Factor in the trinomial form of ax²+bx+c

4x²+15x+9

The solution of the given differential equation by using variable separable is [tex]y=\frac{x^2c}{2}-2[/tex]

An equation involving one or more functions and their derivatives is referred to as a differential equation in mathematics. The rate of change of a function at a particular moment is determined by the function's derivatives. It is mostly employed in disciplines like biology, engineering, and physics. The study of solutions that satisfy the equations and the characteristics of the solutions is the main goal of the differential equation.

The rules to solve differential equations using variables separable,

1) [tex]\frac{dy}{dx}=f(x)/f(y)[/tex]

2) separate terms with the same variable

f(y)dy=f(x)dx

3) Take integration on both sides

4) solve integration by using a suitable method

5) Then get the Solution of the differential equation.

The given differential equation is-

[tex]\frac{dy}{dx}=\frac{2y+4}{x}\\\\\frac{dy}{2y+4}=\frac{dx}{x}\\\\\int\frac{dy}{2y+4}=\int\frac{dx}{x}\\\\\frac{log(2y+4)}{2}=logx+logc\\log(2y+4)=2logxc\\2y+4=x^2c\\2y=x^2c-4\\y=\frac{x^2c}{2}-2[/tex]

learn more about differential equation,

https://brainly.com/question/14620493

#SPJ1

Therefore, the solution to the system of equations is x = 8 and y = 23.

An equation is a statement that shows the equality between two mathematical expressions using symbols, numbers, and/or variables. Equations are used to describe relationships between different quantities, and they are commonly used in many fields, including mathematics, physics, chemistry, engineering, and economics.

by the question.

Let's solve the first equation for y:

y = 3x - 1

Now we substitute this expression for y in the second equation:

2x + 7 = y

We can substitute 3x - 1 for y in this equation:

2x + 7 = 3x - 1

Now we can solve for x:

2x - 3x = -1 - 7

-x = -8

x = 8

Now we can substitute x = 8 into either equation to solve for y. Let's use the first equation:

y = 3x - 1

y = 3(8) - 1

y = 24 - 1

y = 23

To learn more about equations:

https://brainly.com/question/10413253

#SPJ1

Therefore , the solution of the given problem of probability comes out to be 0 0.015, 0.018, 0.045 , 0.061 and 0.045.

Every procedure's criteria-based approaches have as their main objective determining the likelihood that a statement is accurate or that an event will take place. Any number from one to one, where 0 typically represents chance and 1 typically reflects degree of certainty, can be used to symbolize chance. A probability illustration shows the likelihood that a particular occurrence will occur.

Here,

The formula below can be used to calculate the likelihood of drawing precisely k red balls in 4 draws:

=> P(b = k) =  (C(6, k) * C(5, 4-k))/C.(11, 4)

By applying this method, the probability distribution for b can be determined as follows:

=> P(b = 0) = (C(6, 0) * C(5, 4-0)) / C(11, 4) = (1 * 5) / 330 = 0.015

=> P(b = 1) = (C(6, 1) * C(5, 4-1)) / C(11, 4) = (6 * 1) / 330 = 0.018

=> P(b = 2) = (C(6, 2) * C(5, 4-2)) / C(11, 4) = (15 * 1) / 330 = 0.045

=> P(b = 3) = (C(6, 3) * C(5, 4-3)) / C(11, 4) = (20 * 1) / 330 = 0.061

=> P(b = 4) = (C(6, 4) * C(5, 4-4)) / C(11, 4) = (15 * 1) / 330 = 0.045

As a result, the following is the probability distribution for the random variable b that represents the number of red balls pulled in 4 subsequent draws from the box:

b P(b)

0 0.015

1 0.018

2 0.045

3 0.061

4 0.045

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

Debt payments relate to gross income in terms of the debt-to-income (DTI) ratio by total debt payments are divided by total. gross income.

How do debt payments relate to gross income?

The debt-to-income (DTI) ratio is a financial measurement used by lenders to assess a borrower's ability to manage debt payments. It is calculated by dividing the borrower's total debt payments by their total gross income. The resulting ratio is expressed as a percentage and indicates the portion of the borrower's income that goes towards paying their debt obligations.

For example, if a borrower has total debt payments of $1,000 per month and a gross income of $4,000 per month, their DTI ratio would be 25% ($1,000 divided by $4,000). A lower DTI ratio indicates that a borrower has more disposable income available after paying their debts and is generally viewed as a positive factor by lenders when considering a borrower for a loan or credit.

So, correct option is total debt payments are divided by total gross income.

Learn more about gross income here,

https://brainly.com/question/30657802

#SPJ1

Answer:

D. total debt payments are divided by total gross income

Step-by-step explanation:

D. total debt payments are divided by total gross income

The formula for the number of bacteria at time t is given by N = 10,000e^(0.0173t).

The formula for the number of bacteria at time t can be found using the exponential growth formula. The formula for exponential growth is given by;N = N0ertWhere;N is the number of bacteria after t minutes.N0 is the initial number of bacteria.r is the growth rate.t is the time interval.

To find the formula for the number of bacteria at time t, substitute the given values into the exponential growth formula.N0 = 10,000r = ln2/40 = 0.0173 (since the number of bacteria doubles every 40 minutes, the growth rate is equal to the natural log of 2 divided by 40.)t = t minutesN = 10,000e^(0.0173t)

Learn more about Bacteria

brainly.com/question/8008968

#SPJ11

Answer:

The monthly installment for the hire purchase of the motorbike is GHC 27.00

Step-by-step explanation:

To calculate the monthly installment for the hire purchase, we can divide the total cost by the number of months:

Monthly installment = Total cost / Number of months

In this case, the total cost is GHC 540.00 and the number of months is 20:

Monthly installment = GHC 540.00 / 20

Monthly installment = GHC 27.00

Therefore, the monthly installment for the hire purchase of the motorbike is GHC 27.00

Answer:

0

Step-by-step explanation:

if f is an even function, it means that:

f(x) = f(-x) for every x of the domain

So, because 7 is in f's domain, f(7) = f(-7),

and so f(7) - f(-7) = 0

The minimum sample size required for the estimate, considering the z-distribution, is given as follows:

560.

The bounds of the confidence interval are given by the rule presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The margin of error is modeled as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

The parameters for this problem are given as follows:

[tex]M = 0.16, \sigma = \sqrt{5.29} = 2.3, z = 1.645[/tex]

Hence the sample size is obtained as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.16 = 1.645\frac{2.3}{\sqrt{n}}[/tex]

[tex]0.16\sqrt{n} = 1.645 \times 2.3[/tex]

[tex]\sqrt{n} = \frac{1.645 \times 2.3}{0.16}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.645 \times 2.3}{0.16}\right)[/tex]

n = 560. (rounded up).

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Answer: D or the Fourth Choice-The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12

PEDMAS means Parentheses, Exponents, Divide, Multiply,Add,Subtract. The first thing we must solve is what is in the parentheses, that is 14.8 divided by 2. We don't have any exponents, so we move to divide. We have already solved the division sentence that was in the parentheses, so we have to multiply 6x3 next. 6x3 will then be added to the answer that was divided by 14.2 and 2, and lastly we will subtract 12. The only answer choice that follows that pattern is D or The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12.

I hope this helped & Good Luck <3!!!!

Answer:

  (x, y) = (-2, -1) or (1, 2)

Step-by-step explanation:

You want to find the algebraic solutions to the system of equations ...

The x-value of the solutions will be the solutions to ...

  f(x) = g(x)

  f(x) -g(x) = 0

  (x² +2x -1) -(x +1) = 0 . . . . substitute for f(x) and g(x)

  x² +x -2 = 0 . . . . . . . . . simplify

  (x +2)(x -1) = 0 . . . . . factor

The zero product rule says the solutions will be values of x that make one or the other of the factors zero.

  x = -2 or +1 . . . . . . . values that make the factors zero

  y = x +1 = -1 or +2 . . . . from the equation for g(x)

Solutions are (x, y) = (-2, -1) or (1, 2).

We already know that g(x) is satisfied by these x- and y-values.

  f(x) = x² +2x -1 = (x +2)x -1

  f(-2) = (-2 +2)(-2) -1 = 0 -1 = -1 . . . . . (-2, -1) is a solution

  f(1) = (1 +2)(1) -1 = 3 -1 = 2 . . . . . . . . . (1, 2) is a solution

These values agree with the above, so we have shown the solutions satisfy both equations in the system of equations.

Let's start by finding the current monthly revenue of the airline for the given number of passengers and ticket price:

Monthly revenue = number of passengers x ticket price

Monthly revenue = 9000 x $30

Monthly revenue = $270,000

Now, let's find the number of passengers for each $1 increase in the ticket price:

Number of passengers lost = 50

So, for a ticket price increase of $x, the number of passengers will be:

Number of passengers = 9000 - 50x

The ticket price will then be $30 + $x, and the revenue will be:

Revenue = (9000 - 50x) x ($30 + $x)

Revenue = 270,000 - 1500x + 30x + x^2

Revenue = x^2 - 1470x + 270,000

To find the ticket price that will maximize the revenue, we need to find the vertex of the parabola given by the revenue equation. The x-coordinate of the vertex is:

x = -b/2a

Where a = 1, b = -1470, and c = 270,000.

x = -(-1470)/2(1)

x = 1470/2

x = 735

So, the ticket price that will maximize the revenue is $30 + $735 = $765. The maximum monthly revenue is then:

Revenue = (9000 - 50(735)) x ($30 + $735)

Revenue = 105 x $765

Revenue = $80,325

Therefore, the ticket price that will maximize the airline's monthly revenue for the route is $765, and the maximum monthly revenue is $80,325.

The solution q = -10 does not satisfy the original equation. Therefore, there is no solution to the equation.

What are equations?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

To solve the equation [tex]\frac{4}{q}(q-10) = 8[/tex] we can begin by simplifying the left side of the equation:

[tex]\frac{4}{q}(q-10) = 8[/tex]

[tex]\Rightarrow \qquad 4(q-10) = 8q \text {multiply both sides by }q[/tex]

[tex]\Rightarrow \qquad 4q - 40 &= 8q && \text{distribute }4 \\\\\Rightarrow \qquad -40 &= 4q && \text{subtract }4q\text{ from both sides} \\\\\Rightarrow \qquad -10 &= q && \text{divide both sides by }-4.\\\end{align*}[/tex]

Therefore, the solution to the equation is q= -10. We can check our answer by plugging q= -10 back into the original equation:

[tex]\frac{4}{q}(q-10) &= 8 \\\\\\\Rightarrow \qquad \frac{4}{-10}(-10-10) &= 8 && \text{substitute }q=-10\\\\\\\Rightarrow \qquad -\frac{4}{5} \cdot (-20) &= 8 \\\\\\\Rightarrow \qquad 16 &= 8\end{align*}[/tex]

Since the last equation is false, the solution q = -10 does not satisfy the original equation. Therefore, there is no solution to the equation.

Learn more about equations on:

https://brainly.com/question/22688504

#SPJ1

According to the student question, the sampling distribution of the proportion of people who respond "yes" in the samples of 4 individuals is binomial because the number of people who respond "yes" has binomial distribution. The correct answer is A.

The sampling distribution of the proportion of people who respond "yes" in the samples of 4 individuals is binomial because the sample size is sufficiently small and each person's response is independent of the others.

Binomial distribution is used to model the number of successes in a fixed number of independent trials, where the probability of success is constant for each trial. In this case, the proportion of people who respond "yes" is the number of successes out of the total number of trials (i.e., 4 people).

Moreover, the responses of each individual are independent of each other, meaning that the probability of one person answering "yes" does not affect the probability of another person answering "yes."  The correct answer is A.

Your question is incomplete but most probably your full question was

Samples of four people were asked whether gun laws should be more stringent. Respondents had a choice to answer "yes" or "no." The sampling distribution of the proportion of people who respond "yes" in the samples of 4 individuals is

a.  Binomial because the number of people who respond "yes" has binomial distribution

b. Not possible to say because the sample size it too small

c. Not possible to say because population distribution is not known

d. Normal

Learn more about binomials distribution at https://brainly.com/question/31197941

#SPJ11

Answer:

11/20

Step-by-step explanation:

1,10,11,12,13,14,15,16,17,18,19 All have the number "1"

there are 11 of them so 11/20 have the digit 1.

:)

Answer:

To find the fraction of the numbers from 1 to 20 that contain the digit 1, we can count the number of such numbers and divide by the total number of numbers from 1 to 20.

The numbers from 1 to 20 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

The numbers that contain the digit 1 are: 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.

Therefore, there are 11 numbers from 1 to 20 that contain the digit 1.

The fraction of the numbers from 1 to 20 that contain the digit 1 is:

fraction = number of numbers containing 1 / total number of numbers

fraction = 11 / 20

So, the fraction of the numbers from 1 to 20 that contain the digit 1 is 11/20 or 0.55.

(Please could you kindly mark my answer as brainliest you could also follow me so that you could easily reach out to me for any other questions)

If you are 25 years of age, your typing speed is equal to 82.8 units.

In Mathematics, a line of best fit is sometimes referred to as a trend line and it can be defined as a statistical or analytical tool that is typically used by researchers and mathematicians in conjunction with a scatter plot, in order to determine whether or not there is any form of association and correlation between a data set.

Based on the scatter plot, we can logically deduce that an equation which represents the line of best fit include the following:

y = -1.4x + 117.8

When you are 25 years of age, your typing speed can be calculated as follows;

y = -1.4x + 117.8

y = -1.4(25) + 117.8

y = -35 + 117.8

y = 82.8 units.

Read more on line of best fit here: brainly.com/question/12284501

#SPJ1

The total area of the shaded region is 67.92 sq. in.

A sector is a section of a circle that may be described using the following four criteria:

Two radii and an arc surround a section of a circle. The two sectors that make up a circle are referred to as the minor and major sectors. The main sector of the circle is the larger area, while the minor sector is the smaller area. The circle is split into two equally sized sections in the case of semicircles.

Let us suppose the central angle of the shaded portion = x.

From the given figure we observe that angle DEC = 143 degrees, and angle AEB are equal as they are vertically opposite angles.

The angle formed by the shaded regions are same as they are vertically opposite angles.

Thus,

143 + 143 + x + x = 360

286 + 2x = 360

2x = 74

x = 37

Now, the area of the sector is given as:

A = α/360 πr²

Here, r = 10.4 in.

Substituting the values:

A = (37/360)π(10.4)²

A = (0.10)(3.14)(10.4)²

A = 33.96 sq in.

There are two shaded portions thus:

Total area = 2(33.96)

Total area = 67.92 sq. in.

Hence, the total area of the shaded region is 67.92 sq. in.

Learn more about sector area here:

https://brainly.com/question/16367606

#SPJ1

Answer:

Step-by-step explanation:

We are given with a circle whose diameter is 28.2 m

Then, Radius will be diameter/2

=> 28.2 /2

=> 14.1 m

Area of circle = πr²

=> 31.4 × (14.1)²

=> 31.4 × 198.81

=> 624.26 m²

Therefore, the area of the given circle is 624.26 m²

area of trapezium is 30 in².

A trapezium is a four-sided geometric figure that has only one pair of parallel sides. It is also known as a trapezoid in some countries. The parallel sides of a trapezium are called the bases, and the non-parallel sides are called the legs. The height (or altitude) of a trapezium is the perpendicular distance between the two bases.

The area of a trapezium is given by the formula:

A =½(a×b)h

where "a" and "b" are the lengths of the parallel sides of the trapezium, and "h" is the height (or perpendicular distance) between the parallel sides.

Length of two parallel side

a=7.7in

b=2.3in

Height of trapezium, h=6in

Area of trapezium=½(a×b)h

=½(7.7+2.3)×6

=3×10

=30in²

Hence, area of trapezium is 30 in².

To know more about area, visit:

https://brainly.com/question/27683633

#SPJ1

We can start by using the formula for the mean (average):

Mean = (sum of numbers) / (number of numbers)

We are given that the mean of 3, 15, and another number is 40, so we can set up an equation:

40 = (3 + 15 + x) / 3

Multiplying both sides by 3 yields:

120 = 3 + 15 + x

Simplifying this equation gives:

102 = x

Therefore, the missing number is 102.

According to the solving this word problem It will take the slowest pump [tex]\frac{7}{2}[/tex] hours to complete filling the pool.

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve a problem from "real life." In order for kids to understand the word problem, they must be acquainted with the vocabulary that goes along with the mathematical symbols that they are used to.

According to the given information,

The first pump can fill the pool in 4 hours, so its rate is 1/4 of the pool per hour.

The second pump can fill the pool in 6 hours, so its rate is 1/6 of the pool per hour.

The total work done in fraction by both pumps in an hour is:

[tex]\frac{1}{4} + \frac{1}{6} = \frac{5}{12}[/tex]

The remaining work to be completed by the slowest pump is:

[tex]1 - \frac{5}{12} = \frac{7}{12}[/tex]

The ratio of the amount of work left to be done by the weakest pump's work rate determines how long it will take to fill the pool:

[tex]\frac{7}{12} \frac{1}{6} = \frac{7}{12} * 6 = \frac{7}{2}[/tex]

According to the solving It will take the slowest pump [tex]\frac{7}{2}[/tex] hours to complete filling the pool.

To know more about fraction, visit

brainly.com/question/10354322

#SPJ1

Answer:

x = 7 ft

Step-by-step explanation:

[tex]tan 55=\frac{10}{x}\\x=\frac{10}{tan 55}\\x=7.0020\\x=7[/tex]

The probability that daily production is less than 44.4 liters is  96.71%

According to the given data, the mean daily production of a herd of cows is assumed to be normally distributed with a mean of 37 liters and a standard deviation of 4 liters.

We need to calculate the probability that daily production is less than 44.4 liters using technology, not tables.Using technology, we can use the standard normal distribution formula to get the required probability.

We can use the standard normal distribution to calculate the probability that the daily production is less than 44.4 liters. To do this, we first need to standardize the variable:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

Substituting the given values, we have:

z = (44.4 - 37) / 4 = 1.85

Using a standard normal distribution table or a calculator with a normal distribution function, we can find that the probability of a standard normal random variable being less than 1.85 is approximately 0.9671.

Different calculators may have slightly different ways to calculate normal probabilities. Here is an example using a TI-84 calculator:

Therefore, the probability that the daily production is less than 44.4 liters is approximately 0.9671, or 96.71% (rounded to two decimal places).

Learn more about probability at https://brainly.com/question/15310601

#SPJ11

The expression 2⁻³ = 1/8 into logarithmic form is log₂(1/8) = -3

In logarithmic form, the equation 2⁻³ = 1/8 can be written as log base 2 of 1/8 = -3.

Mathematically, we have

log₂(1/8) = -3

This means that the exponent that gives 2⁻³ is -3, and the logarithm base 2 of 1/8 is -3.

Logarithmic form is often used to solve exponential equations where the variable is in the exponent.

In logarithmic form, the variable is moved from the exponent to the logarithm, making it easier to solve for the unknown variable.

Read more about logarithm at

https://brainly.com/question/28041634

#SPJ1

Answer:

C = 11,21 cm

using the formulas :

A (area) = 10 [tex]cm^{2}[/tex]

A = π [tex]r^{2}[/tex]

C = 2 π r

colving for C :

C = 2 *√(π*Α) = 2 *√(π * 10) = 11,20998 cm

Answer: $91.85

Step-by-step explanation:

19.95 + 41.25 + 30.65

= 91.85

And bro, its not that hard to simply calculate it in your head, or even on a paper. Like literally, there's calculators too

The value of v/2 +(3/4 +w) when v = 1 and w = 5/8 is 1 7/8

substitution of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables.

Since V = 1 and W = 5/8, by substituting 1 for V and 5/8 for w in the expression

v/2 +(3/4 +w) = 1/2+ ( 3/4 + 5/8)

= 1/2 + (6+5)/8

= 1/2 + 11/8

= (4+11)/8

= 15/8

= 1 7/8

Therefore the value of v/2 +(3/4 +w) when v is 1 , and w is 5/8 is 1 7/8

learn more about substitution of variable from

https://brainly.com/question/26094713

#SPJ1

Step-by-step explanation:

remember answer 2.

3. I answered already in my other answer.

remember, the diagonals split the angles in half.

so,

d1 = 50°

4. the tangent ratio is sine/cosine (that is the definition of tangent).

c2 = 40°

sin(40) × 5 = OD (half of BD)

cos(40) × 5 = OC

the tangent ratio is

(sin(40) × 5) / (cos(40) × 5) = sin(40)/cos(40) = OD/OC =

≈ 3.2 / 3.8 = 1.6/1.9 =

= 0.842105263...

control : tan(40) = 0.839099631... close enough (we used round numbers with 3 2 and 3.8 - see again 1. and 2.).