The equation of the polynomial with the given roots of 2, -2, and 4 is x³ - 4x² - 4x + 16 = 0.
What is the polynomial equation that has solutions of 2, -2, and 4?Roots are the points where the graph intercepts with the x-axis ( y = 0 ).
Given the roots in the question;
x = 2, -2, 3
Now, the root of x = 2 was found solving for x when x - (2) = y but y = 0.
Hence, (x - 2) is a factor.
Next, the root of x = -2 was found solving for x when x - (-2) = y but y = 0.
Hence, (x + 2) is a factor
And the root of x = 4 was found solving for x when x - (4) = y but y = 0.
Hence, (x + 2) is a factor
Now, combine all the factors into a single equation and simplify.
( x-2 )( x + 2 )( x - 4 ) = y
( x² + 2x - 2x - 4 )( x - 4) = 0
( x² - 4 )( x - 4) = 0
x( x² - 4 ) -4( x² - 4 ) = 0
x³ - 4x - 4x² + 16 = 0
x³ - 4x² - 4x + 16 = 0
x³ - 4x² - 4x + 16 = 0
Therefore, the equation of the polynomial with the given roots of 2, -2, and 4 is x³ - 4x² - 4x + 16 = 0.
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Calculate the distance between Point A (-8,-2) and Point B(6,-1) Leave the answer in radical form.
the distance between Point A (-8,-2) and Point B(6,-1) in Radical form= [tex]\sqrt{197}[/tex]
Distance formula:
The distance between two points formula uses the coordinates of two points in space. In coordinate geometry, the distance between two points can be calculated using the distance formula, present in a two-dimensional or three-dimensional space. The distance formula for two points is also an application of the Pythagoras theorem
the distance formula is used to find the distance between any two points when we already know the coordinates. The points could be present alone on the x-axis or y-axis or on both axes.
Let us consider, that there are two points say A and B in an XY plane. The coordinates of point A are (x1,y1), and of B are (x2,y2). Then the formula to find the distance between two points PQ is given by:
AB=[tex]\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]
Note: If the coordinates of two points P and Q are such that, (x1, 0) and (x2, 0), the distance between PQ will be given by:
PQ = |x2 – x1|
the distance between point origin O(0,0) and P(x,y) is given by:
OP = √((x2 – 0)² + (y2 – 0)²)
OP = √((x2)² + (y2)²)
or simply,
OP = √(x² + y²)
Solution :
where x and y are coordinates of points other than the origin.
Given :
(x1,y1) = (-8,-2)
(x2,y2)= (6,-1)
Solution:
[tex]d=\sqrt{x^{2} +y^{2} } \\d=\sqrt{(6+8)^{2} +(-1+2)^{2} } \\d=\sqrt{14^{2}+1^{2} } \\[/tex]
[tex]d=\sqrt({197)[/tex]
Radical form= [tex]\sqrt{197}[/tex]
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Use the domain {1/2, 1, 2, 4, 8, 16} and plot the points on the graph that would best satisfy the equation y = log2x.
Given equation y = log2x
domain {1/2, 1, 2, 4, 8, 16}.
The graph of six points that would satisfy the equation.
In equation put the value of
x =1/2
y= -1
for x= 1
y=0
for x= 2
y=1
for x= 4
y=2
for x =8
y= 3
for x= 16
y=4
Plot the points {1/2, 1, 2, 4, 8, 16} on a coordinate plane
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What’s the answer?
5x + 12(19 - x) = 19(1678)
13/2^2-10(13/2)+23 find the answer just evaluate
Answer:
Step-by-step explanation:
-38 3/4
If y= 50 degrees and z=85 degrees, then x in degree is=?
the answer will be 55 degrees. please solve
Answer:
Step-by-step explanation:
Learn
Look at this equation:
C
c³ = 125
What is c, the cube root of 125?
10x-15=15x+50 ise x kaçtır?
4(x+5)-2x/3 when x=6
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Given g(x) = 2x + 3, find g(0).
Answer:
g(0) = 3
Step-by-step explanation:
Hello!
Substitute 0 for x in the equation.
Evaluateg(x) = 2x + 3g(0) = 2(0) + 3g(0) = 0 + 3g(0) = 3g(0) is 3.
A local company has K2,500 to set up an annuity to be paid quarterly for 5 years. The payments of that annuity are to be increased in line with the current interest rate. The account pays interest at 10% p.a. compounded quarterly,
a) Calculate the size of each payment during the first year.
b) What is the size of the final payment (payment at the end)?
Answer:
Step-by-step explanation:
(a).
Within 1 year, there would be 4 payments to be made.
therefore, PMT= [tex]\frac{P(1+i)}{n} = \frac{2500(1+0.025)}{4*5} =\frac{2562.5}{20} = $128.125[/tex]
(i) 1st payment will be :PMT $128.125
(ii) 2nd payment will be :128.125*(1.025)^1= $131.33
(iii) 3rd payment will be :128.125*(1.025)^2=$134.61
(iv) 4th payment will be :128.125*(1.025)^3=$137.98
Hence the payments are: $128.125, $131.33, $134.61, and $137.98.
(b).
The size of the final payment [tex]PMT(1+i)^{m-1}[/tex] where m 4 *5= 20
[tex]=128.125(1+0.025)^{20-1} \\=128.125(1.025)^{19} \\=$204.83[/tex]
Roy has $253.97 in his bank account. He loans his friend $81.19. How much money does he have in his
account?
Answer:
172.78
Step-by-step explanation:
A=bh;A=5,h=5
HELP ME
Answer:
b = 1
Step-by-step explanation:
5 = 5b
b = 1
How do I solve this absolute value in quality problem
|2t + 2/3|≤4
Answer: -7/3≤t≤5/3
Step-by-step explanation:
|2t + 2/3|≤4
2t + 2/3≤4
(2t + 2/3≤4)*3
6t+2≤12
6t≤10
t≤10/6
t≤5/3
2t + 2/3>=-4
(2t + 2/3>=-4)*3
6t + 2>=-12
6t>=-14
t>=-14/6
t>=-7/3
-7/3≤t≤5/3
5. This diagram is a straightedge and
compass construction. Which triangle is
equilateral? Explain how you know.
The ΔVZW is Equilateral Triangle .
Equilateral Triangle is defined as the triangle in which all the three sides of the triangle are equal.
For Example ; if a triangle ABC has lengths AB=2cm , BC=2cm and CA=2cm then the triangle ABC can be called as an equilateral triangle as all sides have same length i.e. 2cm .
In the question ,
From the diagram, we have the radius of all the circles are of equal length ,
Since the radius of all the circles are equal in length , their diameter will also be equal in length .
We can see from the diagram that VZ , ZW and WV are the diameters of the circles , So they will be equal in length ,
which means VZ = ZW = WV.
In triangle VZW the sides VZ , ZW and WV are of equal length , hence the triangle will be an Equilateral Triangle.
Therefore , the Triangle VZW is Equilateral Triangle .
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Enter your answer as a proper fraction, or mixed number.
Answer:
3/14
Step-by-step explanation:
Answer:
3/14
Step-by-step explanation:
What is -12 + 12 x 10?
A university wants to know more about the knowledge of students regarding international events. They are concerned that their students are uninformed regarding news from other countries. A standardized test is used to assess students’ knowledge of world events (national reported mean= 65, S = 5). A sample of 30 students is tested (sample mean=58, Standard Error=3.2). Compute a 99 % confidence interval based on this sample data. How do these students compare to the national sample?
A university wants to know more about the knowledge of students regarding international events. They are concerned that their students are uninformed regarding news from other countries. A standardized test is used to assess students’ knowledge of world events (national reported mean= 65, S = 5). A sample of 30 students is tested (sample mean=58, Standard Error=3.2). Compute a 99 % confidence interval based on this sample data. How do these students compare to the national sampl
:Newton’s first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force. In fact, in classical Newtonian mechanics, there is no important distinction between rest and uniform motion in a straight line; they may be regarded as the same state of motion seen by different observers, one moving at the same velocity as the particle and the other moving at constant velocity with respect to the particle. This postulate is known as the law of inertia.
Question 2 of 10
Solve x + 4 = 6.
OA. x = -2 and x = 10
OB. x 2 and x = -10
OC. x = -2 and x = -10
OD. = 2 and x = -2
The solution for x in the equation is x = 2
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the solution of the equation?The equation is given as
x + 4 = 6
Subtract 4 from both sides of the equation
So, we have
x + 4 - 4 = 6 - 4
Evaluate the like terms
So, we have
x = 2
Hence, the solution for x in the equation is x = 2
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graph both lines on the same coordinate plane y=1/3x+3 and y+1=3x
how do i graph this?
Answer:
Step-by-step explanation:
you need to turn the second y equation into the correct format, so it needs to be y=. Subtract the 1 from the left side and but it on the right side. Your equation should y=3x-1. To graph this on paper, you would go 1 down on the y axis, then rise (go up) 3 and run ( go over) one.on a calculator plug it into the y1 function and y2 function and then press graph.
Sharon deposits $8,000 in a 1-year CD at 2% interest, compounded daily.
What is Sharon's annual percentage yield (APY) to the nearest hundredth of a
percent?
Sharon's annual percentage yield (APY) to the nearest hundredth of a
percent is; 2.02%
How to calculate annual percentage yield (APY)?
We are told that;
Amount Deposited = $8000
Interest = 2%
Using the formula for annual percentage yield (APY), we have;
B = 8000 + (1 + (0.02/365))³⁶⁵⁽¹⁾
B = $8161.61
Interest is;
I = $8161.61 - $8,000
I = $161.61
Thus;
APY = 161.61/8000
APY = 0.0202
APY = 2.02%
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Number between 300 and 350
Answer: 314
Step-by-step explanation: I am not sure what this question is asking me to do, but a number between 300 and 350 is 314, if that helps.
Transportation costs include car payments and costs for gasoline, repairs, and so on. What is their average monthly expenditures for transportation costs?
Group of answer choices
$879.92
$433.52
$278.50
$275.00
Answer: 433.52
Step-by-step explanation: it depends if you have the pass or not
If the terminal side of angle θ passes through a point on the unit circle in the first quadrant where y=0, what is the exact measure of θ?
Step-by-step explanation:
y of o but you dont have to use y
The total payroll for a baseball team is 2.48 × 109 dollars, and the total payroll for a football team is 2.8 × 1011 dollars. How many more dollars is the football team's total payroll than the baseball team's total payroll?
0.32 × 109 dollars
2.7752 × 109 dollars
2.7752 × 1011 dollars
3.2 × 1011 dollars
Answer: its c
Step-by-step explanation:
The difference between the payroll of football and baseball is 2.7752 × 10¹¹. Hence, option C is correct.
What is an equation?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right is shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine the value of an unknown variable that represents an unknown quantity.
The payroll of the baseball team is 2.48 × 10⁹ and,
The payroll of the football team is 2.8 × 10¹¹.
So, the football team's payroll is more than the baseball team's payroll by,
(2.8 × 10¹¹) - (2.48 × 10⁹)
= 2.7752 × 10¹¹.
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There are 9 lions there are fewer cubs than lions how many fewer cubs are there ?
Number of cubs are less than 9.
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.
NO. OF LIONS = 9
Cubs are fewer than 9
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Kadeesha is going to a carnival that has games and rides. Each game costs $2.50 and each ride costs $4.75. Kadeesha spent $48.75 altogether at the carnival and the number of games she played is twice the number of rides she went on. Write a system of equations that could be used to determine the number of games Kadeesha played and the number of rides Kadeesha went on. Define the variables that you use to write the system.
Taking into account the definition of a system of linear equations, the system of equations that could be used to determine the number of games Kadeesha played and the number of rides Kadeesha went on is:
[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]
where G is the number of games Kadeesha played and R is the number of rides Kadeesha went on.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns give the solution proposed in both equations.
System of equations in this caseIn this case, a system of linear equations must be proposed taking into account that:
G: number of games Kadeesha played.R: number of rides Kadeesha went on.On the other hand, you know:
Each game costs $2.50 and each ride costs $4.75. Kadeesha spent $48.75 altogether at the carnival. The number of games she played is twice the number of rides she went on.So, the system of equations to be solved is
[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]
Among the different existing methods to solve the system of equations, it is decided to solve it using the substitution method. This method consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, substituting the second equation in the first one you get:
2.50×2R+4.75R=48.75
Solving:
5R+4.75R=48.75
9.75R=48.75
R= 48.75÷ 9.75
R= 5
Remembering that G=2R, you obtain that G=2×5= 10
In summary, the system of equations that could be used to determine the number of games Kadeesha played and the number of rides Kadeesha went on is:
[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]
where G is the number of games Kadeesha played and R is the number of rides Kadeesha went on.
Finally, the number of games played is 10 while the number of rides she went on is 5.
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Write an expression to represent: 9 more than the quotient of 2 and x
Expression for given numerical is: 9+ (2/x)
Given that we have an word equation that is 9 more than the quotient of 2 and x
A quotient is a quantity produced by the division of two numbers.
Quotient of 2 and x is [tex]\frac{2}{x}[/tex].
Nine(9) more than 2/x is = 9+ (2/x)
So we have an expression that is:
9+ (2/x)
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6. What is the area in square feet of a 100 yard by 60 yard foot-
ball field?
Answer:
6000 [tex]yd^{2}[/tex]
Step-by-step explanation:
Take the length and multiply it by the width.
100 x 60 = 6000
Answer:6,000 yards
Step-by-step explanation:
100 yards x 60 yards = 6,000yards
Write the improper fraction 30/7 as a mixed number
Answer:
Step-by-step explanation:
30/7 = 4 2/7
Because 7 only goes into 30, four times (7 x 4 = 28) anything else would be too big.
7 goes into 30 four times, and you get left with a remainder of 2
So you write 4 wholes, then 2/7 because 2 is the remainder it goes on top, and 7 stays in the denominator (bottom)
Solve the formula for the specified variable.
I = Prt
t