Factorise 9x^2y+12xy^2

Answers

Answer 1

Answer:

3x(3xy + 4y^²).

Step-by-step explanation:

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Related Questions

In each of Problems 6 through 9, determine the longest interval in which the given initial value problem is certain to have a unique twice- differentiable solution. Do not attempt to find the solution. 6. ty" + 3y = 1, y(1) = 1, y'(1) = 2 7. t(t – 4)y" + 3ty' + 4y = 2, y(3) = 0, y'(3) = -1 8. y" + (cost)y' + 3( In \t]) y = 0, y(2) = 3, y'(2) = 1 9. (x - 2)y"+y' +(x - 2)(tan x) y = 0, y(3) = 1, y'(3) = 2 = ) y( = = = - =

Answers

(a) The interval (-∞, ∞).

(b) The interval (-∞, ∞).

(d) The interval (-π/2, π/2) \ {0}.

(a) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient function, 3t, is continuous and bounded. Since 3t is a continuous and bounded function for all t in the interval (-∞, ∞), the given initial value problem is certain to have a unique twice-differentiable solution for all t in (-∞, ∞).

(b) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient functions, t(t - 4), 3t, and 4, are continuous and bounded. Since t(t - 4), 3t, and 4 are continuous and bounded functions for all t in the interval (-∞, ∞), the given initial value problem is certain to have a unique twice-differentiable solution for all t in (-∞, ∞).

(c) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient functions, cost and In|t|, are continuous and bounded. Since cost and In|t| are continuous and bounded functions for all t in the interval (-∞, ∞), the given initial value problem is certain to have a unique twice-differentiable solution for all t in (-∞, ∞).

(d) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient functions, x - 2, 1, and (x - 2)tanx, are continuous and bounded. Since x - 2, 1, and (x - 2)tanx are continuous and bounded functions for all x in the interval (-π/2, π/2) \ {0} , the given initial value problem is certain to have a unique twice-differentiable solution for all x in (-π/2, π/2) \ {0}.

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The given question is incomplete, the complete question is:

determine the longest interval in which the given initial value problem is certain to have a unique twice- differentiable solution. Do not attempt to find the solution. (a) ty" + 3y = 1, y(1) = 1, y'(1) = 2 (b) t(t – 4)y" + 3ty' + 4y = 2, y(3) = 0, y'(3) = -1 (c) y" + (cost)y' + 3( In |t|) y = 0, y(2) = 3, y'(2) = 1 (d) (x - 2)y"+y' +(x - 2)(tan x) y = 0, y(3) = 1, y'(3) = 2

{(x, y): y= 3x + 2| and xe (-2, -1, 0, 1, 2)).
(-2,__)

12
3
0

Answers

It looks like you're given a set

{(x, y) : y = 3x + 2}

i.e. the set of points (x, y) = (x, 3x + 2), and you're told that x is taken from the set {-2, -1, 0, 1, 2}.

When x = -2, the corresponding value of y is

y = 3•(-2) + 2 = -6 + 2 = -4

The diagram shows the height of a cone that holds ice cream. The cone has a volume of 4.5 π cubic inches. Which measurement is closest to the radius of the cone in inches?

Answers

On solving the query we can say that The slant height, along with the function cone's height and radius, makes a right triangle as it measures from the apex to a certain point on the circular base.

what is function?

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

You are informed that the cone in this scenario has a volume of 4.5 cubic inches. Using the aforementioned calculation, you can determine the radius if you know the cone's height.

Alternately, you may use the Pythagorean theorem to calculate for the radius if you know the cone's slant height. The slant height, along with the cone's height and radius, makes a right triangle as it measures from the apex to a certain point on the circular base.

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In a triangle with angles measuring a, b and c degrees, the mean of b and c is a. What is the
value of a?

Answers

Answer:

Step-by-step explanation:

$a+b+c=180\\\frac{b+c}{2}=a \rightarrow b+c=2a\\\\a+2a=180\\3a=180\\a=60$

Therefore, the value of a is 60 degrees

How many four-character passwords can be formed using the characters A, B, C, 1, 2 if the characters can be repeated

Answers

Answer: 625

Work Shown:

The set {A,B,C,1,2} has five items. There are four slots to fill.

So we have 5^4 = 5*5*5*5 = 625 different possible passwords where the characters can be repeated.

625 four-character passwords can be formed.

----------------------------

Each character of the password is independent of previous characters, which means that the fundamental counting principle is used to solve this question.

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

----------------------------

4 independent characters.Each with 5 outcomes(A, B, C, 1 or 2).

Thus, the number of passwords is:

$5 \times 5 \times 5 \times 5 = 5^4 = 625$

625 four-character passwords can be formed.

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CHECK PHOTO Intercepts of the graph BE SURE TO BE CORRECT PLEASE no work needed

Answers

Answer:

X intercept: (-40, 0)

Y intercept: (0, 15)

Step-by-step explanation:

Those are the points that intercept each line.

Answer: X intercept: (-40, 0)

Y intercept: (0, +15)

Step-by-step explanation:

PLEASE HELP

2/3x =10

Show your work in details if you can, I have a hard time understanding this.

Answers

$\\ \sf\longmapsto \dfrac{2}{3}x=10$

$\\ \sf\longmapsto \dfrac{2x}{3}=10$

$\\ \sf\longmapsto 2x=3(10)$

$\\ \sf\longmapsto 2x=30$

$\\ \sf\longmapsto x=\dfrac{30}{2}$

$\\ \sf\longmapsto x=15$

$ \begin{cases}\large\bf{\red{ \implies}} \tt \frac{2}{3} x \: = \: 10 \\ \\ \large\bf{\red{ \implies}} \tt \frac{2x}{3} \: = \: 10 \\ \\ \large\bf{\red{ \implies}} \tt 2x \: = \: 3 \: \times \: 10 \\ \\ \large\bf{\red{ \implies}} \tt 2x \: = \: 30 \\ \\ \large\bf{\red{ \implies}} \tt \: x \: = \:\frac{ \cancel{30} \: \: ^{15} }{ \cancel{2}} \\ \\ \large\bf{\red{ \implies}} \tt \: x \: = \: 15 \end{cases}$

Which numbers are 0.6 units away from 1.3 on a number line

Answers

1.9 and 0.7 because you have to add 0.6 and 1.3 to get one of the numbers and you have to subtract 0.6 from 1.3 to get the other number

For a certain species of frog, the optimal temperature range for the tadpoles in degrees Celsius is 20°

Answers

EXPLANATION

Let's see the facts:

The optimal is 20 °

The conversion equation is:

F=9/5C + 32

So, replacing the given range on the equation give us:

F= 9/5(20) + 32 = 68 °

F=9/5(35) +32 = 95 °

So, the optimal rage in degrees Fahrenheit is 68 °

A three-sided fence is to be built next to a straight section of river, which forms the fourth side of a
rectangular region. The enclosed area is to equal 128 m². Find the minimum perimeter and the
dimensions of the corresponding enclosure.

Answers

Answer:

perimeter: 32 mdimensions: 16 m parallel to the river; 8 m wide

Step-by-step explanation:

You want the length of the minimum perimeter fence to enclose 3 sides of a rectangular area of 128 m² with one side of the enclosure provided by a river. You also want the enclosure dimensions.

Perimeter

If x represents the dimension of the enclosure parallel to the river, then the other dimension of the enclosure is found from ...

A = LW

128 = x·W

W = 128/x

There will be two sides of this length, so the perimeter is ...

P = L +2W = x +2(128/x)

P = x + 256/x

Minimum

This has an extreme value (minimum) where its derivative is zero:

dP/dx = 0 = 1 -256/x²

Solving for x gives ...

x² = 256

x = √256 = 16

and the perimeter is ...

P = 16 +256/16 = 32

The other dimension is 128/16 = 8.

The minimum perimeter is 32 meters; the enclosure is 16 by 8 meters.

Additional comment

This can be solved without using derivatives by working the reverse problem: the largest area for a given perimeter.

Using the same definition of x, the area in terms of perimeter is ...

A = x · (P -x)/2

This is a quadratic equation with a maximum halfway between its zeros at x=0 and x=P. So, the value of x for maximum area is x = P/2. That area is ...

A = (P/2)(P -P/2)/2 = (P/2)(P/4) = P²/8

Or, the minimum perimeter for a given area is ...

P = √(8A)

In this problem, that is ...

P = √(8·128) = √1024 = 32

The dimensions of the enclosure are (P/2)×(P/4) = 16×8.

the current in the electronic circuit in the mobile phone was 0.12a the potential difference across the battery was 3.9V. calculate the resistance of the electronic circuit in the mobile phone

Answers

Answer:

Step-by-step explanation:

V = 3.9V

I = 0.12A

Ohm's Law, V = IR

Rearranging Ohm's Law, R = V/I

R = 3.9/0.12 = 32.5Ω

You own a small storefront retail business and are interested in determining the average amount of money a typical customer spends per visit to your store. You take a random sample over the course of a month for 12 customers and find that the average dollar amount spent per transaction per customer is $116.194 with a standard deviation of $11.3781. Create a 90% confidence interval for the true average spent for all customers per transaction.1) ( 114.398 , 117.99 )2) ( 112.909 , 119.479 )3) ( -110.295 , 122.093 )4) ( 110.341 , 122.047 )5) ( 110.295 , 122.093 )

Answers

Answer:

(110.295, 122.093).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 12 - 1 = 11

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 11 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.9}{2} = 0.95$. So we have T = 1.7959

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.7959\frac{11.3781}{\sqrt{12}} = 5.899$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 116.194 - 5.899 = 110.295

The upper end of the interval is the sample mean added to M. So it is 116.194 + 5.899 = 122.093

(110.295, 122.093).

1/3(-9 - 24h) = 37 help please!

Answers

Answer:

h = -5

Step-by-step explanation:

1/3(-9 - 24h) = 37

Multiply each side by 3

3*1/3(-9 - 24h) = 37 *3

-9-24h = 111

Add 9 to each side

-9-24h+9 = 111+9

-24h = 120

Divide by -24

-24h/-24 = 120/-24

h = -5

Answer:

h = -5

Step-by-step explanation:

$\frac{1}{3}\left(-9-24h\right)=37\\\\\mathrm{Multiply\:both\:sides\:by\:}3\\3\times\frac{1}{3}\left(-9-24h\right)=37\times\:3\\\\Simplify\\-9-24h=111\\\\\mathrm{Add\:}9\mathrm{\:to\:both\:sides}\\-9-24h+9=111+9\\\\Simplify\\-24h=120\\\\\mathrm{Divide\:both\:sides\:by\:}-24\\\frac{-24h}{-24}=\frac{120}{-24}\\\\Simplify\\h=-5$

what is the solution to square root 6x - 3 = 2 square root x?

Answers

Answer:

No solution

Step-by-step explanation:

$\sqrt{6x-3}=2\sqrt{x} \\ \\ 6x-3=4x \\ \\ -3=2x \\ \\ x=-\frac{3}{2} $

However, this would make the right hand side of the equation undefined over the reals, so there is no solution.

for each of the number lines, write an absolute value equation in the form |x-c|=d, where c and d are some numbers, to satisfy the given solution set.

Answers

An absolute value is the numerical value of a number without consideration of its sign. It can be represented graphically by a straight line known as a number line. Absolute value equations are equations that include absolute values of variables or unknown quantities. The following are examples of how to write an absolute value equation in the form |x-c|=d to fit the provided solution sets:

Example 1:

Solution set: {x|x≤-3 or x≥1}
Absolute value equation: |x-(-1)|=4
Explanation: -1 is the midpoint of the two ranges (-3 and 1) in the solution set. |x-(-1)|=|x+1| is the absolute value expression for the midpoint -1. The distance d from -1 to the solutions' furthest endpoints, 1 and -3, is four, hence the value of d in the absolute value equation is 4.
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Can someone help me with this pleasee here is the picture

Answers

The system of equations as an augmented matrix is $\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]$

Writing the system of equations as an augmented matrix

From the question, we have the following parameters that can be used in our computation:

x = 100

-5m - 7c = 350

-5m - 9c = 200

The above means that the variables in the system of equations are

x, m and c

So, we have the following representation

x m c

1 0 0 100

0 -5 -7 350

0 -5 -9 200

When represented as an augmented matrix, we have

$\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]$

Hence, the augmented matrix is $\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]$

Answers

Answer:

so let's start

Step-by-step explanation:

$total \: sales = 412454 \\ 7\% = \frac{7}{100} \\ = 0.07 \\ 0.07 \: is \: rate \: of \: commision \: on \: total \: sales \\ 0.07 \times 412454 = 28871.78 \: dollars \\ but \: 5\% \: is \: given \: as \: percentage \: of \: the \: amount \: from \: 7\% \: commission \\ 5\% = \frac{5 }{100} \\ = 0.05 \\ 0.05 \times 28871.78 = 1443.589 \: dollars \: \\ total \: income \: = 28871.78 + 1443.586 \\ = 30.315.369 \: dollars \\ \\ thanks$

This is for 11th grade math

Answers

Answer : H(x) = —10x + 12

Find the perimeter of the following triangle.
Write your answer as a mixed number in simplest form.
Be sure to include the correct unit in your answer.

1/7/18 yd
5/12 yd
1/2/9 yd

Answers

Answer:

If I did my math correctly, I'm pretty sure the answer is 3 1/36 yards.

Step-by-step explanation:

1. First, you have to turn them all into an improper fraction.

1 7/18 becomes 25/18

1 2/9 becomes 11/9

5/12 remains the same as it's already an improper fraction.

2. Find a common denominator, which is 36

25/18 becomes 50/36

11/9 becomes 44/36

5/12 becomes 15/36

3. Add them all together and you get 109/36

4. Turn it into a mixed number, and in this case, is 3 1/36

Solution is 3 1/36

Answer:

3 1/36

Step-by-step explanation:

what is 8÷530 TYPE FAST

Answers

Answer:

0.0150

Step-by-step explanation:

8÷530

0.0150

it is correct

0.01 or 66.25 66.2 66

A sample of 150 CBC students was taken, and each student filled out a
survey. The survey asked students about different aspects of their college
and personal lives. The experimenter taking the survey defined the
following events:
A=The student has children
B = The student is enrolled in at least 12 credits
C = The student works at least 10 hours per week
The student found that 44 students in the sample had children, 73 were
enrolled in at least 12 credits, and 105 were working at least 10 hours per
week. The student also noted that 35 students had children and were
working at least 10 hours per week.
Calculate the probability of the event BC for students in this sample. Round
your answer to four decimal places as necessary.

Answers

Answer:

The probability of the event BC

= the probability of B * C = 48.6667% * 70%

= 34.0667%

Step-by-step explanation:

Probability of A, students with children = 44/150 = 29.3333%

Probability of B, students enrolled in at least 12 credits = 73/150 = 48.6667%

Probability of C, students working at least 10 hours per week = 105/150 = 70%

Therefore, the Probability of BC, students enrolled in 12 credits and working 10 hours per week

= 48.6667% * 70%

= 34.0667%

Janet is comparing prices of bottled water. One bottle of water costs $1.92 and contains 12 ounces. Another bottle of water costs $2.40 and contains 16 ounces. Which bottle of water costs less per ounce?
What number goes in the blank.

Answers

Answer:

The 16 ounce bottle is the cheapest costing only .15 cents per ounces wile the 12 ounce bottle costs .16 cents and ounce.

Step-by-step explanation:

Yes correct answer I have that question on my test

How are exponential functions characterized? Exponential functions are characterized by the fact that: a. the graph will always be positive c. their growth rate is less than their value b. their growth rate is proportional to their value d. the value is greater than the growth rate Please select the best answer from the choices provided A B C D

Answers

Answer:

Option B.

Step-by-step explanation:

Their growth rate is more proportional to their value and exponential functions are mainly characterized by the fact that their rate of growth is proportional to their own value.

Jane buys p packets of plain crisps and c packets
of cheese and onion crisps. Write down an
expression for the total number of packets of
crisps Jane buys.

Answers

The expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

How to obtain the total number of packets?

The amounts of packets of crisps purchased are given as follows:

p packets of plain crisps.c packets of cheese and onion crisps.

The expression for the total number of packets of crisps that Jane buys is given by the addition of these two amounts.

Hence the expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

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Felipe rented a truck for one day. There was a base fee of $17.95, and there was an additional charge of 86 cents for each mile driven. Felipe had to pay $270.79 when he returned the truck. For how many miles did he drive the truck?

Answers

Answer:

421.4 miles

Step-by-step explanation:

Numner of miles= ($270.79-$17.95)/86 cents

= $252.84/$0.60

=421.4 miles

The net of a triangle prism is shown.what is the surface area of the prism

Answers

The total surface area of the triangular prism using the net is 640 square meters

Calculating the total surface area using the net.

From the question, we have the following parameters that can be used in our computation:

The net of a triangular prism (see attachment)

The surface area of the triangular prism from the net is calculated as

Surface area = sum of areas of individual shapes that make up the net of the triangular prism

Using the above as a guide, we have the following:

Area = 2 * 8 * 17 + 8 * 16 + 2 * 1/2 * 15 * 16

Evaluate

Area = 640

Hence, the surface area is 640 square meters

Answers

Answer:

Let's assume the original price of the stock was x.

When the company announced it overestimated demand, the stock price fell by 40%.

So, the new price of the stock after the first decline was:

x - 0.4x = 0.6x

A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.

So, the new price of the stock after the second decline was:

0.6x - 0.6(0.6x) = 0.24x

Given that the current stock price is $2.40, we can set up the equation:

0.24x = 2.40

Solving for x, we get:

x = 10

Therefore, the stock was originally selling for $10.

f(x)\sqrt(3x+1) for x=8

Answers

Answer:

f(8) = ± 5

Step-by-step explanation:

assuming you mean

f(x) = $\sqrt{3x+1}$

substitute x = 8 into f(x) , that is

f(8) = $\sqrt{3(8)+1}$ = $\sqrt{24+1}$ = $\sqrt{25}$ = ± 5

The thermal plot of a gaming system during play time is defined by 10ln(15t^3) − 2T + 100 = T + 10t for 0 < t ≤ 5, where t represents time in hours and T represents temperature in °C. For which condition does the system reach a possible maximum or minimum temperature?

30 − 10t = 0
450t^2 − 10 = 0
6 − 90t^3 = 0
15t^2 − 10 = 0

Answers

Answer:

450t^2 − 10 = 0

Step-by-step explanation:

really would like help with this guys

Answers

Answer:

The answer is D.

Step-by-step explanation:

Range of a function is determined by the y-axis.

Domain of a function is determined by the x-axis.

So in this graph, the maximum value of y is 2 and the minimum is -3.

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