The factored form of the equation P(x) = x³ + 3x² + x + 3 is P(x) = (x+1)(x² + 2x + 3).
An equation is a mathematical expression that shows that two things are equal.
One common method for finding the factored form of a polynomial equation is to use the Rational Root Theorem, which states that if a rational number a/b is a root of the polynomial equation, then (x-a/b) is a factor of the polynomial equation.
We can then use long division to divide the polynomial by the linear factor, repeat the process with the remaining polynomial, and continue this process until the polynomial is fully factored.
The polynomial equation
=> P(x) = x³ + 3x² + x + 3
can be factored as
=> (x+1)(x² + 2x + 3).
The equation P(x) = (x+1)(x² + 2x + 3) is now written as a product of two linear factors, (x + 1) and (x² + 2x + 3).
To know more about equation here.
https://brainly.com/question/10413253
#SPJ4
Rosa is using a recipe that serves six and uses one and three quarters cups of pasta. Choose the amount of pasta she will use if she wants to make eight servings. (2 points)
two and one third cups
three and three quarters cups
four and one quarter cups
two and one quarter cups
Answer: To calculate the amount of pasta needed for eight servings, we need to multiply the original amount of pasta in the recipe by 8/6.
So, 1.75 cups * 8/6 = 2.3 cups of pasta.
Therefore, Rosa will use 2.3 cups or four and one quarter cups of pasta if she wants to make eight servings.
Step-by-step explanation:
A spherical boulder is 24 feet in diameter and weighs almost 6 tons find the volume
The volume of the spherical boulder is 7234.56 cubic feet.
What is the diameter?
A line connecting the center and the circumference at its opposite ends is called the diameter. Its length is double that of the circle's radius.
The formula for the volume of a sphere is [tex]V=\frac{4}{3}\pi r^{3}[/tex].
Given the diameter of the sphere is 24 feet.
therefore radius is equal to 12 feet.
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi (12)^{3} \\V=\frac{4}{3} *3.14*1728\\V=7234.56[/tex]
To learn more about the volume of the sphere, refer to the link below:
https://brainly.com/question/22807400
#SPJ1
CAN SOMEONE HELP WITH THIS?✨
4966.5
Step-by-step explanation:
Starting at finding out how the population will increase in 3 years we take 3 and divide it by 4. This produces an increase of 75% every 3 years. If we multiply 2838 by 75% we get 2128.5. If we add it back to 2838, we get 4966.5
Write down the reciprocal of the following fractions
4
Answer: 4/1 is 1/4 but what are the 4 fractions your talking about?
Step-by-step explanation:
A researcher is funded to obtain an estimate for the population proportion of smokers who have tried using e-cigarettes. She plans to interview 100 smokers. Previous studies have estimated that 20% of smokers have tried e-cigarettes.
The researcher decides to present the 99% confidence interval. What is the best interpretation for this interval?
A. She is 99% confident that the sample proportion is within the interval.
B. There is 99% likelihood that another sample of 100 will have an overlapping confidence interval.
C. She is 99% confident that the population parameter is within the interval.
D. There is a 1% probability that the population parameter is higher than the interval.
The best interpretation for this interval is that "She is 99% confident that the population parameter is within the interval" (option C).
What is the meaning of confidence interval?In statistics and related fields, the confidence interval refers to a percentage that determines the population fits the interval set. Due to this, a high confidence rate is considered to be positive.
What does the confidence interval mean in this case?In this case, the confidence interval implies that the researcher is 99% confident that the population parameter is within the interval (option C)
Learn more about the confidence interval in https://brainly.com/question/24131141
#SPJ1
let a where b and c are square. show that a is invertible if and only if both b and c are invertible.
The square matrix A is invertible, i.e., inverse of A is exist, if and only if the inverse of matrices B and C exists.
We have a matrix A such that
[tex]A = \begin{bmatrix} B & 0 \\0 & C \\ \end{bmatrix}[/tex]
where, B and C are square matrices. We have to prove or show that matrix A is invertible iff B and C are invertible. We shall prove it by using the inverse and determinant of matrices. The determinant is a scalar value which is associated with the square matrix. If X is a matrix, then the determinant of a matrix is denoted by |X|. Inverse of matrix A is calculated by using formula as below,
A = adj(A)/|A|. As we see a matrix A is invertible if and only if it has non-zero determinant. Also for a diagonal matrix its determinant is product of diagonal entries here diagonal entries are again matrices so |A|=|B|×|C|. From here we can clearly says |A| ≠ 0 if and only if |B| ≠ 0 and |C| ≠ 0. Hence, the matrix A is invertible iff B and C are invertible.
To learn more about Invertible matrix, visit :
https://brainly.com/question/28217495
#SPJ4
Complete question :
Let A = [ B, 0 ; 0, C], where B and C are square. show that A is invertible if and only if both B and C are invertible.
Write the decimal number in words 17.43
Consider the rabbit pairs that illustrate the pattern in the Fibonacci sequence. These rabbits produce exactly 1 pair of new rabbits after reaching maturity at age 2 months. Imagine that the rabbits and all their offspring live forever. Also, imagine the field the rabbits live in can expand in size so that its side length is exactly equal to the number of pairs of rabbits living in the field. What is the side length of the field at the end of two years? Explain and show your work
The side length of the field after two years (24 months) would be 46368.
How to determine the side length of the fieldThe Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, starting from 0 and 1: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
To determine the side length of the field after two years, we can calculate the number of rabbit pairs after two years.
At the end of the first month, there is 1 pair of rabbits.
At the end of the second month, there are 1 + 1 = 2 pairs of rabbits.
At the end of the third month, there are 1 + 1 = 2 pairs of rabbits.
At the end of the fourth month, there are 2 + 1 = 3 pairs of rabbits.
At the end of the fifth month, there are 3 + 2 = 5 pairs of rabbits.
At the end of the sixth month, there are 5 + 3 = 8 pairs of rabbits.
At the end of the seventh month, there are 8 + 5 = 13 pairs of rabbits.
At the end of the eighth month, there are 13 + 8 = 21 pairs of rabbits.
At the end of the 24th month, there are fibonacci(24) = 46368 pairs of rabbits.
Learn more about Fibonacci at:
https://brainly.com/question/11149413
#SPJ1
Verify that the indicated function y p(x) is an explicit solution of the given first-order differential equation.
(y-x)y' =y-x+ 2; y=x+2√x+3
When y = x + 2√x +3,
y'= -x+2
Thus, in terms of x,
(y - x)y' =
y-x+2=
Since the left and right hand sides of the differential equation are equal when x + 2√x + 3 is substituted for y, y = x + 2√x + 3 is a solution.
Proceed as in Example 6, by considering p simply as a function and give its domain. (Enter your answer using interval notation.)
Then by considering p as a solution of the differential equation, give at least one interval I of definition.
O(-6, -3)
O(-3,00)
(-∞, -3)
x.
(-6, 3)
O[-3, 3]
Need Help?
Read It
Watch it
[tex]y=\frac{2x\pm\sqrt{5x^2-(4x^2-16x+4\bar{c})} }{2(1)}[/tex]Solve the given DE, [tex](y-x)\frac{dy}{dx} =y-x+2[/tex].
Rewriting,
=> [tex](y-x)\frac{dy}{dx} =y-x+2[/tex]
=> [tex](y-x)dy =(y-x+2)dx[/tex]
=> [tex]-(y-x+2)dx+(y-x)dy =0[/tex]
=> [tex](-y+x-2)dx+(y-x)dy =0[/tex]
Check to see if this is an exact DE by taking the partial derivative of M with respect to y and N with respect to x.
[tex]M=(-y+x-2)dx[/tex]
=> [tex]M_{y} =-1[/tex]
[tex]N=(y-x)dy[/tex]
=> [tex]N_{x}=-1[/tex]
[tex]M_{y} =N_{x}[/tex], so this is an exact DE. Now integrate M with respect to x and N with respect to y.
[tex]\int\ ({-y+x-2)} \, dx[/tex]
=>[tex]-xy+\frac{x^2}{2}-2x[/tex]
[tex]\int\ ({y-x)} \, dy[/tex]
=> [tex]=\frac{y^2}{2} -xy[/tex]
So we can say the solution to the given DE is, [tex]\frac{x^2}{2}+\frac{y^2}{2}-xy-2x=c[/tex].
123123423423423x12444423234234234
Answer:
1.5322e+30
Step-by-step explanation:
calculator, there were too many numbers!
Calculate the five-number summary of the given data. Use the approximation method. 18, 15, 1, 14, 18, 11, 12, 20, 13, 19, 14, 8, 24, 18, 17 Answer Enter your answers in ascending order, separating each answer with a comma.
The five-number summary of the given data 18, 15, 1, 14, 18, 11, 12, 20, 13, 19, 14, 8, 24, 18, 17 is ,
Put the numbers in ascending order 1, 8, 11, 12, 13, 14, 14, 15, 17, 18, 18, 18, 19, 20, 24.The minimum is 1 and the maximum is 24The median is 17Find the Lower quartile = 12 , Upper quartile = 19minimum = 1, Q1 = 12, median = 17, Q3 = 19, and maximum = 24.Your data set's five-number summary offers you a general notion of how it is organised. You will, for instance, have your best value and lowest value (the maximum). The main reason you'll want to locate a five-number summary is to find other valuable statistics, like the interquartile range, also known as the middle fifty, even if it's important in and of itself.
The five number summary includes 5 items:
Step 1: Put your numbers in ascending order (from smallest to largest). For this particular data set, the order is:
1, 8, 11, 12, 13, 14, 14, 15, 17, 18, 18, 18, 19, 20, 24.
Step 2: For your data set, determine the lowest and maximum. This ought to be obvious now that your math is correct.
In the example in step 1, the minimum (the smallest number) is 1 and the maximum (the largest number) is 24.
Step 3: Find the median. The median is the middle number.
median = 17
Step 4: (This is not technically necessary, but it makes Q1 and Q3 easier to find).
(1, 8, 11, 12, 13, 14, 14, 15), 17, (18, 18, 18, 19, 20, 24).
Step 5: Find Q1 and Q3. Q1 can be thought of as a median in the lower half of the data, and Q3 can be thought of as a median for the upper half of data.
(1, 8, 11, 12, 13, 14, 14, 15), 17, (18, 18, 18, 19, 20, 24).
Step 6: Write down your summary found in the above steps.
minimum = 1, Q1 = 12, median = 17, Q3 = 19, and maximum = 24.
Learn more about Five number summary:
https://brainly.com/question/26671030
#SPJ4
A teacher randomly chooses a two-person leadership team from a group of four qualified students. Three of the students, Sandra, Marta, and Jane, are girls. The fourth student, Franklin, is a boy.
Using the sample space of possible outcomes listed below, where each student is represented by the first letter of his or her name, answer each of the following questions.
What is
�
(
�
)
P(A)P, left parenthesis, A, right parenthesis, the probability that the first student is a boy?
What is
�
(
�
)
P(B)P, left parenthesis, B, right parenthesis, the probability that the second student is a girl?
What is
�
(
�
and
�
)
P(A and B)P, left parenthesis, A, start text, space, a, n, d, space, end text, B, right parenthesis, the probability that the first student is a boy and the second student is a girl?
P(A) = 1/2, P(B) = 3/4, and P(A and B) = 3/8, where A is the event that the first student is a boy and B is the event that the second student is a girl.
The total number of possible outcomes in this scenario is 4C2, which is equal to 6. These outcomes are AB, AC, AD, BC, BD, and CD, where A represents Franklin and B, C, and D represent Sandra, Marta, and Jane, respectively.
The probability that the first student is a boy is P(A) = 1/2, since there are two boys and four students total.
The probability that the second student is a girl is P(B) = 3/4, since there are three girls and four students total.
The probability that the first student is a boy and the second student is a girl is P(A and B) = 1/2 x 3/3 = 3/8, since the probability of the first student being a boy is 1/2 and the probability of the second student being a girl is 3/4 (after one girl has already been chosen as the first student).
Therefore, the probability that the first student is a boy is 1/2, the probability that the second student is a girl is 3/4, and the probability that the first student is a boy and the second student is a girl is 3/8.
Read more about probabilities at:
brainly.com/question/11234923
#SPJ1
In formally proving that lim…….
The value of m in the limit is (-13 + sqrt(169 + 4ε)) / 2, where -84.875 < ε < 1.
What is the value of mTo prove that lim as x approaches 6 of (x^2+x) = 42, we need to find a δ > 0 such that if 0 < |x - 6| < δ, then |(x^2+x) - 42| < ε, where ε > 0 is arbitrary.
We can start by working with the expression |(x^2+x) - 42| and trying to bound it by ε. We have:
|(x^2+x) - 42| = |x^2 + x - 6^2 - 6 + 36| = |(x-6)(x+7)|.
To get a bound on |(x-6)(x+7)|, we can assume that 0 < |x - 6| < δ, where δ > 0 is some quantity we need to determine. This means that:
|x-6| < δ.
We can then use the triangle inequality to bound |x+7| as follows:
|x+7| <= |x-6| + |13| < δ + 13.
Thus, we have:
|(x-6)(x+7)| <= |x-6|*|x+7| < δ(δ+13).
Now, we want to choose δ such that δ(δ+13) < ε. Let's choose:
δ = min(ε/m, 1),
where m is some constant we need to determine. We want to make sure that this choice of δ satisfies δ(δ+13) < ε.
Substituting δ = min(ε/m, 1) into the inequality δ(δ+13) < ε, we get:
min(ε/m, 1)(min(ε/m, 1) + 13) < ε.
Simplifying this inequality gives:
min(ε/m, 1)^2 + 13min(ε/m, 1) - ε < 0.
Since we want to choose the smallest possible value of δ that satisfies this inequality, we want to choose m to be the largest value that satisfies this inequality.
The discriminant of the quadratic equation is:
b^2 - 4ac = 13^2 + 4ε.
Since ε > 0, we know that the discriminant is positive, so there are two roots to the quadratic equation. The largest root is:
(-13 + sqrt(169 + 4ε)) / 2.
So, we can choose:
m = (-13 + sqrt(169 + 4ε)) / 2.
Then, we have:
min(ε/m, 1) = ε/((-13 + sqrt(169 + 4ε)) / 2).
Substituting this value of δ into the inequality δ(δ+13) < ε, we get:
ε^2 / (13 - sqrt(169 + 4ε)) < ε.
This simplifies to:
ε < 13 - sqrt(169 + 4ε).
Squaring both sides and rearranging, we get:
4ε^2 + 338ε - 1444 < 0.
This quadratic inequality holds if and only if:
(-338 - sqrt(338^2 + 441444)) / (24) < ε < (-338 + sqrt(338^2 + 441444)) / (24).
Simplifying this gives:
-84.875 < ε < 1.375.
Thus, we have found that if we choose:
m = (-13 + sqrt(169 + 4ε)) / 2,
where:
-84.875 < ε < 1.
Learn more on limits here;
https://brainly.com/question/1444047
#SPJ1
A random sample of 223 students were asked if they owned a pet or not. The following contingency table gives the two-way classification of their responses.
The probabilities of the random sample of 223 students are solved
P ( male ) = 0.475
P ( female ) = 0.525
P ( male | pet ) = 0.538
P ( female | no pet ) = 0.547
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the total number of students be = 223 students
Let the total number of male students be = 49 + 57 = 106 students
Let the total number of female students be = 64 + 53 = 117 students
Now , the equation will be
Let the number of male students who own a pet = 57 students
Let the number of male students who does not own a pet = 49 students
And ,
Let the number of female students who own a pet = 53 students
Let the number of female students who does not own a pet = 64 students
The probability of choosing a male student P ( male ) = number of male students / total number of students
The probability of choosing a male student P ( male ) = 106 / 223
The probability of choosing a male student P ( male ) = 0.475
And ,
The probability of choosing a female student P ( female ) = number of male students / total number of students
The probability of choosing a female student P ( female ) = 117 / 223
The probability of choosing a female student P ( female ) = 0.525
And ,
Probability of choosing a male student who owns a pet P ( male | pet ) = number of male students who own a pet / number of male students
P ( male | pet ) = 57 / 106
P ( male | pet ) = 0.538
The probability of choosing a female student who does not own a pet is P ( female | no pet ) = number of female students who does not own a pet / number of female students
P ( female | no pet ) = 64 / 117
P ( female | no pet ) = 0.547
Hence , the probabilities are solved
To learn more about probability click :
https://brainly.com/question/17089724
#SPJ1
log8(_)-log8 7 = log8 5/7
fill in the blank (_)
[tex]\begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_8(x)-\log_8(7)=\log_8\left( \cfrac{5}{7} \right)\implies \log_8(\stackrel{x }{5})-\log_8(7)=\log_8\left( \cfrac{5}{7} \right)[/tex]
a) Use the Intermediate Value Theorem to show that the following equation has a solution on the given interval.b) Use the graphing utility to find all the solutions to the equation on the given interval.c) Illustrate your answers with an appropriate graph.
evaluate the integral below by interpreting it in terms of areas in the figure. the areas of the labeled regions are
The integral evaluates to 11, which is the sum of the areas of the three regions (R1 + R2 + R3 = 4 + 5 + 6 = 11).
R1 = 4, R2 = 5, R3 = 6
The integral evaluates to 11, which is the sum of the areas of the three regions (R1 + R2 + R3 = 4 + 5 + 6 = 11).
The integral is given by:
∫ (R1 + R2 + R3) dA
where R1, R2, and R3 are the areas of the labeled regions in the figure.
By interpreting the integral in terms of areas, we can calculate the value of the integral. The integral evaluates to 11, which is the sum of the areas of the three regions (R1 + R2 + R3 = 4 + 5 + 6 = 11).
The complete question is :
Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the labeled regions are A = 3, B = 4, C = 5, and D = 6.
∫DBCA x dA
Learn more about integral here
https://brainly.com/question/18125359
#SPJ4
Put the following equation of a line into slope-intercept form, simplifying all fractions.
4y−6x=24
Answer:
[tex]y = \frac{3}{2}x + 6[/tex]
Step-by-step explanation:
Rearranging the equation:
[tex]4y = 6x + 24[/tex]
The coefficient of y has to be '+1' for the above equation to be considered as the slope-intercept form.
Dividing both sides of the equation by '4':
[tex]\frac{4}{4}y = \frac{1}{4}(6x + 24)[/tex]
Expand the brackets by applying the Distributive Law:
[tex]\frac{4}{4}y = \frac{6}{4}x + \frac{24}{4}[/tex]
[tex]y = \frac{6}{4}x + 6[/tex]
Divide the numerator and the denominator present in the coefficient of x by the Highest Common Factor '2':
[tex]y = \frac{3}{2}x + 6[/tex]
An experiment involves 30 participants. From these, a group of 5 participants is to be tested under a special condition. How many groups of 5 participants are possible?
Answer:
6
Step-by-step explanation:
30 divided by 5 = 6
6 is the maximum possible number of groups possible.
A store bought a hand-crafted toy chest at a cost of $921.60 and marked it up 115%. Sebastian bought it and paid 2% sales tax. What was his total cost
Todd keeps his 4-room house very clean. It takes 1 hour and 36 min to clean his whole house. How long does it take him to clean one room?
Answer:
24 min
Step-by-step explanation:
1 hr 36 min = 96 min
96 min / 4 = 24 min
Need help asap!!
The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift. Apportion 21 salespeople using Hamiltons method given the information below
Hamilton's method of allocating can be used to assign the 21 salespeople in the table in the following order:
2, 5, 6, 8.
What do you mean by Hamilton's method of apportioning?Alexander Hamilton was the one who first suggested the strategy that now carries his name. In 1791, Congress approved of his strategy, but President Washington disapproved of it. It was commonly used from 1852 through 1911. He begins by figuring out exactly how many objects each group requires.
We'll use the terminology of shift and hours since the relevant question is about the allocated salesperson in order to calculate the appropriate number of salespeople for each shift.
Now total no. of customers given = 125 + 305 + 439 + 515 = 1375
Now total no of salesperson available = 21.
So, the divisor = 1375/21 = 65.47
Hamilton's approach is now used to determine the number of salespeople assigned by dividing the average number of customers per shift by the divisor.
So, the salesperson assigned are:
Morning = 125/65.47 = 2
Midday = 305/65.47 = 5
Afternoon = 430/65.47 = 6
Evening = 515/65.47 = 8 (Decimals rounded according to Hamilton's principle).
To know more about Hamilton's method of apportioning, visit:
brainly.com/question/24180735
#SPJ1
If the lengths of two adjacent sides of a parallelogram area a and b, and if the acute angle formed by these two sides is theta, show that the product of the lengths of the two diagonals is given by the expression (a^2 + b^2)^2 - 4a^2b^2cos^2theta
√(a² + b²)² - 4a²b²cos²θ is the product of the lengths of the two diagonals is given by the expression.
What is a mathematical expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division.
An expression's structure is as follows: Number/variable, Math Operator, Number/Variable is an expression.
we have AB as a, AD as b and the angle between them is theta.
So using the cosine rule, we have
BD = √a² + b² - 2abcosθ
So now consider the triangle ABC
Here AB is a, BC is b and the angle is 180-theta
So using cosine rule, we get AC as
AC = √a² + b² - 2abcosθ( 180 - θ )
AC = √a² + b² - 2ab(-cosθ )
AC = √a² + b² - 2abcosθ
Now we have the two diagonals AC and BD. So multiplying, we get
AC × BD = √a² + b² + 2abcosθ × √a² + b² - 2abcosθ
Simplifying, we get
AC × BD = √(a² + b² + 2abcosθ) × (√a² + b² - 2abcosθ)
AC × BD = √(a² + b²)² - (2abcosθ)²
AC × BD = √(a² + b²)² - 4a²b²cos²θ
Learn more about the expression
brainly.com/question/29052794
#SPJ4
Nancy wants to share some money between three different charities. She
splits £370 into three amounts that she calls A, B and C.
The ratio A: Bis 2: 5.
The ratio A: C is 3:8.
Work out how much money C represents.
Step-by-step explanation:
To find the amount of money represented by C, we need to find the value of A and B first.
Since the ratio A:B is 2:5, we can assume that B is 5 times the amount of A.
Let's assume the amount of money represented by A is x.
Then B = 5x and C = 8x.
We know that the total amount of money split is £370, so we can write an equation:
x + 5x + 8x = £370
14x = £370
x = £26.43
So, the amount of money represented by C is 8x = 8 * £26.43 = £211.44
Construct a know-show table for each of the following statements and then write a formal proof for one of the statements.
(a) If m is an odd integer, then m + 1 is an even integer.
(b) If x is an even integer and y is an odd integer, then x + y is an odd integer
(c) If m is an even integer, then 3m^2 + 2m + 3 is an odd integer.
Step-by-step explanation:
(a)
If m is an odd integer, then m + 1 is an even integer.
m (odd integer) m + 1 (even integer)
1 2
3 4
5 6
... ...
Proof:
Suppose m is an odd integer. We can write m as 2n + 1 for some integer n. Then,
m + 1 = (2n + 1) + 1 = 2n + 2
Since 2n + 2 is clearly an even integer, it follows that m + 1 is an even integer if m is an odd integer.
(b)
If x is an even integer and y is an odd integer, then x + y is an odd integer
x (even integer) y (odd integer) x + y (odd integer)
0 1 1
2 3 5
4 5 9
... ... ...
Proof:
Suppose x is an even integer and y is an odd integer. We can write x as 2n and y as 2m + 1 for some integers n and m. Then,
x + y = 2n + (2m + 1) = 2(n + m) + 1
Since n + m is clearly an integer, it follows that x + y is an odd integer if x is an even integer and y is an odd integer.
(c)
If m is an even integer, then 3m^2 + 2m + 3 is an odd integer.
m (even integer) 3m^2 + 2m + 3 (odd integer)
0 3
2 27
4 99
... ...
Proof:
Suppose m is an even integer. We can write m as 2n for some integer n. Then,
3m^2 + 2m + 3 = 3(2n)^2 + 2(2n) + 3 = 12n^2 + 4n + 3
Since 12n^2 + 4n + 3 is clearly an odd integer, it follows that 3m^2 + 2m + 3 is an odd integer if m is an even integer.
PLEASE HELP!!!!!!!!!!!
What are the benefits and limitations of quadratic models in real world applications such as bridge design?
The benefits of using quadratic models in real-world applications include: -They are versatile and can be used for a variety of problems.
Why are Quadratic Models important?Researchers may find the quadratic model to be a useful data analytic approach for helping them identify the combined impacts of achievement goals on academic accomplishment.
We anticipate that future studies on the impact of academic achievement goals will frequently use the quadratic model to analyze their data.
Situations that can be approximated by quadratic functions include tossing a ball, firing a cannon, jumping off a platform, and hitting a golf ball.
Read more about quadratic models here:
https://brainly.com/question/1214333
#SPJ1
Luciano walked 7/18 mile on Saturday morning. On Sunday, she walked 5/9 mile. How much more did she walk on Sunday than on Saturday. Shade the box next to any answer.
The distance Luciano walked more on Sunday is given by the equation A = ( 1/6 ) of a mile
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 distance Luciano walked more on Sunday be A
Now , the equation will be
The distance walked by Luciano on Sunday = ( 5/9 ) mile
The distance walked by Luciano on Saturday = ( 7/18 ) mile
So , the distance Luciano walked more on Sunday A = distance walked by Luciano on Sunday - distance walked by Luciano on Saturday
Substituting the values in the equation , we get
The distance Luciano walked more on Sunday A = ( 5/9 ) - ( 7/18 )
On simplifying the equation , we get
The distance Luciano walked more on Sunday A = ( 10 - 7 ) / 18
The distance Luciano walked more on Sunday A = 3/18 miles
The distance Luciano walked more on Sunday A = 1/6 miles
Hence , the equation is A = 1/6 of a miles
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
Square has a perimeter of 36 find the area
Answer:
A = 81 units²
Step-by-step explanation:
the sides of a square (s) are congruent
given perimeter = 36 , then
s = 36 ÷ 4 = 9
the area (A) of a square is calculated as
A = s²
then
A = 9² = 81 units²
please help me with this question thank you
The average rate of change of a function f(x) on the interval [4, 9] is -67.
What is the average rate of change?
The average rate of change of a function between two points is the same that the slope of the line passes through these points (secant line).
The given table:
The average rate of change of a function f(x) over the interval [a, b] is
= f(b) - f(a)/b-a.
Interval : [4, 9]
f(9) = -419,
f(4) = -84
The average rate of change of a function f(x) on the interval [4, 9] is
= f(9) - f(4)/9 - 4.
= -419 - (-84) / 5
= -297/ 5
= -67
Hence, The average rate of change of a function f(x) on the interval [4, 9] is -67.
To learn more about the average rate of change visit,
https://brainly.com/question/11627203
#SPJ1
In 1994, the city of Amuel had a population of 1,256 people. That same year a factory opened near the town, and many people moved into the city limits. The population grew to 1,381 people in 1995, and in 1996 the population of Amuel reached 1,519 people. Assume this rate of growth continued until the factory closed in 2007. How many people were living in Amuel when the factory closed? Explain. Round to the nearest whole number, if needed.
Answer:
4604 (when rounded to the nearest whole number)
Step by step explanations:
Using the exponential growth formula, we can determine Amuel's population at the time the factory shut down: N = N0 * e^(rt) (rt) Where r is the growth rate, t is the number of years the growth takes place, N is the ultimate population, N0 is the starting population, and r represents growth.
We may use the population data from 1995 and 1996 to get the growth rate: r = ln(1,381 / 1,256) / (1996 - 1995) (1996 - 1995)
Putting the numbers in: r = 0.117
Next, we determine how many years the growth took place: t = 13 years (2007 - 1994) Lastly, we enter the values into the formula as follows: N = 1,256 * e^(0.117 * 13)
Calculating the answer, we discover: 4,604 persons (N = 1,256 * 3.63) Consequently, there were about 4,604 residents there when the facility shut down in 2007.