I NEED HELP ASAP!! I WILL GIVE BRAINLEST!!

Answer: A general solution of a differential equation is a solution that contains all possible solutions of the equation, including all arbitrary constants. It provides a general form of the solution that can be customized to fit the specific conditions of the problem.

For example, the general solution of a second-order linear homogeneous differential equation of the form

y'' + p(x)y' + q(x)y = 0

is a combination of two linearly independent functions, often represented by y = c1y1(x) + c2y2(x), where c1 and c2 are arbitrary constants and y1(x) and y2(x) are two linearly independent solutions of the differential equation.

The general solution represents the most general form of the solution that takes into account all possible solutions, including all arbitrary constants. To find a specific solution, one must apply initial or boundary conditions to determine the values of the arbitrary constants.

Step-by-step explanation:

The surface area of the cube will be 181.50 square cm.

Suppose that: The side length of the considered cube is L units. Then, we get:

Surface area of that cube = 6L² square units.

From the diagraph, the edge length of the rectangular prism is 5.5 cm long, 5.5 cm wide, and 5.5 cm tall. Then the rectangular prism is a cube. Then the surface area of the cube is given as,

Surface area of that cube = 6 × (5.5)² square cm

Surface area of that cube = 6 × 30.25 square cm

Surface area of that cube = 181.50 square cm

The surface area of the cube will be 181.50 square cm.

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Answer:

Yes

8e - 2  in words is 2 less than the product of 8 and e

Step-by-step explanation:

product of 8 and e ==> 8e

two less than the product of 8 and e ==> 8e - 2

Answer:

Step-by-step explanation:

To find the function rule for the relationship between x and f(x), we can perform a linear regression analysis on the given data points. This can be done using a spreadsheet software or a statistical software. One way to do this is to use the equation of a straight line, which is y = mx + b, where y is the output (f(x)), x is the input, m is the slope, and b is the y-intercept.

The slope m can be calculated as:

m = (Δy / Δx) = (f(x2) - f(x1)) / (x2 - x1) = (9 - 6) / (3 - 0) = 3

The y-intercept b can be calculated as:

b = f(x) - mx = 6 - 3x

So the function rule is:

f(x) = 3x + 6

To graph the function, we can plot the given data points and then draw a straight line that passes through those points. The graph of the function should look like this:

[!graph of f(x) = 3x + 6]

The function rule for the relationship between x and f(x) can be found using a similar process. Using the given data points, we can calculate the slope and y-intercept:

m = (Δy / Δx) = (f(x2) - f(x1)) / (x2 - x1) = (-2 - (-3)) / (1 - 0) = 1

b = f(x) - mx = -3 - x

So the function rule is:

f(x) = x - 3

The graph of the function should look like this:

[!graph of f(x) = x - 3]

For the third example, we can find the function rule using a similar process:

m = (Δy / Δx) = (f(x2) - f(x1)) / (x2 - x1) = (6 - 4) / (2 - 1) = 2

b = f(x) - mx = 4 - 2x

So the function rule is:

f(x) = 2x + 4

The graph of the function should look like this:

[!graph of f(x) = 2x + 4]

Step-by-step explanation:

To find the volume of this solid, we will use the method of cylindrical shells. We will integrate the cross-sectional area of a cylinder, given by πr^2, over the height of the solid. The height of the solid is given by the difference between the upper and lower bounds of the region, which are y = sin(x) and y = 0, respectively. The radius of each cylindrical shell is given by the height y = sin(x).

So, the volume of the solid is given by the integral:

V = ∫[0, π/2] π * [sin(x)]^2 dx

Using the antiderivative of π * sin^2(x), which is -π * cos(x), we can find the definite integral:

V = -π * [cos(x)] from 0 to π/2

Evaluating the definite integral and simplifying, we get:

V = (2π - 2) units^3

So, the volume of the solid is (2π - 2) units^3.

Answer:

Step-by-step explanation:

V = (2π - 2) units^3

So, the volume of the solid is (2π - 2) units^3.

The value of x when y = 1 is 2.

Option D is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

x varies inversely with y.

This means,

x ∝ 1/y

x = k/y

And,

xy = 2

This means,

k = 2

Now,

For y = 1,

xy = 2

x = 2/y

x = 2/1

x = 2

Thus,

x is 2 when y = 1

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To calculate the sample variance for the homicide rate per 100,000 individuals in a sample of selected cities in the United States, you need to use the following formula:

Sample Variance = (∑ (x - X) 2) / (n - 1)

Where x is each homicide rate value in the sample, X is the mean of the homicide rate values, and n is the number of values in the sample.

For example, if the sample contains the following homicide rate values:

100, 200, 300, 400

The mean (X) would be 250, and the sample variance would be:

Sample Variance = ( ∑ ( x - 250 ) 2) / (4 – 1)

= (100,000 + 50,000 + 10,000 + 0) / 3

= 160,000 / 3

= 53,333.3

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Answer:

x = 13

good luck

Answer: 2:3

Step-by-step explanation:

from there you can multiply by 2 and find the other ratios

The number Joe is thinking of is -36.

To find the number Joe is thinking of, use algebraic expression and equation.

Let x be the number Joe is thinking of

According to the problem, "Eleven more than one third of the number is -1". We can translate this into an algebraic expression such as:

x/3 + 11 = -1

To find the value of x, we'll isolate it on one side of the equation:

x/3 = -12

Next, we'll multiply both sides of the equation by 3 to cancel out the fraction:

x = -36

Therefore, the number Joe is thinking of is -36.

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1. Complete the identities

a = -4

b = 34

c = 1

d = 3

2. Complete the identities

3x - 24 = 3(x - 8)

0 + x = x

5(x + 5) = 5x + 25

(a + b) + c = c + (a + b)

(x - a)(x - b) = x² - (a + b)x + ab

Before solving the above equation, we need to know the algebraic formula. The algebraic formula is

a(x + b) = ax + ab

1.

- 6(x - 4) + 2(x + 5) = ax + b

⇒ -6x + 24 + 2x + 10 = ax + b

   -6x + 2x + 24 + 10 = ax + b

   -4x + 34 = ax + b

So we get the values ​​a and b.

-4x = ax ⇔ a = -4

b = 34

− 3(x + c) − 4(x + d) = - 7x - 15

-3x - 3c - 4x - 4d = -7x - 15

-3x - 4x - 3c - 4d = -7x - 15

-7x - (3c + 4d) = -7x - 15

-7x + 7x - (3c + 4d) = - 15

- (3c + 4d) = - 15

3c + 4d =  15

Let c = 1

3c + 4d =  15

3(1) + 4d = 15

3 + 4d = 15

4d = 15 - 3

4d = 12

d = 3

2.

3x - 24

= 3 × x - 3 × 8

= 3(x - 8)

.... + x = x

-x + x = 0

5(x + 5) = 5 × x + 5 × 5

            = 5x + 25

(a + b) + c = c + (a + b)

Let (x + a)(x + b)

(x + a)(x + b) = x² + ax + bx + ab

                    = x² + (a + b)x + ab (not eligible)

Let (x + a)(x - b)

(x + a)(x - b) = x² + ax - bx - ab

                    = x² + (a - b)x - ab (not eligible)

Let (x - a)(x + b)

(x - a)(x + b) = x² - ax + bx - ab

                    = x² - (a - b)x - ab (not eligible)

Let (x - a)(x - b)

(x - a)(x - b) = x² - ax - bx + ab

                    = x² - (a + b)x + ab (eligible)

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Answer:

Step-by-step explanation:

el awnser es 0.265 libras mas

The measure of ZPQR is approximately 113°

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects. A geometer is a mathematician who specializes in geometry.

Therefore, to find the measure of ZPQR, we would follow the following steps:

Let x= measure of <PQR

Hence, the measure of <PQR

296 = x/360 x 3.14 x 2 x 150

Hence, x = 113.12 °

Approximately, the measure of ZPQR is 113 °

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Answer: the person above is right

Step-by-step explanation: have a good day:)

The solution of the given expression for multiplication is 3 / 2.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression of the multiplication is 1¹/₂ x 9 / 10.

The numbers will be multiplied as below:-

E =  1²/₃ x 9 / 10.

E = ( 5 / 3 ) x ( 9 / 10 )

E = 3 / 2

Therefore, the solution will be 3 / 2.

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In linear equation, 4.9 kilograms is an average elephant's brain .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

An average human's brain is 1.5 kilograms.

   =   1.5 + 3 4/10

   = 1.5 + 3.4

    =  4.9

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a) We convert per minute to per hour so we multiply it by 60 to get:

=> 504km/h

b) We convert per second to per hour so we multiply it by 3600 to get:

=> 1134000m/h

=> We then convert meters into km to get:

=> 1134km/h

c) We convert per minute to per hour so we multiply it by 60 to get:

=> 14520m/h

=> Now we convert meters into km once again so we get:

=> 14.52km/h

d) We convert per second to per hour so we multiply it by 3600 to get:

=> 450000cm/h

=> We now convert cm into km which means we divide it by 100,000

=> 4.5km/h

Active reading, mnemonics, practice testing, and spaced repetition are just a few examples of study methods that matrics/Grade 12s can use to study their work more effectively.

Study methods are strategies or techniques that students use to learn and retain information more effectively. Here are four study methods that matrics/Grade 12s could use to study their work more effectively:

1. Active Reading: Active reading is a technique where students actively engage with the text while reading it. This helps students to focus on the most important concepts and better understand the material.

2. Mnemonics: Mnemonics are memory aids that help students remember information by creating an association between new information and something that is already familiar to them.

3. Practice Testing: Practice testing involves creating practice quizzes or tests to help students test their knowledge and identify areas where they need to focus their studying. This technique has been shown to be highly effective in improving memory retention and recall.

4. Spaced Repetition: Spaced repetition involves spacing out study sessions over a longer period of time rather than cramming all the studying into one session. This technique helps students retain information for longer periods of time and can help reduce stress and anxiety associated with last-minute cramming.

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Answer:

Below

Step-by-step explanation:

This is changing the form of the parabola from quadrtatic form to vertex form using the 'complete the square method'

2x^2 - 12x + 23    first, to complete the square the x^2 coefficient must be =1

       so factor out 2 form the x components

2 (x^2 -6x)        + 23      now....take 1/2 of the 'x' coefficient ( this would be -3)

                                        square it and add this value in the parentheses and subtract it on the outside of the parentheses ( it will be multiplied by the '2' when you need to subtract it....making it -18) )

2 (x^2 - 6x +9 )  - 18    + 23      now reduce the underlined portion

2(x-3)^2   +5        Done .

Answer:

Below

Step-by-step explanation:

4 [tex]\sqrt[2]{k}[/tex]      or just     4 [tex]\sqrt{k}[/tex]

The 1/2 power exponent means square root

  if it had been 1/5   then the answer would be   4 [tex]\sqrt[5]{k}[/tex]

The team plans to use 30% of all donations and car wash proceeds for new equipment, so they will have $430 * 0.30 = $129 to spend on new equipment.

We can start by finding the total amount of money raised from the car wash and donations on Saturday and Sunday.  If the team charged $5 per car wash, then the total amount of money raised from car washing on Saturday is 25 * 5 = $125. The total amount raised from donations and car washing on Saturday is $125 + 95 = $220. Similarly, the total amount of money raised from car washing on Sunday is 19 * 5 = $95. The total amount raised from donations and car washing on Sunday is $95 + 115 = $210. The total amount of money raised over the weekend is $220 + $210 = $430. The team plans to use 30% of all donations and car wash proceeds for new equipment, so they will have $430 * 0.30 = $129 to spend on new equipment.  Next, we can find the total amount raised from donations over the weekend. On Saturday, the team raised $25 + 95 = $120 from donations. On Sunday, the team raised $19 + 115 = $134 from donations. So, the total amount raised from donations is $120 + $134 = $254. Finally, we can find the total amount the team raised over the weekend by adding the amount raised from car washes and the amount raised from donations: $220 + $254 = $474.

Since the team plans to use 30% of all donations and car wash proceeds for new equipment, they will have 0.30 * $474 = $142.20 to spend on new equipment.

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Answer:

brainliest plss

Step-by-step explanation:

5p(2p-3)(p+7)=0

p=0

(2p-3)=0

(p+7)=0

p=0

p=3/2

p=-7

Answer:

p = 0, p = ³/₂, p = -7

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Zero Product Property}\\\\If\; $a \cdot b = 0$ \;then either \;$a = 0$ \;or\; $b = 0$ (or both).\\\end{minipage}}[/tex]

Given equation:

[tex]5p(2p-3)(p+7)=0[/tex]

Using the Zero Product Property, set each factor equal to zero and solve for p.

Factor 1

[tex]\begin{aligned}5p&=0\\5p \div 5&=0 \div 5\\p&=0\end{aligned}[/tex]

Factor 2

[tex]\begin{aligned}2p-3&=0\\2p-3+3&=0+3\\2p&=3\\2p \div 2&=3 \div 2\\p&=\dfrac{3}{2}\end{aligned}[/tex]

Factor 3

[tex]\begin{aligned}p+7&=0\\p+7-7&=0-7\\p&=-7\end{aligned}[/tex]

Therefore, p = 0, p = ³/₂, p = -7.

The probability that Jaya likes neither book is 1 - 0.6 = 0.4, or 40%. To two decimal places, the answer is 0.40.

The probability that Jaya will like neither book can be found by subtracting the probability that she likes at least one book from 1.
The probability that Jaya likes at least one book is the sum of the probabilities that she likes the first book, the second book, or both books:
P(likes at least one book) = P(likes first book) + P(likes second book) - P(likes both books)
P(likes at least one book) = 0.5 + 0.4 - 0.3 = 0.6
So, the probability that Jaya likes neither book is 1 - 0.6 = 0.4, or 40%. To two decimal places, the answer is 0.40.

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Step 1: Calculate the probability that the Captain will hit the pirate ship. Since the Captain has a probability of \dfrac{1}{2} 2 1 ​ start fraction, 1, divided by, 2, end fraction of hitting the pirate ship, the probability that the Captain will hit the pirate ship is 0.5.

Step 2:Calculate the probability that the pirate will hit the Captain's ship. Since the pirate only has one good eye, he hits the Captain's ship with probability \dfrac{2}{7} 7 2 ​ start fraction, 2, divided by, 7, end fraction, the probability that the pirate will hit the Captain's ship is 0.286.

Step 3: Calculate the probability that both ships will hit each other. To calculate the probability that both ships will hit each other, multiply the probability that the Captain will hit the pirate ship (0.5) by the probability that the pirate will hit the Captain's ship (0.286). This gives us a total probability of 0.143.

Therefore, the probability that both ships will hit each other is 0.143.

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The graph of the function f(x) = x² - 10x. and the graph of the function

g(x) = x² - 30x.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over the x-axis, (x, -y).

The graph of the first function is a quadratic function.

f(x) = (x - 0)(x - 10).

f(x) = x² - 10x.

Now, g(x) = (x - 0)(x - 30).

g(x) = x² - 30x.

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Answer:

Step-by-step explanation:

The definition of k is not given.  Is k the slope?  

See the attached graph of all the equations.  The referenced equation, f(x) = 2x+3 is the top equation and the line is shown in black.  This line has a slope of 2 and a y-intercept of +3.

The g(x) functions are also graphed, and noted.  Two of the g(x) equations are the same as the reference equation:  25 and 26.  Both have a slope of 2 and a y-intercept of +3.

#23 has a slope of 6 and a y-intercept of 9.  This has the steepest rise of all the lines (higher slope).

#24 has a slope of 1 and a y-intercept of +1.  This has the slowest rise, but it is still a positive sdlope (going up)

The volume of the swimming pool will be 2400 cubic feet.

The capacity of an object is measured by its volume. For instance, a cup's volume is said to be 100 ml if it can hold 100 ml of water in its brim. The amount of space occupied by a three-dimensional object can also be used to define volume.

Given that a swimming pool is shaped like a right rectangular prism with a length of 20 feet, a height of 8 feet, and a width of 15 feet.

The volume of the swimming pool will be calculated as:-

Volume = L x W x H

Volume = 15 x 20 x 8

Volume = 2400 cubic feet

Therefore, the volume of the pool will be 2400 cubic feet.

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1) Note that Math curriculum typically covers concepts such as number and operations, algebra, geometry, and statistics/probability. Problem-solving and procedural fluency are emphasized, as well as addressing missed concepts.

2) Instruction in math often includes hands-on activities, real-world problem-solving, visual models, and abstract reasoning. Emphasis on concept development and connecting math to real life.

3) Common instructional methods in basic math include direct instruction, teacher-led practice, and independent work with a gradual release of responsibility. Emphasis on understanding concepts through concrete examples.

Procedural fluency refers to the ability to efficiently and accurately perform mathematical procedures, such as computations and formulaic processes.

It's important because it enables students to tackle complex problem-solving with ease and confidence.

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Answer:

(y-3)/4

Step-by-step explanation:

(y-3)(y+3)/(4(y+3))

Answer:

97

Step-by-step explanation:

Gold:silver

=5:3

=40:24

silver:bronze

=8:11

=24:33

total number=40+24+33=97