What are the leading coefficient, constant term and degree, if any, of the algebraic expression (x+sqrt 3)(x-sqrt3)

Given:

\(y=\frac{x^3+5x+4}{x^2+4}\)

Find:

\(dy=??\)

Rules/Methods that will be used:

Product rule: \(\Longrightarrow \frac{d}{dx}[\frac{f(x)}{g(x)} ] = \frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}\)

Power Rule: \(\Longrightarrow \frac{d}{dx}[x^n]=nx^{n-1}\)

Constant Rule: \(\Longrightarrow \frac{d}{dx}[k]=0\)

\(\Longrightarrow y=\frac{x^3+5x+4}{x^2+4} \Longrightarrow dy=\frac{(x^2+4)(\frac{d}{dx}[x^3+5x+4])-(x^3+5x+4)(\frac{d}{dx}[x^2+4] )}{(x^2+4)^2}\)

\(\Longrightarrow dy=\frac{(x^2+4)(3x^2+5)-(x^3+5x+4)(2x)}{(x^2+4)^2}\)

Simplify the expression.

\(\Longrightarrow dy=\frac{(x^2+4)(3x^2+5)-(x^3+5x+4)(2x)}{(x^2+4)^2} \Longrightarrow dy=\frac{(3x^4+17x^2+20)-(2x^4+10x^2+8x)}{(x^2+4)^2}\)

\(\Longrightarrow dy=\frac{x^4+7x^2-8x+20}{(x^2+4)^2}\)

The expression cannot be simplified further.  

\(Thus, dy=\boxed{\frac{x^4+7x^2-8x+20}{(x^2+4)^2}} \therefore Sol.\)

The area for the shaded region is obtained as 2 units.

In order to find the area, first find the intersection points of the two curves. Then, the area of the region can be found by taking the integration from the intersection point.

The curves in the graph in the form of equation are as follows,

y = x² + 3                     (1)

x = (y - 5)² - 2

=> y = √(x+ 2) + 5       (2)  

Part A :

The intersection points of the two curves are (-1.5, 5.5), (-1, 4) and (0.5, 3.5).

Thus, to calculate the area the limit is from x = -1.5 to x = 0.5.

Part B :

The expression of the integral is given as,

\(\int\limits^{-1}_{-1.5} {(x^{2} + 3 ) - (5 + \sqrt{x + 2} )} \, dx + \int\limits^{0.5}_{-1} {(5 + \sqrt{x + 2} ) -(x^{2} + 3 ) } \, dx\)

Part C :

The area is found by evaluating the integral as follows,

\(\int\limits^{-1}_{-1.5} {(x^{2} + 3 ) - (5 + \sqrt{x + 2} )} \, dx + \int\limits^{0.5}_{-1} {(5 + \sqrt{x + 2} ) -(x^{2} + 3 ) } \, dx\)

= [-1/3 + 3.375/3 + 3(-1 - (-1.5))] - [5(-1 - (-1.5)) + 2/3(\(1^{3/2} - 0.5^{3/2}\))] + [5(0.5 - (-1)) -(0.125/3 + 1/3 + 3(0.5 - (-1))]

= 2.291 - [2.5 + 2/3 × 0.647] + [5 × 1.5 - 4.8716]

= 2.291 - 2.927 + 2.6284

= 1.9924

Which is approximately 2.

Hence, the area between the curves is given as 2 units.

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g(x) = -2√x + 8 is the function that has the same range as f(x) = -2√(x - 3) + 8. Both functions have the range of y ≤ 8

The function that has the same range as f(x) = -2√(x - 3) + 8 is g(x) = -2√x + 8. Both functions have the range of y ≤ 8.There are a few steps involved in determining which function has the same range as f(x) = -2√(x - 3) + 8. The range of a function refers to all the possible output values that the function can produce.Let's begin by examining the original function:f(x) = -2√(x - 3) + 8The square root symbol (√) implies that x-3 must be greater than or equal to 0. If x-3 is negative, then the function would produce an imaginary result.

Let's solve for x when f(x) = 0:0 = -2√(x - 3) + 8-8 = -2√(x - 3)4 = √(x - 3)16 = x - 3x = 19This tells us that the x-value that produces an output of 0 is x = 19. To determine the range, we need to find the maximum and minimum output values. We can use a graphing calculator or sketch a graph to determine the shape of the function and the range.The shape of the function suggests that the range is y ≤ 8, which means that the maximum value of the function is 8. This tells us that any function with the same maximum output value of 8 will have the same range as f(x).

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Answer:

The answer is C or 44/12

Step-by-step explanation:

1/2 is equivalent to 3/6

1 4/6 is equivalent to 1 4/6 or 10/6

1 2/4 is equivalent to 1 3/6 or 9/6

When you add all of these together you get 22/6

Then you multiply 22/6 by 2 to get 44/12

Answer:

the answer is 7 because the square of 49 is 7 and it asks for the side to equal it.

Step-by-step explanation:

We got x = 16.54 by using Pythagorean theorem .

What is the Pythagorean theorem in plain English?

angle of semicircle is always be 90° .

   18² = 7.1² + x²

    324 = 50.41 + x²

     x² = 324 - 50.41

          = 273.59

    x = √ 273.59

    x = 16.54

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Answer:

First, divide 30 by 15

Step-by-step explanation:

15b = 30

15/15b = 30/15

b = 2

The value of the logarithm equation is given by x = [ ln ( 4 ) - 5 ] / 4

The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm

The properties of Logarithm are :

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

Given data ,

Let the logarithm equation be represented as A

Now , the value of A is

e⁽ ²ˣ ⁺ ⁵ ⁾ = 4   be equation (1)

On simplifying the equation , we get

Taking logarithm on both sides of the equation , we get

2x + 5 = ln ( 4 )

On simplifying the equation , we get

ln ( 4 ) = 2x + 5

Subtracting 5 on both sides of the equation , we get

2x = ln ( 4 ) - 5

Divide by 2 on both sides of the equation , we get

x = [ ln ( 4 ) - 5 ] / 4

Hence , the equation is  x = [ ln ( 4 ) - 5 ] / 4

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The expression that is equivalent to the given value would be = 18-i . That is option C.

An equivalent expression is defined as the type of expression that is similar to a given value when simplified.

The given expression = ( 3 + 4i) ( 2 - 3i)

Expand the given expression by removing the brackets as follows:

= =2(3+4i)−3i(3+4i)

=(6+8i)−(9i−12)

= (6+12)+i(8−9)

=18−i.

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The solutions of the system of equations are (-2, 1) and (-4, 5). The answer is D) (-4,5) and (-2,1).

What is equation ?

In mathematics, an equation is a statement that two expressions are equal. It typically contains one or more variables, which are unknowns that can take on different values. An equation is written using an equal sign (=) to indicate that the expressions on either side have the same value.

To solve the system of equations y = -\((x+2) ^{2}\) + 1 and y = 2x + 5, we can set the two expressions for y equal to each other and solve for x:

-\((x+2) ^{2}\) + 1 = 2x + 5

Expanding the left side and simplifying, we get:

-x*x - 4x - 4 + 1 = 2x + 5

-x*x - 6x - 8 = 0

Dividing both sides by -1, we get:

x*x+ 6x + 8 = 0

Factoring the left side, we get:

(x+2)(x+4) = 0

So the solutions for x are x = -2 and x = -4.

To find the corresponding y-values for each solution, we can plug in each value of x into either equation and solve for y. Let's use the equation y = -\((x+2) ^{2}\)+ 1:

When x = -2, y = -\((x+2) ^{2}\) + 1 = -(0) + 1 = 1.

When x = -4, y =-\((x+2) ^{2}\)+ 1 = -(-4) + 1 = 5.

Therefore, the solutions of the system of equations are (-2, 1) and (-4, 5).

The answer is D) (-4,5) and (-2,1).

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Answer:

A) (-4,-3) and (-2,1)

Step-by-step explanation:

If you graph the system on desmos and graph the points you will see that those are the points that give a solution to the system

Answer:

Step-by-step explanation:

At least 9 means more than 9 and includes 9

x ≥ 9     and    [9,  +∞)

At most 9 means numbers less than 9

x≤9       and  (-∞, 9]

more than 9 means bigger than 9 but not including 9

x > 9     and    (9,  +∞)

fewer than 9 means less than 9 but not including 9

x<9       and  (-∞, 9)

strictly between 7 and 9   means between 7 and 9 but not including

7<x<9      and    (7,9)       (This is the only one I'm unsure of.  Strictly, not sure if it includes or doesn't include, usually it just says include or doesn't include)

between 7 and 7 inclusive.   means it's just =7  There's no boundaries

x=7

no more than 7 means less than 7 and includes 7

x ≤ 7   and   (-∞, 7]

Answer:

$20.39

Step-by-step explanation:

19.99x1.02= 20.3898

round to nearest cent which is 20.39

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{2\% of 19.99}}{\left( \cfrac{2}{100} \right)19.99}\implies 0.3998~\hfill \underset{total~price}{\stackrel{19.99+.03998}{\approx 20.39}}\)

The probability that it is raining and the flight is delayed is 0.011, or approximately 0.011 rounded to the nearest thousandth.

Let's use the formula for calculating the probability of the intersection of two events: P(A and B) = P(A) × P(B|A), where P(B|A) is the probability of event B occurring given that event A has occurred.

Let A be the event that it is raining, and B be the event that the flight is delayed. We are looking for P(A and B).

We know that:

P(A) = 0.1 (the probability that it will rain)

P(B) = 0.11 (the probability that the flight will be delayed)

P(not A and not B) = 0.88 (the probability that it will not rain and the flight will leave on time)

We can use the complement rule to find P(A or B):

P(A or B) = 1 - P(not A and not B)

P(A or B) = 1 - 0.88

P(A or B) = 0.12

Now we can use the formula for the intersection of two events:

P(A and B) = P(A) × P(B|A)

We know that P(A) = 0.1, and we need to find P(B|A), the probability of the flight being delayed given that it is raining.

We can use Bayes' theorem to find P(B|A):

P(B|A) = P(A and B) / P(A)

P(B|A) = (P(A) × P(B|A)) / P(A)

P(B|A) = P(B and A) / P(A)

We can rearrange this to get:

P(A and B) = P(B|A) × P(A)

Substituting the values we know:

P(B|A) = P(A and B) / P(A)

0.11 = P(A and B) / 0.1

P(A and B) = 0.11 × 0.1

P(A and B) = 0.011

Therefore, the probability that it is raining and the flight is delayed is 0.011, or approximately 0.011 rounded to the nearest thousandth.

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The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

Answer:

90

Step-by-step explanation:

The statement is false, as the PEMDAS order must be respected, that is, parenthesis operations are done first, then exponents, then multiplication/division and finally addition/subtraction.

The precedence of operations is defined by the PEMDAS acronym, with a highest to lowest order of precedence, as follows:

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The expected mean of the sampling distribution and the standard deviation of the sampling distribution is $29.50.

Standard deviation

In statistics, standard deviation refers  the square root of variance by determining each data point's deviation relative to the mean.

Given,

Here we know that a statistics student is trying to decide whether she should take a gamble and play bingo. And the average bingo player earns $9 per game, distributed normally, with a population standard deviation of $8.

And we need to find if a sample of 25 bingo players are selected at random from the population, select the expected mean of the sampling distribution and the standard deviation of the sampling distribution below.

0; = $0.32 0; = $8 O = $1.60 Mi = $9 Hi = $1.80

Here the standard deviation of the sample distribution is calculated as,

=> σₓ = √1.80 = 1.34

Here we know that the distribution is normal then the mean of the sampling distribution is equal to the mean of the population, based on this theory, the resulting value is $29.50.

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The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.

Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:

y - 3 = 1(x - (-1))

Simplifying:

y - 3 = x + 1

Now, we can rewrite the equation in the standard form:

y = x + 4

Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

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Answer:

Looks like an exponential function (that is shifted downwards)

Step-by-step explanation:

The value of x from the parallelogram ABCD is 10.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

Given that, ∠A=120-2x, ∠B=70+x, ∠C=105-x² and ∠D=40+4x.

The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary.

Here, ∠A and ∠D are consecutive angles

Now, 120-2x+40+4x=180

⇒ 160+2x=180

⇒ 2x=20

⇒ x=10

So, ∠A=120-2x=100, ∠B=70+x=80, ∠C=160-6x=100 and ∠D=40+4x=80

Therefore, the value of x is 10.

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"Your question is incomplete, probably the complete question/missing part is:"

The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary. Given the angle measures, prove that quadrilateral ABCD is a parallelogram by finding the value of x. ∠A=120-2x, ∠B=70+x, ∠C=160-6x and ∠D=40+4x.

Hello! :)

(7,-6)

(4, -6)

We are given two points and asked to find the slope, so this is the formula we can use:

\(\frac{y2-y1}{x2-x1}\)

\(\frac{-6-(-6)}{4-7}\)

\(\frac{-6+6}{4-7} \\\frac{0}{-3} \\0\)

Hence, our final answer is 0.

Here's something that you should remember:

Hope it helps.

If you have any query, feel free to ask!

~An excited gal

\(MagicalNature\) here to help

The perimeter of the given triangle with given lengths is; 78

The perimeter of a triangle is defined as the sum total of the 3 side lengths of the triangle.

Now, we are given the triangle as QRS.

We are given that;

A is the midpoint of QR

B is the midpoint of RS

C is the midpoint of SQ

Thus;

QA = RA = 10

BR = SB = 15

SQ = 28

Thus;

Perimeter of Triangle = 2(10) + 2(15) + 28 = 78

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Answer:

Step-by-step explanation: I hope this helps you! you should just be able to click on the image.

Answer:

Answer:

$1.70 per share

Step-by-step explanation:

37.90-36.20=1.70

Answer:

A: $3; B: $15

Step-by-step explanation:

Cost of Yani's original cereal: $10/box

Cost of super-saving brand: $7/box (as given by the 7 in y=7x)

A: Difference = 10-7 = 3

B: 5 boxes of original brand = 5×10 = $50

   5 boxes of super-saving brand = 5×7 = 35

   Savings = 50-35 = $15

Answer: $4 senior, $7 child

Step-by-step explanation:

(3s + 9c = 75)

8s + 5c = 67

The number of years it would it take for there to be one person for every square yard is 108,325.68 years.

When there is one person for every square yard, it means that the population and land area are equal in value.

Number of years = (In FV / PV) / r

(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years

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