x ≤ 1
Step-by-step explanation:
the rest are wrong because of the equal to sign in inequalities
i think i have question b figured out (please correct me if im wrong) but question a is really confusing and i need some help
Find the altitude of the top of the hill by adding the difference to the altitude of the check point 3:
151 + (- 173) = 151 - 173 = - 21 ftQuestion b)Find the difference between the two altitudes:
2237 - (- 69) = 2237 + 69 = 2306 ftYou got it correct.
A die is rolled twice. What is the probability rolling a 3 first, followed by rolling an even number? Leave your answer as a reduced fraction.
The probability of rolling a 3 first, then an even number, is 1/12.
What do we mean by probability?Probability is simply the likelihood of something occurring. When we are uncertain about the outcome of an event, we can discuss the probabilities of various outcomes—how likely they are. Statistics is the study of events governed by probability.So, in the given situation the first roll has no effect on the second roll because they are separate events.
Because they are independent, the probabilities of the two events can be multiplied.
The probability of getting a 3 is 1/6.The probability of getting an even number is 1/2 (2, 4, 6).Now, we will multiply the two probabilities as follows:
1/6 × 1/2 = 1/12Therefore, the probability of rolling a 3 first, followed by rolling an even number is 1/12.
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The summary of the payroll for the monthly pay period ending July 15 indicated the following:
Sales salaries $125,000
Federal income tax withheld 32,300
Office salaries 35,000
Medical insurance withheld 7,370
Social security tax withheld 10,200
Medicare tax withheld 2,550
Required:
Journalize the entries to record (a) the payroll and (b) the employer's payroll tax expense for the month. The state unemployment tax rate is 3.1%, and the federal unemployment tax rate is 0.8%. Only $25,000 of salaries are subject to unemployment taxes. Refer to the Chart of Accounts for exact wording of account titles.
The journal entries to record (a) the payroll and (b) the employer's payroll tax expense for the month are as follows:
Journal Entries:a) The payroll:
Debit Sales salaries $125,000
Debit Office salaries 35,000
Credit:
Federal income tax withholding payable 32,300
Medical insurance withholding payable 7,370
Social security tax withholding payable 10,200
Medicare tax withholding payable 2,550
Cash $107,580
To record the monthly payroll.b) The employer's payroll tax expense:
Debit Payroll Tax Expense $975
Credit:
Federal Unemployment Tax Payable $200
State Unemployment Tax Payable $775
To record the employer's payroll tax expense for the month.Data and Transaction Analysis:SUTA = 3.1% of $25,000 = $775
FUTA = 0.8% of $25,000 = $200
Sales salaries $125,000
Federal income tax withheld 32,300
Office salaries 35,000
Medical insurance withheld 7,370
Social security tax withheld 10,200
Medicare tax withheld 2,550
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solve for c enter thr number
Answer: c=√29
Step-by-step explanation:
We use Pythagoras' theorem:
[tex]c^2=5^2+2^2\\c^2=5*5+2*2\\c^2=25+4\\c^2=29\\[/tex]
Extract the square root of both parts of the equation:
[tex]\sqrt{c^2}=\sqrt{29} \\ c=\sqrt{29}[/tex]
8. A baseball is thrown from a height of 40 feet and goes up at a rate of 2.5 feet per second. A football is
thrown from a height of 25 feet and goes up at a rate of 3 feet per second. After how many seconds
would the two reach the same height?
The time taken depends upon velocity and distance so the time taken by both balls to reach the same height will be 30 seconds.
What is velocity?Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.
Units of velocity are given by ⇒ meter/second
For example, if a car drives 50 meters for 10 seconds and it is constant then 50/10 = 5 meters/second will be the velocity.
Difference between their initial height = 40 - 25 = 15 feet
It means if baseball cover x feet distance then football will cover x + 15 feet.
Now,
Time = distance covered / velocity
Since the time will be the same for both balls to meet them.
So,
Distance covered by baseball/velocity of baseball = Distance covered by football/ velocity of football
x/2.5 = (x + 15)/3
3x = 2.5x + 37.5
0.5x = 37.5
x = 75
So,
Time taken = 75/2.5 = 30 seconds.
Hence "After 30 seconds both balls will go to reach the same height".
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A woman traveled 2437.2 miles in 18 hours 20 minutes. Find the average speed of her flight in miles per hour. (Change
18 hours 20 minutes into hours and use the formula d=rt.)
Answer:Average Speed = 126.6 mph
Step-by-step explanation:
Lisa works as a tutor at Springfield high school. She can work up to 20 hours a week and gets paid $15 dollars an hour. Find a reasonable domain and range for Lisa’s possible weekly earnings.