Form a polynomial whose zeros and degree are given Zeros: -2, multiplicity 1; 3, multiplicity 2; degrees 3
Answers
The polynomial of 3rd degree whose zeros and degree are given as for zero of (-2), multiplicity 1 and for zero of (3), multiplicity 2 is \(f(x)=(x^{3}-10x^{2} -15x+18)\)
As per the question statement, a 3rd degree polynomial has a zero of (-2), multiplicity 1 and another zero of (3), multiplicity 2.
We are required to determine the polynomial.
Since, (-2) is a zero of the polynomial, then \([x-(-2)]=(x+2)\) will be a factor of the polynomial. And since for zero of (-2), multiplicity is 1, this means that the factor of (x + 2) is only multiplied once.
Similarly, as (3) is another zero of the polynomial, then \((x-3)\) will be a factor of the polynomial. And since for zero of (3), multiplicity is 2, this means that the factor of (x - 3) will be multiplied twice, i.e., \((x-3)^{2}\).
Therefore, our function, say, f(x) will be \((x+2)(x-3)^2\)
\(or, f(x) = (x+2)(x-3)^2\\or, f(x) = (x + 2)(x^{2} +9-12x)\\or,f(x) =x^{3}+9x-12x^{2} +2x^{2} +18-24x\\ or, f(x)=x^{3}+(2x^{2}-12x^{2})+(9x-24x)+18\\or, f(x)=(x^{3}-10x^{2} -15x+18)\)
Hence, our required polynomial is \(f(x)=(x^{3}-10x^{2} -15x+18)\)
Polynomial: A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s)Degree of a Polynomial: The highest value of power of the variable of a polynomial is known as the degree of the polynomial.Zero of a Polynomial: The value of the variable for which, the polynomial or equation equates to zero, is known as Zero of the Polynomial.To learn more about Polynomials, Degrees and Zeroes, click on the link below.
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Related Questions
-1000 2/3 is not real fraction. True or false
Answers
True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.
The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.
In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.
To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.
It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.
In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.
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Question 10 of 25 What is the recursive formula for this geometric sequence? -2,-16, -128, -1024,... A. ○ B. C. (a, D. 3₁ = :-2 an = 2n-1 = = -2 an = an-1.8 • a₁ = 8 an = an-1• (-2) (a₁ = -8 30 = 20-1.2 SUBMIT
Answers
Answer:
\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2
Step-by-step explanation:
a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r
here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then
\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2
What is the constant up a proportionally in a equation y=x/g
Answers
Answer:
Step-by-step explanation:
\(y=(\frac{1}{g} )x\)
Constant up a proportionally is \(\frac{1}{g}\).
The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
Select one:
a.
bus
b.
car
c.
subway
d.
train
Answers
Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.
How to Interpret a Box-and-whisker Plot?
In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.
The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.
Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.
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What should be subtracted from minus 3 / 4 so has to get 5 / 6 ?
Answers
Answer:
Step-by-step explanation:
Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and
6,which is 12.
3*3/4*3=9/12
5*2/6*2=10/12
Step 2:Subtract 9/12 from 10/12,which is 1/12.
what the difference between graphing lines and graphing inequalities?
what the difference between arithmetic and geometric ?
how do you explain using sigma notation ?
how to simplify into logarithmic?
Answers
Answer:
Step-by-step explanation:
graphing lines is just what it sounds like, you are taking the equation of the line and putting it on the graph. graphing inequalities shows the area of the coordinate plane that satisfies the inequality, it almost always splits the graph.
arithmetic: -6 , 1 , 8 , 15 , 22
geometric: 2 , 4 , 8 , 16, 32
i need help asap
than you!
Answers
The highest height for the daily rainfall were for 5 and 6 inches
How to Interpret Dot Plots?Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.
From the given dot plot, we see the number of times for each height of rainfall.
Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.
Thus, we conclude those were the highest heights for the daily rainfall.
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The distance is 1,163 miles and the driving is 17 hours and 38 minutes
Answers
Answer:
Step-by-step explanation:
17 hours multiplied by 60 (60 seconds in 1 minute) = 1020 minutes + 38 minutes = 1058 minutes.
Miles per hour = distance/time
1163/1058 = 1.10 miles per hour
Find the equation of the parabola with the following properties. Express your answer in standard form.
Symmetric with respect to the line y = 2
Directrix is the line x = 11
P = -3
Answers
The equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1
What is the equation of the parabola?To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.
Alternatively, we can use PF = PM to find the equation of the parabola.
vertex is half way between the focus and directrix
It's a downward opening parabola, general form
y= a(x-h)^2 + k
where (h,k) = vertex= (-3,-1)
plug in another point on the parabola to solve for a which gives
am answer with either x coefficient = -1'/4 or =4 Check the math.
one or the other is right another point is the y intercept = 9a-1
Another point is directly to the right of the focus (-1, -2) It's 2 down from the directrix and 2 to the right of the focus, equidistant. plug that point into y= a(x+3)^2 -1 and solve for "a"
-2 = a((-1+3)^2 -1
-2 = 4a -1
4a = -
a = -1/4
The parabola is y = (-1/4)(x+3)^2 -1
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Match each letter to its correct term. Efficiency Unobtainable Impossible Inefficiency Underutilization 1. A 2. B 3. C
Answers
Each letter should be matched to its correct term as follows;
1. A ⇔ Efficiency.
2. B ⇔ Impossible.
3. C ⇔ Inefficiency.
What is a production possibilities curve?In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;
Technology is fixed.Resources are fixed.Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;
A ⇔ Efficiency: it represent points on the production possibilities curve.B ⇔ Impossible: it represent points outside the production possibilities curve.C ⇔ Inefficiency: it represent points on the interior of a production possibilities curve.Read more on production possibilities here: brainly.com/question/26460726
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t a school. number of boys/number if girls =9/7. there are 116 more boys than girls. work out the total number of students at the school
Answers
Answer:
928
Step-by-step explanation:
Ratio of boys to girls is 9:7, so boys are 9/(9+7) = 9/16 of the total, and the girls are 7/16
the difference is 9/16-7/16 = 2/16 = 1/8, so
x * 1/8 = 116
x = 116*8 = 928
Someone please help (show work)
Answers
Answer:
See answers below :)
Step-by-step explanation:
-2(2 - 5) + 10 + (-5) =
-2(-3) + 10 - 5 =
6 + 10 - 5 =
11
8 - 2(9 - 5)^2 - 1 =
8 - 2(4)^2 - 1 =
8 - 2(16) - 1 =
8 - 32 - 1 =
-25
The box is a rectangular prism. He covered all the sides with the of the box with special wallpaper that cost a total of $504. How much wallpaper cost per square foot length is 6 feet width is 5 feet and height is 3 feet.
Answers
The cost of the wallpaper per square foot is $4.
To find the cost per square foot of the wallpaper, we first need to calculate the total surface area of the box. A rectangular prism has six faces, and each face is a rectangle.
The front and back faces have dimensions 6 feet by 3 feet, so their combined area is 6 ft * 3 ft * 2 = 36 square feet.
The top and bottom faces have dimensions 5 feet by 3 feet, so their combined area is 5 ft * 3 ft * 2 = 30 square feet.
The left and right faces have dimensions 6 feet by 5 feet, so their combined area is 6 ft * 5 ft * 2 = 60 square feet.
The total surface area of the box is 36 + 30 + 60 = 126 square feet.
Since the cost of the wallpaper is $504, we divide the total cost by the total surface area to find the cost per square foot: $504 / 126 sq ft = $4 per square foot.
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The graph shows a coordinate plane that goes from negative 8 to 8 in each direction. The graph also shows two lines that intersect at ( 2 , 3 ). That point is labeled "solution." That's right. When you have two or more linear equations, it is called a "system of linear equations". The solution to a system of linear equations consists of the - and -value that make BOTH equations true. Graphically, this appears as the point where the lines intersect. In this case, the solution is the ordered pair , as shown on the graph. If you are trying to decide whether a system of equations has a solution, would you rather have the equations or the graphs? Why?
Answers
To visualize the solution of a system of equations, a graph is ideal, as we can see whether the functions intersect or not.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the problem. The pair/tuple/... containing these values is called the solution of the system.
The equations that construct a system are functions, and the solution of a system is at the point of intersection of these functions. The intersection of two points is easier to visualize graphically then calculating, hence a graph is ideal, as we can see whether the functions intersect or not, while for the function we would have to calculate.
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Simplify: –3(y + 2)2 – 5 + 6y.
Answers
Answer:
-17
Step-by-step explanation:
–3(y + 2)2 – 5 + 6y
(–3y -6)2 – 5 + 6y
-6y -12 - 5 + 6y
-17
Point O is the center of the circle in the diagram. What is
mzBCA?
A. 80°
B. 75°
C. 70°
D. 65°
Answers
Rewrite this number in standard (decimal) notation without the use of exponents or scientific notation:
8.587 x 10^4
answer=
Answers
The answer is: 85870
What plus what equals -8 ?
Answers
Answer:
-4+-4
Step-by-step explanation:
Two number whose sum equal to - 8 are - 11 and 4.
We have to given that,
To find two numbers whose sum equal to - 8.
Now, Let us asume that,
Two numbers are - 11 and 4.
Sum of both numbers are,
- 11 + 4
= - 8
Hence, Two number whose sum equal to - 8 are - 11 and 4.
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show that a vector space over an infinite field cannot be written as a union of finitely many proper subspaces
Answers
The proof for the statement given in question is as follows,
By analogy, if V is the set-theoretic union of n proper subspaces Wi (1in), then |F|n1.
Proof:
We can assume that the union of the other subspaces contains no Wi
Then (v + Fu)Wi= and (v + Fu) Wj (ji) ,
can only contain one vector because else Wj would contain u.
Hence
| v + Fu |=|F|≤n−1.
Corollary: Avoidance lemma for vector spaces.
Assume E is a vector space spanning an infinite field. If a subspace is contained in a finite union of subspaces, it is contained in one of them.
It should be noted that there is a similar Avoidance lemma for prime ideals in commutative rings.
A vector space (also known as a linear space) is a set whose members, known as vectors, can be added together and multiplied ("scaled") by integers known as scalars. Scalars are frequently real numbers, but they can also be complex numbers or, more broadly, members of any field.
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Question content area top
Part 1
A car with a full tank that holds 11.6 gallons of gasoline is using 1.45 gallons per hour. Is the tank more than half full of gasoline after 3.5 hours? Explain your answer.
Answers
Answer:
Yes, the tank is more than half full of gasoline after 3.5 hours.
Step-by-step explanation:
To calculate the amount of gasoline left in the tank after 3.5 hours, we need to subtract the amount used (1.45 gallons per hour) from the total capacity (11.6 gallons). So 11.6 - (1.45 x 3.5) = 9.3 gallons, which is more than half the tank's capacity of 11.6 gallons. Hope this helps!
Which problem can be solved by performing this multiplication?
3/4×8/9
Responses
Evan practiced piano this week for 3/4 hour. Last week he practice for8/9 hour. How much longer did Evan practice last week than this week?
Jada rode her bike 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike. How far did Sarah ride her bike?
Amelie drove 3/4 mile. She then drove another 8/9 mile. How many miles did she drive in all?
Three out of 4 containers hold lemonade. Each container holds 8/9 quart of lemonade. How much lemonade do the containers all hold?
Answers
The multiplication 3/4×8/9 can be used to address the problem in response (B). which is the correct answer that would be an option (B).
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
As per option (B),
Jada rode her bike for 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike.
Sarah rides her bike = Sarah rode (8/9) of the (3/4) that Jada rode.
Sarah rides her bike = 3/4 × 8/9
Therefore, this problem can be solved by performing the above multiplication.
Hence, the correct answer would be an option (B).
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TThe Education Trust publishes data on U.S. colleges and universities. Six-year graduation rates and student-related expenditures per full-time student for 2007 were reported for the seven primarily undergraduate public universities in California with enrollments between 10,000 and 20,000. Suppose that a 90% confidence interval for the prediction of student expenditures at a university with a graduation rate of 40% was (5,304, 8,686).
Required:
a. Determine the point estimate for the prediction of student expenditures at a university with a graduation rate of 40%.
b. Calculate the margin of error.
c. Calculate the standard error of the prediction of student expenditures at a university with a graduation rate of 40%.
Answers
Answer:
a) The point estimate is 6995.
b) The margin of error is of 1691.
c) The standard error is of 1000
Step-by-step explanation:
a. Determine the point estimate for the prediction of student expenditures at a university with a graduation rate of 40%.
The point estimate is the mean of the two bounds of the confidence interval. So
\(P = \frac{5304 + 8686}{2} = 6955\)
The point estimate is 6995.
b. Calculate the margin of error.
The margin of error is the difference between the bounds and the point estimate. So
M = 8686 - 6995 = 6995 - 5304 = 1691
The margin of error is of 1691.
c. Calculate the standard error of the prediction of student expenditures at a university with a graduation rate of 40%.
Now I have to expand a bit into the confidence interval.
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.9}{2} = 0.05\)
Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.05 = 0.95\), so Z = 1.645.
The margin of error is:
\(M = zs\)
In which s is the margin of error.
We have that M = 1691. So
\(M = zs\)
\(s = \frac{M}{z} = \frac{1645}{1.645} = 1000\)
The standard error is of 1000
The value of the digit 3 in 730,500 is the value of the digit 3 in 73,050
Answers
Answer:
3 in 730500
tens of thousands
3 in 73050
thousands
Answer:
10 times
Step-by-step explanation:
the value of the digit 3 in 730,500 is 10 times the value of the digit 3 in 73,050
730,500 (digit 3) = 30,000
73,050 (digit 3) = 3,000
30,000/3,000 = 10
The perimeter of a rectangle is 80 cm. Find the lengths of the sides of the rectangle giving the maximum area.Enter the answers for the lengths of the sides in increasing order.
Answers
Answer:
The lengths of the sides are 20 cm and 20 cm
Step-by-step explanation:
Given
Perimeter, P = 80cm
Represent the length and width with L and W, respectively;
\(P= 2*(L + B)\)
Substitute 80 for P
\(80 = 2 * (L + B)\)
Divide through by 2
\(40 = L + B\)
\(L + B = 40\)
Make L the subject of formula
\(L = 40 - B\)
Area of a rectangle is calculated as thus;
\(Area = L * B\)
Substitute 40 - B for L
\(Area = (40 - B) * B\)
Express this as a function
\(A(B) = (40 - B)* B\)
\((40 - B)* B = A(B)\)
Set A(B) = 0 to determine the roots
Hence;
\((40 - B)* B = 0\)
\(40 - B = 0\) or \(B = 0\)
\(40 = B\) or \(B = 0\)
\(B = 40\) or \(B = 0\)
The maximum area of a rectangle occurs at half the sum of the roots;
So;
\(B= \frac{B_1 + B_2}{2}\)
\(B= \frac{40+0}{2}\)
\(B= \frac{40}{2}\)
\(B = 20\)
Recall that \(L = 40 - B\)
\(L = 40 - 20\)
\(L = 20\)
Hence the lengths of the sides are 20 cm and 20 cm
Point T is the midpoint of A B If TB = 6, find the length of AB.
Answers
Answer:
12
Step-by-step explanation:
TB= TA
6= TA
TA+TB= AB
6+6=12
A gas can hold 10 L of gas how many cans could we filled filled with 7 L of
Answers
Answer:
2 cans
Step-by-step explanation:
if x=-2/3 and y=0.6 what would 1/4xy equal in simplest form
Answers
Answer:
0.625
Step-by-step explanation:
x=2/3, y=0.6
then 1/4xy = 1/(4×2/3×0.6)
= 0.625
evaluate 47 + 2d, for d = 3
Answers
100 Points! Algebra question. Write a quadratic equation in standard form with -1/2, 3/4 as its roots. Photo attached. Thank you!
Answers
Answer:
Step-by-step explanation:
Given:-
•α=
•β=
To Find:-
♦The Quadratic Equation using the Given details?
AnsWer:-
↓Quadratic Formula↓
→k[x²-(α+β)x+αβ]
→α+β=+
•Take LCM•
→α+β=+
→α+β=
→αβ=×
→αβ=
↑Using these Values in The Formula↑
→k[x²-(x)+() ]
★Let k=8★
→8[x²-(x)+() ]
→8x²-(-2x)+(-3)
→8x²+2x-3=quadratic Equation
(2a^3 b^4) ^4=
What is the answer to this problem ?
Answers
Answer: 16a^12 b^16
Step-by-step explanation:
Everything in the parenthesis to the 4th power.
2a^4= 16a
3*4=12
b^4*4=b^16