"Now that you’ve created your hypotheses, it’s time to prove them. First, look at the sum of two rational numbers. Let’s say they are two rational numbers, x and y. Because they’re rational, they can be written as a ratio of integers. Let x = a/b and y = C/D, where a, b, c, and d are integers and b and d do not equal 0. The process for finding the sum x + y in terms of a, b, c, and d is shown." Question:Based on this sum and using the closure property of integers, what conclusion can you make about the sum of two rational numbers? Explain your answer.

The volume of the solid generated when the region bounded by y = 9x and y = 27x/x is revolved around the x-axis is given by V = 27lnx - 9x + c

To calculate this volume, we need to calculate the area of the cross-section of a shell at x.

The cross-section is found by taking the difference of the two curves, y = 9x and y = 27x/x, at that particular x in the form of a rectangle.

The height of the rectangle is y₂ - y₁ and the width is the interval dx. Therefore, the area of the cross-section is given by

A(x) = (y₂ - y₁)dx = [(27x/x - 9x)dx].

The volume of the solid is then given by the formula

=> V = ∫A(x)dx.

Substituting in the expression for A(x), we have

=>  V = ∫(27x/x - 9x)dx.

Integrating this expression, we get V = 27lnx - 9x + c, where c is an arbitrary constant.

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Answer:

It's B

Step-by-step explanation:

Edge 2021

The roots of the polynomial equation A = x⁶ - 16x² - 4x⁴ - 64 is given by the relations x₁ = -2 and x₂ = 2

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

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 polynomial equation be represented as A

Now , the value of A is

A = x⁶ - 16x² - 4x⁴ - 64   be equation (1)

On simplifying , we get

The two roots of the polynomial are 2i and -2i

And , x⁶ - 16x² = 4x⁴ - 64

Taking x² as the common factor , we get

x² ( x² - 16 ) = 4 ( x⁴ - 16 )

when x = -2

4 ( 0 ) = 4 ( 16 - 16 )

0 = 0

when x = 2

4 ( 0 ) = 4 ( 16 - 16 )

0 = 0

Therefore , the roots of the equation are 2i , -2i , 2 and -2

Hence , the polynomial equation has roots 2i , -2i , 2 and -2

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Answer: x=1/4=0.25

Step-by-step explanation:

5+2⋅(6x)=8

Multiply 2 and 6 to get 12.

5+12x=8

Subtract 5 from both sides.

12x=8−5

Subtract 5 from 8 to get 3.

12x=3

Divide both sides by 12.

x=3/12

Reduce the fraction by 3/12 to lowest terms by extracting and canceling out 3.

their for the Answer: is x=1/4

And....?

There's not enough info for me to answer.

-14 is the value of the expression b - 3a at a =6 and b = 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

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The correct options for the given rational numbers are (a) ii and iv.

P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. The natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers.

To compare the rational numbers, we need to perform the given operations and determine their relative magnitudes:

i. -2.3 - 1.3 = -3.6

ii. -2.3 -1.3 = -3.6

iii. -2.3 > -3.3

iv. -2.3 -3.3 = -5.6

Comparing i and ii, we see that they are equal. Therefore, both options i and ii are true.

Comparing iii, we see that -2.3 is greater than -3.3. Therefore, option iii is true.

Comparing iv, we see that -5.6 is less than both -2.3 and -3.3. Therefore, option iv is false.

So, the correct options are (a) ii and iv.

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Answer:

5:3

Step-by-step explanation:

have a great day

Answer:

5:3

Step-by-step explanation:

Answer:

the answer is yes

Step-by-step explanation:

hdhdhdhdhhdhdhdhdhdhd

Answer:

(18*y+5)-((10*x-61))=0

Step-by-step explanation:

should be your answer ║

(18*y+5)-((10*x-61))=0

Given the polynomial 8x^3 + 24x^2 + 18x, the resultant polynomial produced after factoring is 8x^3 + 24x^2 + 18x = 2x(2x + 3)(2x + 3)

To factor the polynomial 8x^3 + 24x^2 + 18x, we can start by factoring out the greatest common factor (GCF) if there is one. In this case, the GCF is 2x, so we can write:

8x^3 + 24x^2 + 18x = 2x(4x^2 + 12x + 9)

Next, we look for factors of the quadratic term 4x^2 + 12x + 9. Since the coefficient of the x^2 term is 4, we need to find two numbers whose product is 4 * 9 = 36 and whose sum is 12. These numbers are 6 and 6. So we can rewrite the quadratic term as:

4x^2 + 12x + 9 = 4x^2 + 6x + 6x + 9

Now, we can group the terms and factor by grouping:

4x^2 + 6x + 6x + 9 = (4x^2 + 6x) + (6x + 9) = 2x(2x + 3) + 3(2x + 3)

Notice that we have a common binomial factor of (2x + 3) in both terms. We can factor it out:

2x(2x + 3) + 3(2x + 3) = (2x + 3)(2x + 3)

Finally, we have factored the polynomial completely as:

8x^3 + 24x^2 + 18x = 2x(2x + 3)(2x + 3)

In this process, we used the distributive property and factoring by grouping to factor the polynomial. No special product rules were applied in this case.

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The correct answers are that Earth’s North Pole is close to the magnetic south pole, magnets allowed to move freely align themselves to point north, and the north pole on a compass is attracted to Earth’s south pole. I really hope this helps you!!

By ASA or SAS the triangles can be proves congruent.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance.

As, from the given figure we can find some equal parts.

First we have two triangles named KOE and LOB

Now, in both triangles

EO = OB  ( given)

<KOE =< LOB (Vertically opposite angle)

Now, we have one side and one angle congruent.

There are two possibilities now either we have another pair of side to make SAS Congruence or we have another angle congruent to make ASA congruence.

So, either KO = OL or

<LBO = <OKE.

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Therefore , the solution of the given problem of trigonometry comes out to be -1 is the simplified formula.

Some claim that the fusion of various fields contributed to the development of astrophysics. With the aid of precise mathematical methods, many metric issues can be resolved or the output of a computation can be determined. The scientific investigation of all six fundamental geometric calculations is known as trigonometry. They are known by a number of names and abbreviations, such as sine, variance, angle, and others. (csc).

Here,

Let's first use trigonometric identities to separately simplify each term:

=> cos(x - 90°) equals sin(x)

=>  cos(x - 180°) = -cos(x)

=> tan(x) = cos(x) / sin(x)(x)

=>  x(cos(-)) = x(x)

=> (180° + x) sin = -sin(x)

When we replace the equation with these simplifications, we get:

=> cos(x) * sin(180° plus x) * cos(x) * (-cos(x)) + (sin(x) / cos(x))

=>  sin(180° plus x) * sin(-cos2(x))

=>  -cos²(x) - sin(x)*sin(180° + x) (using the equation sin(x)*sin(x)) = -sin^2(x))

Using the identity sin2(x) +cos2(x) = 1, we get = -1.

Consequently, -1 is the simplified formula.

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Answer:

I'm not sure about the question, but the one thing that is needed for a function is the "=" sign.  Only option c has an equals sign.  The others, as written, are just expressions, not equations.

Step-by-step explanation:

Even option c doesn't conform to the y = mx + b form, but it is far ahead of the other options.

Answer:

x=3 y=1

x=4 y=2

x=5 y=3

x=6 y=4

Step-by-step explanation:

add y to both sides to get:

2x-4=y

pull out the 2 from 2x-4 to get:

2(x-2)-y = 0

We need to know that x-2 cannot equal 0 or else the solution will be negative. So we need to make x-2 equal to any other number that is not negative and make y the inverse of x-2 so they cancel out and be zero. so some solutions are:

x=3 y=1

x=4 y=2

x=5 y=3

x=6 y=4

Answer:

D

Step-by-step explanation:

f(x)=x-14     g(x)=x^2+14

fog=f(g(x)

=f(x^2-+14)

=f(x^2+14)-14

fog(x)=x^2

Answer:

9/49

Step-by-step explanation:

5 4/9 =49/9 and49/9*9/49=1 then reciprocal of 49/9 is9/49

The solution of f(x)=g(x) to the nearest hundredth if f(x)= x^2-2 g(x) = x-1 is 1.62 or -0.62

Given the following function below:

f(x) = x^2 - 2
g(x) = x - 1

Since f(x) = g(x), hence;

x^2 - 2 = x - 1
x^2 - x - 1 = 0

Factorize to have:

x = 1/2 +√5/2  or x= 1/2 - √5/2

x = 1.62 or -0.62

Hence the solution of f(x)=g(x) to the nearest hundredth if f(x)= x^2-2 g(x) = x-1 is 1.62 or -0.62

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Step-by-step explanation:

7 dollars + .0825 tax = 7 .58

  leaving $1.92 max tip ( out of 9.50 to spend)

                           ( this is a 27% tip on your purchase....more than adequate)

The data described in the tables is best modeled by a linear function or an exponential function both linear.

Hence, The data described in the tables is best modeled by a linear function or an exponential function both linear.

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Step-by-step explanation:

\(4.25 \times {10}^{ - 3} \)

HOPE IT HELPS YA

The value of the scientific notation of the number 0.0078 is,

⇒ 4.25 × 10⁻³

We have to give that,

Convert 0.00425 from standard form to scientific notation.

Since Scientific notation is a way of writing very large or very small numbers.

For example; 230,000,000 can be written in scientific notation as

2.3 x 10⁸.

Hence, Convert 0.00425 from standard form to scientific notation as,

⇒ 0.00425

⇒ 4.25 × 10⁻³

Therefore, the scientific notation of the number 0.00425 is,

⇒ 4.25 × 10⁻³

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Answer:

y = 48

Step-by-step explanation:

Plug in 7 for x:

y = x² - 1

y = (7)² - 1

Simplify. Remember to follow the order of operations, PEMDAS.

PEMDAS stands for:

Parenthesis

Exponents (& roots)

Multiplication

Division

Addition

Subtraction

~

First, solve the power, then subtract:

y = (7)² - 1

y = (7 * 7) - 1

y = (49) - 1

y = 48

48 is your value for y.

~

If the device needs 3 volts and 1.2 Amp, then the minimum number of AA batteries which are required to power this equipment is 3.

In order to find minimum number of AA batteries needed to power the portable communication-device, we compare voltage and current requirements of device with specifications of AA batteries.

We know that,

AA battery voltage: 1.5 volts

AA battery current: 0.5 Amps

Device voltage requirement: 3 volts

Device current requirement: 1.2 Amps

First, we calculate voltage requirement. Since each AA battery provides 1.5 volts, we calculate how many batteries are needed to reach the desired 3 volts by dividing the device voltage requirement by the battery voltage:

3 volts / 1.5 volts = 2 batteries

So, at least 2-AA batteries are needed to satisfy voltage requirement.

Next, we consider current requirement, each AA battery can provide up to 0.5 Amps, so we check if this is sufficient to meet the device's current requirement of 1.2 Amps.

Since the device requires 1.2 Amps, and each AA battery can provide 0.5 Amps, we can find how many batteries are needed by dividing device current requirement by battery current,

So, (1.2 Amps)/(0.5 Amps) = 2.4 batteries,

We can't have a fraction of a battery, on rounding up to nearest whole number. We need at least 3-AA batteries to satisfy current-requirement.

Therefore, 3 AA batteries are required.

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Average Speed = 160÷5= 32km/hr

Given,

A ferry traveled from Jetty A to Jetty B in 3 h. It then traveled from Jetty B back to Jetty A in 2 h. The distance between the two jetties was 80 km.

To find,

Total time for the whole journey,

Solution: Time is taken from Jetty A to Jetty B = 3 hours

and Jetty B to Jetty A = 2 hours

Total time = 3 h + 2 h = 5 h

Average Speed = Total Distance ÷ Total Time

Since, Total distance = 80×2= 160

Average Speed = 160÷5= 32km/hr

a) 5 hours

b) 32km/hr

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By some estimates 80-90 percent of employee learning occurs via on the job training.

This is the term that is used to refer to the training that people would receive based on the fact that it is preparing them to have the competent skills that are useful for a particular job. It is one of the ways that employers help to get their employees ready for the task at hand.

It has been reported from available data that on the job training is a great component of employee learning.

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The probability of selecting at least one defective screw is 1 - 21/40 = 19/40.

The probability that at least one of my two screws is defective is calculated as follows:

The first box contains 8 screws, of which 2 are defective.

Thus, the probability of selecting a non-defective screw is 6/8, or 3/4.

Likewise, in the second box, there are 7 screws that are not defective.

Thus, the probability of selecting a non-defective screw is 7/10.

The probability of selecting at least one defective screw from either box is equivalent to one minus the probability of selecting two non-defective screws.

The probability of selecting two non-defective screws is 3/4 * 7/10

= 21/40.

Therefore, the probability of selecting at least one defective screw is 1 - 21/40

= 19/40.

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The given function is

lim (x,y)→(0,0) x²y⁴ - x⁴y² / x+4.

The above function can be written as:

(x²y⁴ / x+4) - (x⁴y² / x+4)

On taking LCM, we get the following function:

(x²y⁴ - x⁴y²) / x+4(x²y²) (y² - x²) / x+4y²(x²) (y² - x²) / (x+4) (y²)

Now, applying the limit, x→0, y→0

So, substituting x = 0 and y = 0, we get,

0 * (y²) / 4 * (y²) = 0

Thus, the answer is 0

In this problem, we have to determine the given limit of a function lim (x,y)→(0,0) x²y⁴ - x⁴y² / x+4.

In order to solve this problem, we will make use of the limit laws and factorization.

Limit laws that are to be used are:

(1) Sum rule: lim [f(x) + g(x)] = lim f(x) + lim g(x)

(2) Product rule: lim [f(x) * g(x)] = lim f(x) * lim g(x)(

3) Quotient rule: lim [f(x) / g(x)] = lim f(x) / lim g(x), provided lim g(x) ≠ 0

Let us solve the problem step by step:

The given function is lim (x,y)→(0,0) x²y⁴ - x⁴y² / x+4.

The above function can be written as: (x²y⁴ / x+4) - (x⁴y² / x+4)

On taking LCM, we get the following function:

(x²y⁴ - x⁴y²) / x+4(x²y²) (y² - x²) / x+4y²(x²) (y² - x²) / (x+4) (y²)

Now, applying the limit,x→0, y→0

So, substituting x = 0 and y = 0, we get,0 * (y²) / 4 * (y²) = 0

Thus, the answer is 0.

Therefore, the given limit of a function lim (x,y)→(0,0) x²y⁴ - x⁴y² / x+4 is equal to 0.

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Answer:          

x3/24 in a simplify form

Step-by-step explanation:

The function that represents the given equation is:

f(x) = 3x + 8

The equation is -12x + 4y = 32. To solve for y as a function of x, we need to isolate y on one side of the equation.

Adding 12x to both sides, we get 4y = 12x + 32.

To solve for y, we divide both sides of the equation by 4. This gives us y = 3x + 8.

Hence, the function that expresses y as a function of x is:

f(x) = 3x + 8.

Using this function, we can determine the value of y corresponding to any given x value. For example, if we substitute x = 5 into the function, we have f(5) = 3(5) + 8 = 15 + 8 = 23. Therefore, when x is 5, y is 23 according to the function f(x) = 3x + 8.

In summary, the function f(x) = 3x + 8 represents the relationship between x and y in the given equation, allowing us to calculate the corresponding y value for any given x value.

Therefore, the function that represents the given equation is:

f(x) = 3x + 8

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