Find two integers whose sum is -2 and product is -24

Answer:

(n - 1)/2

Step-by-step explanation:

F = (1 - 1/n) + (1 - 2/n) + (1 - 3/n) + ...(1 - n/n)

  = (1 + 1 ... + 1) - (1/n + 2/n + 3/n + ...n/n)

     (there are n terms of 1)

  = n - (1 + 2 + 3 + ... + n)/n

  = n - [n x (n + 1)/2]/n

  = n - [n x (n + 1)]/[2 x n]

  = n - (n+1)/2

  = (2n - n - 1)/2

  = (n - 1)/2

Hope this helps!

Answer:

Jamie has 44 pairs of shoes

Step-by-step explanation:

Let

Jamie= x pairs of shoes

Suzie= 33 less than twice the amount of shoes Jamie has

2x - 33 = 55

Solve:

2x - 33 = 55

Collect like terms

2x = 55 + 33

2x = 88

Divide both sides by 2

2x / 2 = 88 / 2

x = 44

Jamie = x = 44 pairs of shoes

Therefore, Jamie has 44 pairs of shoes

The solutions for the given problem are as follows:

\(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\) has no RHP roots.

\(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\) has no RHP roots.

The following are the solutions to determine RHP roots in the given polynomials in Control System:

Polynomial: \(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\)

To identify the number of RHP (Right Half Plane) roots of the given polynomial \(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\), the number of sign changes in the coefficients of the polynomial's terms can be counted.

Using the Descartes rule of sign, the number of sign changes in the polynomial's coefficients will indicate the number of positive or RHP roots present in the polynomial.

Therefore, there is no change in the sign of coefficients in the polynomial p(S).Thus, the number of RHP roots of the polynomial \(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\)is zero.

Polynomial: \(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\)

The given polynomial is \(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\).

The coefficients of the polynomial are as follows:

a5 = 1, a4 = 1, a3 = 6, a2 = 6, a1 = 1, and a0 = 25.

According to the Routh-Hurwitz criterion, the RHP roots of the polynomial p(S) are given by the following conditions:

For the polynomial \(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\), the Routh array can be written as:

1    6    25 0
1    6    25 0
6    155 0
5    25    0
25 0

Thus, the polynomial p(S) has no RHP roots since the Routh array contains no changes of sign.

Therefore, the given polynomial has no RHP roots.

Hence, the solutions for the given problem are as follows:

\(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\) has no RHP roots.

\(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\) has no RHP roots.

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The problem of changing the word s into the word t can be stated in terms of finding a path in this graph from vertex s to vertex t, where each intermediate vertex (word) in the path differs from the previous one by only one character and belongs to D.

a. To model this as a graph problem, we can treat each word in the dictionary D as a vertex in the graph. Then, we can create an edge between two vertices (words) if they differ by only one character. For example, there would be an edge between 'hit' and 'hot', as they differ by only one character ('i' and 'o'). The problem of changing the word s into the word t can be stated in terms of finding a path in this graph from vertex s to vertex t, where each intermediate vertex (word) in the path differs from the previous one by only one character and belongs to D.

b. To construct the graph, we can iterate through all pairs of words in D and check if they differ by only one character. This takes O(n²) time. Once we have identified the edges in the graph, the size of the graph is also up to O(n²), since there can be at most n vertices and n² edges (when every vertex is connected to every other vertex). Therefore, constructing the graph takes O(n²) time, and the size of the graph is up to O(n²).

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The following triangles are congruent.

Yes AAA

Answer;

-2.8m

Step-by-step explanation;

It's just adding m terms, and yes it's adding decimals but you can do it in your head if your good at arithmetic if not your calculator is there to help you out dw

so -5.1m+2.3m is

Answer: -2.8

Step-by-step explanation:

it the answer

Answer:

Factor by grouping, (5n+4)(n+3), or alternatively, (n+3)(5n+4)

Answer:

(n +3)(5n + 4)

Step-by-step explanation:

5n^2 + 19n + 12

= 5n^2 + 15n + 4n + 12

= 5n(n + 3) + 4(n + 3)

= (n +3)(5n + 4)

Hence Factorized.

Answer:

French = 5 ; German = 11

Step-by-step explanation:

G + F = 16

G = 6 + F

6 + F + F = 16

6 + 2F = 16

2F = 16 - 6

2F = 10

2/2 F = 10/2

F = 5

G = 5 + 6 = 11

Answer:

\((4+j)-3\)

Step-by-step explanation:

Hope this helps

The percent of the field goals did Samuel make will be 77.5%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Samuel made 31 out of 40 field goals during football practice. The percent of the field goals did Samuel make will be:

= 31 / 40 × 100

= 77.5%

The percentage is 77.5%.

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Factory B can supply tires with the most consistent weight.

To determine which factory can supply tires with the most consistent weight, we need to compare the standard deviations of the weights provided by each factory.

The standard deviation measures the dispersion or variability of a set of data. A lower standard deviation indicates less variability, which means the weights of the tires are more consistent.

From the given information, Factory A has a standard deviation of 5 g, Factory B has a standard deviation of 2.5 g, and Factory C has a standard deviation of 7 g.

Comparing the standard deviations, we find that Factory B has the lowest value of 2.5 g. This indicates that the weights of the tires from Factory B have the least variability, making them the most consistent.

Therefore, Factory B can supply tires with the most consistent weight, as its standard deviation of 2.5 g is the lowest among the three factories.

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Answer:  

 46.8

Step-by-step explanation:

Answer:

f(1) = 9

Step-by-step explanation:

f(x)=(x-4)^2

Find f(1) means let x =1.

f(1)=(1-4)^2

   = (-3)^2

   = 9

Answer:

f ( 1 ) = 9

Step-by-step explanation:

To find f(1), we substitute x = 1 into the function f(x) = ( x - 4 )²

f ( 1 ) = ( 1 - 4 )²

f ( 1 ) = ( -3 )²

f ( 1 ) = 9

Therefore, f ( 1 ) = 9.

Answer:

-definition of cosine

-definition of sine

-Pythagorean Theorem

-Substitution

-laws of exponents

Step-by-step explanation:

The blanks are filled by the definition of cosine, the definition of sine,  Pythagorean Theorem, substitution, and laws of exponents respectively.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Given the right triangle shown below, prove cos²(θ) + sin²(θ) = 1.

A triangle with sides x, y, and hypotenuse r.

Angle θ is opposite to side y.

As per the Laws of Cosine,

cos(θ) = x/r, and

As per the Laws of Sine,

sin(θ) = y/r.

Multiplying both sides of the above equations by r,

x = r cos(θ) and

y = r sin(θ).

The Pythagorean Theorem states that x² + y² = r².

By Substitution method, we have [r cos(θ)]² + [r sin(θ)]²= r².

Applying the Laws of Exponents, the equation can be written as r² cos²(θ) + r² sin²(θ) = r².

Dividing both sides of the equation by r² results in cos²(θ) + sin²(θ) = 1.

Hence, the blanks are filled by the definition of cosine, the definition of sine,  pythagorean theorem, substitution, and laws of exponents respectively.

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Answer:

Step-by-step explanation

33

Answer:

2,3,5

Step-by-step explanation:

First, 10^3 is 1000 and 3.6 x 1000 = 3600.

So, the factors of 3600 are 2,3,5

Through this photo if this helps:

3.6 x 10³ as a product of the powers of its prime factors is

\(2^4\) x 3² x 5²

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

3.6 x 10³

This can be written as,

= 3.6 x 1000

= 36/10 x 1000

= 3600

Now,

3600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5

2, 3, and 5 are prime numbers.

This means,

\(2^4\) x 3² x 5²

Thus,

The powers of prime factors are

\(2^4\) x 3² x 5²

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Answer:

Step-by-step explanation:

We worry about 2 things:

-terms power

-coefficient for each term

(3x-4)^5, has 2 terms 3x and -4

-Start with the first term to the highest power 5 and second term to the lowest power 0, then the high power goes down and low power increases until the first term has the lowest power 0 and the second term has the highest power 5.

-The coefficients for each term we take it from the Pascal triangle.

For the the power 5 the coefficients are 1, 5, 10, 10, 5, 1

\((3x-4)^{5} = 1*(3x)^{5} *(-4)^{0} +5*(3x)^{4} *(-4)^{1} +10*(3x)^{3} *(-4)^{2}+10*(3x)^{2} *(-4)^{3}+5*(3x)^{1} *(-4)^{4}+1*(3x)^{0} *(-4)^{5}\)

Simplify:

\((3x-4)^{5} = 3^{5} x^{5} -20*3^{4} x^{4} +160*3^{3} x^{3}-640*3^{2} x^{2}+1280*3x-1024\)

\((3x-4)^{5} = 243 x^{5} -1,620x^{4} +4,320 x^{3}-5,760x^{2}+3,840x-1024\)

Answer:

your the problem

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

A quick way of doing this mentally would be:

1 times 12 = 12

and 1/2 times 12 is the same as half of 12 so 6

6 + 12 = 18

The length of the tank is 2.1 yards or 7 feet.

In mathematics, the volume is a measure of the amount of space occupied by a three-dimensional object.

We can use the formula for the volume of a rectangular prism to find the length of the tank. The formula is:

V = lwh

where V is the vοlume, l is the length, w is the width, and h is the height.

We are given that the vοlume ο f the tank is 210 cubic yards, the width is 9 1/3 yards, and the height is 3 1/3 yards.

Substituting these values into the formula, we get:

210 = l × (28/3) × (10/3)

Simplifying, we get:

210 = (280/9) × (10/3) × l

210 = 100 × l

l = 210/100

l = 2.1

Hence, the length of the tank is 2.1 yards or 7 feet.

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Answer:

i wil tell you

Step-by-step explanation:

if you will work hard and you can earn double money

so you can double the money in 6 years

Answer:

30.

Step-by-step explanation:

Apologies if I am late, but I believe this is the answer!

The transformations are applied in the following order: horizontal translation, horizontal scaling, vertical reflection, and vertical scaling.

The transformations are applied in the following order:

Horizontal translation: The function is shifted 9 units to the right by subtracting 9 from the input variable x.

f(x) → f(x - 9)

Horizontal scaling: The function is compressed horizontally by a factor of 1/3 by dividing the input variable x by 3.

f(x - 9) → f(1/3(x - 9))

Vertical reflection: The function is reflected about the x-axis by multiplying the output values of f by -1.

f(1/3(x - 9)) → -f(1/3(x - 9))

Vertical scaling: The function is stretched vertically by a factor of 8 by multiplying the output values by 8.

-f(1/3(x - 9)) → -8f(1/3(x - 9))

Therefore, the transformations are applied in the following order: horizontal translation, horizontal scaling, vertical reflection, and vertical scaling.

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well, the area is simply the product of its length and width, however let's firstly convert hte  mixed fractions to improper fractions.

\(\stackrel{mixed}{4\frac{2}{4}}\implies \cfrac{4\cdot 4+2}{4}\implies \stackrel{improper}{\cfrac{18}{4}} ~\hfill \stackrel{mixed}{7\frac{5}{6}} \implies \cfrac{7\cdot 6+5}{6} \implies \stackrel{improper}{\cfrac{47}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{18}{4}\cdot \cfrac{47}{6}\implies \cfrac{846}{24}\implies \cfrac{6\cdot 141}{6\cdot 4}\implies \cfrac{6}{6}\cdot \cfrac{141}{4}\implies \cfrac{141}{4}\implies 35\frac{1}{4}\)

Answer:

∠B = 55

Step-by-step explanation:

∠A + ∠B + ∠C = 180  {Angle sum property}

35 + ∠B + 90  = 180

        ∠B + 125 = 180

                  ∠B = 180 - 125

                  ∠B = 55

Answer:

Yes, 23 is a prime number, because its only factors are 1 and itself.

Answer: each store gets 787 pairs and 1 is left over

Step-by-step explanation:Divide 4723 by 6

The amplitude of the wave is 17 cm, the wavelength is approximately 0.390 cm, the period is approximately 0.449 s, and the speed is approximately 0.868 cm/s.

In the equation given: y = (17 cm)cos(5.1 cmπ​x−14 sπ​t)

Part A: The amplitude of the wave is the coefficient of the cosine function, which is the value in front of it. In this case, the amplitude is 17 cm.

Amplitude (A) = 17 cm

Part B: The wavelength of the wave can be determined by looking at the argument of the cosine function. In this case, the argument is 5.1 cmπ​x. The wavelength is given by the formula:

λ = 2π / k

where k is the coefficient in front of x. In this case, k = 5.1 cmπ.

Wavelength (λ) = 2π / 5.1 cmπ ≈ 0.390 cm

Wavelength (λ) ≈ 0.390 cm

Part C: The period of the wave (T) is the time it takes for one complete oscillation. It can be calculated using the formula:

T = 2π / ω

where ω is the coefficient in front of t. In this case, ω = 14 sπ.

Period (T) = 2π / 14 sπ ≈ 0.449 s

Period (T) ≈ 0.449 s

Part D: The speed of the wave (v) can be calculated using the formula:

v = λ / T

where λ is the wavelength and T is the period.

Speed (v) = 0.390 cm / 0.449 s ≈ 0.868 cm/s

Speed (v) ≈ 0.868 cm/s

Therefore, the amplitude of the wave is 17 cm, the wavelength is approximately 0.390 cm, the period is approximately 0.449 s, and the speed is approximately 0.868 cm/s.

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Check the picture below.

so we only want the area in pink.

\(\stackrel{\textit{left and right}}{2(4)(11)}~~ + ~~\stackrel{\textit{front and back}}{2(4)(11)}\implies \text{\LARGE 176}~cm^2\)

The utility functions in options a, b, c, and f are not risk-averse on the interval [a,b], while the utility functions in options d and e are risk-averse on the interval [a,b].

In economics and finance, risk aversion refers to a preference for less risky options over riskier ones. Utility functions are mathematical representations of an individual's preferences, and they help determine whether someone is risk-averse, risk-neutral, or risk-seeking. A risk-averse individual would have a concave utility function, indicating a decreasing marginal utility of wealth.

For options a, b, c, and f, the utility functions are and f(x) = -ln(x), g(x) = \(-e^(^-^x^)\), h(x) = \(-4x^2\) - 10x, respectively. These utility functions do not exhibit concavity, which means they are not risk-averse. Instead, they either show risk-seeking behavior (options a and b) or risk-neutrality (options c and f).

On the other hand, options d and e have utility functions f(x) = ln(x), g(x) = 1/(e^(2x)), h(x) = \(-x^2\) + 10,000x and f(x) = ln(-2x), g(x) = -1/(\(e^(^2^x^)\)), h(x) = \(x^2\) - 100,000x, respectively. These utility functions display concavity, indicating a decreasing marginal utility of wealth. Thus, options d and e can be considered risk-averse on the interval [a,b].

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Answer:

1 kg here you go this is the answer