derive the laplace transform of the ramp function x(t) = mt, whose slope is the constant m.

Answer:

D. 64x4964, x, 49

Step-by-step explanation:

The expression [4x4(2x3)]2 means to square the result of the expression inside the brackets.

4x4 = 16x4

2x3 = 6x3

So, [4x4(2x3)] = [16x4(6x3)] = 96x7.

Squaring this result, we get

[4x4(2x3)]2 = 96x7 * 96x7 = (96 * 96)x(7 * 7) = 9216x49 = 9216x^49.

Therefore, the expression [4x4(2x3)]2 is equivalent to 64x49, x, 49.

Answer:

see below

Step-by-step explanation:

z+66+z+69+43z=180

so 45z=180-66-69 = 45

so z=1

so angle U= 43 its opposite side length ST is the smallest

same logic for the other 2.

66+1=67

69+1=70

so ST<US <TU

The rate of change is -5.

The number of treat left in the bag after 20 dyas is 70.

A bag of cat treats has 170 individual treats inside. Your cat can eat 5 treats per day. Therefore, the rate of change can be calculated as follows:

The rate of change is the rate at which one quantity is changing with respect to another quantity.

Therefore, using equation

y = mx + b

where

Therefore,

y = 170 - 5x

where

Hence,

rate of change = -5

Let's find the treat left in the bag after 20 days

y = 170 - 5x

y = 170 - 5(20)

y = 170 - 100

y = 70

Therefore, 70 treat is left in the bag.

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The coordinate of the point P that lies on the line segment AB will be (-1, -1).

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

Given the points A(-4, 1) and B(8, -7). AP to PB is in the ratio of 1 to 3. Then the coordinate of the point P is given as,

x = (1 × 8 + 3 × (-4)) / (1 + 3)

x = (8 - 12) / 4

x = -4 / 4

x = -1

y = (1 × (-7) + 3 × 1) / (1 + 3)

y = (- 7 + 3) / 4

y = -4 / 4

y = -1

The coordinate of the point P that lies on the line segment AB will be (-1, -1).

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The length of the rectangular pool is x + 7.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Area of a rectangular shape = Length × Width

Given that,

Area = x² + 15x + 56

Width = x + 8

Substituting,

x² + 15x + 56 = Length (x + 8)

Length = (x² + 15x + 56) / (x + 8)

Factorize x² + 15x + 56.

x² + 15x + 56 = (x + 7) (x + 8)

So length = x + 7

Hence the length of the pool can be represented as x + 7.

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Answer:

The next four multiples of 5/10 are:

1.              ➡️                       1/2

2.             ➡️                       3/4

3.             ➡️                        1

4.             ➡️                      1 1/4

The expression's result is -2 [tex]\sqrt[3]{89}[/tex] when it is stated that a = 64 and b = -5. Scientific operation, expression, and numeral

Multiplying, split, adding, and withdrawing are all possible in mathematics. As an example, consider the following expression: Scientific operation, expression, and numeral The elements that make up a mathematical expression include numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) One can contrast two expressions or sentences. The terms "expression" or "algebraic expression" refer to any mathematical statement that has variables, numbers, and also an arithmetic procedure between them. For instance, the statement 4m + 5 consists of the terms 4m and 5, as well as the variable m from the given expression, all of which are divided by the arithmetic sign +.

given

a = 64

b = -5

= -2[tex]\sqrt[3]{a+b^{2} }[/tex]

= -2  [tex]\sqrt[3]{89}[/tex]

The expression's result is -2 [tex]\sqrt[3]{89}[/tex] when it is stated that a = 64 and b = -5.

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The correct question is :- What is the value of this expression when a = 64 and b = -5 ?

-2[tex]\sqrt[3]{a+b^{2} }[/tex]

The formula that shows how to find C, circumference, when d, diameter is given is C = πd.

Circumference is the line that bounds a circle or other two-dimensional (2D) figure.

Diameter is any straight line between two points on the circumference of a circle that passes through the centre/center of the circle.

The diameter can be used to find the radius of a circle using the following formula;

D = 2r

Circumference of a circle = 2πr

Substituting D in the equation for circumference......

Circumference of a circle = 2πd/2

Circumference of a circle = πd

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The transitive term accurately completes the proof

What is the vertical angle theorem?

According to the vertical angle theorem, the vertical angles that are created when two lines intersect are congruent. The opposing angles of two intersecting lines must be congruent, or identical in value.

Here, we have

Given: segment UV is parallel to segment WZ. According to the given information, segment UV is parallel to segment WZ, while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem.

we are given a line of thought trying to prove different entities proven to be congruent by different arguments or proof.

Eventually, the two are associated using a property called transitivity. This property is used to associate A and C when A is equal to B and B is equal to C.

Hence, the transitive term accurately completes the proof.

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Matrix A belongs to the permutation and Markov classes.

This is the case for matrix A, as it has one 1 in each row and column and 0s everywhere else. Matrix A is also a Markov matrix, which means that all the entries are non-negative and the sum of each row is equal to 1. This can be seen by summing each row, which yields 1+0+0 = 1, 0+1+0 = 1, and 1+0+0 = 1.

Matrix B belongs to the orthogonal, projection, and diagonalizable classes. Matrix B is orthogonal, which means that it is a square matrix whose columns and rows are orthonormal unit vectors (i.e. the dot product of any two columns or rows is 0). This is the case for matrix B, as the dot product of any two columns or rows yields 0. Matrix B is also a projection matrix, which means that it is a square matrix whose columns are all of unit length (i.e. the dot product of any two columns or rows is 1). This can be seen by taking the dot product of any two columns or rows, which yields 1. Finally, matrix B is diagonalizable, which means that it can be transformed into a diagonal matrix using a similarity transformation. This can be seen by calculating the eigenvalues and eigenvectors of matrix B, which yields the same diagonal matrix.

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Answer:

-2, -1, 0, 6

Step-by-step explanation:

The range is the outputs or the y values.  I just put them in order from least to greatest

(1, -2)

(9, -1)

(2, 0)

(-6, 6)

The length of the line segment ML is 15 cm.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

The area of a trapezoid is (1/2)×(sum of the two parallel sides)×height.

From the given information,

m∠LJ = m∠LM = 90°.

So, m∠LJ + m∠LM = 180°.

Line segment ML is parallel to JK.

Therefore, NP is the midline of the trapezoid.

ML + JK = 2NP.

JK = 2NP - ML.

9 = 24 - ML.

ML = 15 cm.

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The required payment for the SUV after the discount was applied is 136,000. Option C is correct.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
All SUVs are marked down by 15%.
Cost of G wagon = 160, 000
Cost after discount = 160000 - 15% of 160,000
                             = 136000

Thus, the required payment for the SUV after the discount was applied is 136,000. Option C is correct.

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The amount after discount is $136000.

Given is that Mercedes is running a special in which all SUVs are marked down for 15%. Mr. Estes purchased a G wagon for 160,000.

The amount after the discount was applied is -

D = 15% of 160000

D = (15/100) x 16000

D = 15 x 160

D = 2400

A = 160000 - 2400 =

A = 136000

Therefore, the amount after discount is $136000.

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To fill the blank of the given table above is represented below as follows:

1= 11.4 grams

2= 22.8 grams

6= 68.4 grams

10 = 114 grams

If 2 packages = 22.8 g

1 package = X grams

Make X the subject of formula;

x grams = 22.8/2 = 11.4grams

If 1 package = 11.4 grams

6 packages = y grams

Make y the subject of formula;

y = 6×11.4

y = 68.4 grams

If 1 package = 11.4 grams

z packages = 114 grams

make z the subject of formula;

z = 114/11.4

z = 10 packages.

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Tthe required simplified solution of the given expression is -3.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression
=  -3(9)⁰
= -3(1)     [a⁰ = 1]
= -3

Thus, the required simplified solution of the given expression is -3.

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The time complexity average of this problem is O(n³). It involves three nested loops, each loop iterating n times. Therefore, the time complexity is O(n³).

The time complexity of this problem is O(n³). This problem involves three nested loops, each loop iterating n times. This means that the problem requires at least O(n³) time to complete. In the outer loop, which is the first loop, the value of i is initialized to 1 and then the loop iterates n times, meaning that the outer loop requires O(n) time. In the second loop, which is the nested loop, the value of j is initialized to 1 and then the loop iterates n times, meaning that the second loop requires O(n) time. In the third loop, which is the innermost loop, the value of k is initialized to 1 and then the loop iterates n times, meaning that the third loop requires O(n) time. Since the three loops are nested, the total time complexity of this problem is the product of the time complexities of the three loops, which is O(n³). Therefore, the time complexity of this problem is O(n³).

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The number of ways to have 3 hearts and 2 diamonds in a 5 card hand is 286 * 78 = 22,308 ways.

The number of ways to choose 3 hearts from the 13 available hearts is given by the binomial coefficient C(13,3). The number of ways to choose 2 diamonds from the 13 available diamonds is given by C(13,2). The total number of ways to choose 3 hearts and 2 diamonds from the deck of 52 cards is the product of these two binomial coefficients: C(13,3) * C(13,2).

i.e.

There are 13 hearts and 13 diamonds in a deck of 52 cards.

To choose 3 hearts, we have C(13,3) = 13!/(3!(13-3)!) = 286 ways.

To choose 2 diamonds, we have C(13,2) = 13!/(2!(13-2)!) = 78 ways.

Therefore, the number of ways to have 3 hearts and 2 diamonds in a 5 card hand is 286 * 78 = 22,308 ways.

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The value of x is 4 which means that the first digit in the sequence is 4, the second digit is 5, the third digit is 6, and so on.

This problem is asking for the value of x in a sequence of 14 digits where the sum of any three consecutive digits is equal to 15. To solve for x, we can use the information provided and basic algebra.

Let's assign a variable to each of the 14 digits in the sequence. For example, let x be the first digit, (x + 1) be the second digit, (x + 2) be the third digit, and so on. Then, the sum of any three consecutive digits must equal 15:

x + (x + 1) + (x + 2) = 15

Expanding and solving for x, we get:

3x + 3 = 15

3x = 12

x = 4

So, the value of x is 4. This means that the first digit in the sequence is 4, the second digit is 5, the third digit is 6, and so on. By continuing this pattern, we can fill in the entire sequence of 14 digits such that the sum of any three consecutive digits is equal to 15.

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Answer:

Step-by-step explanation:

Divide both sides by 9. Xavier had $8.

if Lucy has 9 times as much as Xavier 8 times 9 =72

The solution of the inequality 3x + 4y ≤ 5 is (2, -1)

In mathematics, Inequality is a mathematical statement that gives unequal comparisons between algebraic terms or algebraic equations using the signs like less than, greater than, etc. The solution to an inequality is a value that satisfies the given inequality.    

Here we have

The inequality 3x + 4y ≤ 5  

To be the solution to given inequality, the ordered pair must satisfy the given equation  

So to find the correct solution check which of the following will satisfy the given inequality.    

At A. (7, 2)  

=>  3x + 4y ≤ 5  

=>  3(7) + 4(2) ≤ 5    

=>  29 ≤ 5   [ which is not true ]  

∴ A. (7, 2) is not a solution to the given inequality  

At B. (2, -1)

=> 3(2) + 4(-1) ≤ 5    

=> 6 - 4 ≤ 5  

=> 2 ≤ 5     [ which is true ]

∴ B. (2, -1) will be a solution to the given inequality  

C. (6, 1)

=> 3(6) + 4(1) ≤ 5    

=> 18 + 4 ≤ 5    

=> 22 ≤ 5    [ which is not true ]

∴ C. (6, 1) is not a solution to the given inequality

D. (5, -1)​  

=> 3(5) + 4(-1) ≤ 5  

=> 15 - 4 ≤ 5  

=> 11 ≤ 5   [ which is not true ]

∴ D. (5, -1)​ is not a solution to the given inequality

Therefore,

The solution of the inequality 3x + 4y ≤ 5 is (2, -1)

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The number of pounds in 32 kg would be 70.5479.

A pound is an imperial unit used to measure bulk or weight. A kilogram is a metric measuring unit. The letters lb and lbm stand for pounds. Kilo or kg are used to denote kilograms. 0.4535 kilograms make up one pound.

In both the British imperial system and the United States' customary system, weight is measured in pounds. Measuring a person's weight is one common application of pounds.

The weight of a kilogram is 2.2046 pounds. We convert kilograms (kg) to pounds (lb) using the formula 1 kg = 2.2 lb. By multiplying by 2.2, we may convert a kilogram to a pound. We divide by 2.2 to change a pound into a kilogram.

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When calculating the percent of pitches thrown at least 92 mph, we subtract from 100% to find the percentage of pitches that fall within a certain threshold (in this case, 92 mph).

When calculating the percentage of pitches thrown at a certain speed, say 92 mph, we use 100% as a reference point. 100% means all of the pitches. By subtracting the percentage of pitches thrown below 92 mph from 100%, we find the percentage of pitches that were thrown at 92 mph or above. This helps us understand what proportion of pitches were thrown at this speed or higher, compared to the total number of pitches thrown. By doing this, we can see how many pitches fall within a certain threshold, in this case 92 mph or above.

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Answer:

11 units

Step-by-step explanation:

-5 to zero is 5 units

zero to 6 is 6 units.

Answer:

1/2

Step-by-step explanation:

So the point of this question is to compare all of the answers and see which one fits best.  To do this, first change the denominator to match 5/8.  To convert 1/2 into eighths, multiply 2 by 4 so you get eight.  Since you did that, you have to do the same to the numerator.  Therefore:  

1/2 = 4/8

Is 4/8 less than 5/8?  Yes.  Is it greater than 1/9?  Yes, but how?  Do the same thing but instead convert 1/2 into ninths.  Multiple 2 by 4.5 to get 9 and 1 by 4.5 to get 4.5.  

1/2 =  4.5/9

4.5/9 is greater than 1/9, so you answer would be 1/2.  

Normally you would test every answer, but to save time I'll just stop there because the first option was correct.  I hope you understand.  :)

Answer:

1/2

Step-by-step explanation:

1/2 = 4/8 which is less than 5/8.

1/9 = 2/18

1/2 = 9/18 which is greater than 2/18 (same as 1/9)

The selling price for the jacket is $36.

To determine the selling price of the jacket, we need to calculate the markup percentage on the original price of $20. A markup percentage is the increase in price over the original cost. In this case, the markup percentage is 80%, which means the selling price is $20 + ($20 * 0.8) = $20 + $16 = $36.

Here is the breakdown of the calculation:

Original cost of the jacket: $20

Markup percentage: 80%

Markup amount: $20 * 0.8 = $16

Selling price: $20 + $16 = $36

Therefore, The selling price for the jacket is $36.

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Answer: 10/12

Step-by-step explanation:

Make 1/4 have the same denominator as 7/12. 1/4=3/12. 7/12+3/12 = 10/12

1. Considering the equation [tex]z^{16}[/tex] = −1−i.The value of z which satisfies this equation and which has the second smallest positive argument θ, 0<θ<2π as z=r[tex]e^{i\theta}[/tex] where r = [tex]\underline{2^{1/32}}[/tex] and θ = 13π/64.

2. Considering the equation [tex]z^{13}=(-1+\sqrt{3i})[/tex]. The value of z which satisfies this equation and which has the second smallest positive argument θ,0<θ<2π as z=r[tex]e^{i\theta}[/tex] where r = [tex]\underline{2^{1/13}}[/tex] and θ = 8π/39.

1. The equation is z^{16} = -1 - i.

We have express our answer in the form of

[tex]\; z = re^{i\theta }[/tex]

When we enter it into the first equation, we obtain,

[tex]r^{16}e^{16i\theta }=-1-i\; \; \; \; \; \; \; \; \; \; \; \;[/tex]--(2)

Using the modulus of both sides, we obtain,

[tex]\left |r^{16} \right |\: \: \left | e^{16i\theta } \right |=\sqrt{\left ( -1 \right )^{2}+\left ( -1 \right )^{2}}[/tex]

Simplifying

[tex]\; \; \; \; \; r^{16}=\sqrt{2}[/tex]

Taking root of 16 on both side, we get

[tex]r=2^{1/32}[/tex]

Plugging this value of 'r' back in equation (2), we get,

[tex]\sqrt{2}\; \; e^{16i\theta }=-1-i[/tex]

Divide by √2 on both side, we get

[tex]e^{16i\theta }=-\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}i[/tex]

We can write [tex]e^{16i\theta }[/tex] as

[tex]\; \; \; \;cos16\theta +isin16\theta =-\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}i[/tex]

On comparing, we get

[tex]\; \; \; \;cos16\theta=-\frac{1}{\sqrt{2}}\;, \; \; \; \; \; \; \; sin16\theta =-\frac{1}{\sqrt{2}}[/tex]

Angle must therefore be in the third quadrant.

[tex]16\theta=\pi +\frac{\pi }{4}=\frac{5\pi }{4}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;16\theta=\frac{5\pi }{4}+2\pi =\frac{13\pi }{4}[/tex]

[tex]\theta=\frac{5\pi }{64}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;\theta=\frac{13\pi }{64}[/tex]

So, second smallest positive argument = 13π/64.

2) The equation is [tex]z^{13} = -1 +\sqrt{3i}[/tex].

We have express our answer in the form of

[tex]\; z = re^{i\theta }[/tex]

When we enter it into the first equation, we obtain,

[tex]r^{13}e^{13i\theta }=-1+\sqrt{3}i\; \; \; \; \; \; \; \; \; \; \; \;[/tex]

Using the modulus of both sides, we obtain,

[tex]\left |r^{13} \right |\: \: \left | e^{13i\theta } \right |=\sqrt{\left ( -1 \right )^{2}+\left ( \sqrt{3} \right )^{2}}[/tex]

Simplifying

[tex]r^{13}=2[/tex]

Taking root of 13 on both side, we get

[tex]r=2^{1/13}[/tex]

Reintroducing this 'r' value into the equation from [tex]r^{13}e^{13i\theta }=-1+\sqrt{3}[/tex], we get,

[tex]2e^{13i\theta }=-1+\sqrt{3}i[/tex]

Divide 2 on both side, we get

[tex]e^{13i\theta }=-\frac{1}{2}+\frac{\sqrt{3}}{2}i[/tex]

We can write [tex]e^{13i\theta }[/tex] as

[tex]\; \; \; \;cos13\theta +isin13\theta =-\frac{1}{2}+\frac{\sqrt{3}}{2}i[/tex]

[tex]\; \; \; \;cos13\theta=-\frac{1}{2}\;, \; \; \; \; \; \; \; sin13\theta =\frac{\sqrt{3}}{2}[/tex]

Angle must therefore be in the second quadrant.

[tex]13\theta=\pi -\frac{\pi }{3}=\frac{2\pi }{3}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;13\theta=\frac{2\pi }{3}+2\pi =\frac{8\pi }{3}[/tex]

[tex]\theta=\frac{2\pi }{39}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;\theta=\frac{8\pi }{39}[/tex]

So, second smallest positive argument = 8π/39.

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The price for wrapping small gifts is $2 and the price for wrapping large gifts is $7

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

Yesterday they wrapped 12 small gifts and 45 large gifts earning a total of $339

say small gifts = g and large gifts is = G

12g + 45G = $339

Today they wrapped 35 small gifts and 42 large gifts, and earned $364

35g + 42G = $364

The simultaneous equation

12g + 45G = $339

35g + 42G = $364

solving the simultaneous equation gives

g = $2 and G = $7

Hence the price for wrapping small gifts is $2 and that of big gifts is $7

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The negation of the statement ∀x∃y(2 < x ≤y) is ∃x∀y(x ≤2 ∨ y < x) and the negation of the statement ∀y∃x(y > 0 →x ≤0) is ∃y∀x(y ≤0 ∨ 0 < x).

(a) ∃x∀y(x ≤ 2 ∨ y < x)

This statement can be read as: There exists an x such that for all y, x is less than or equal to 2 or y is less than x.  To calculate this, we can look at the inequalities in both directions. We know that x is greater than 2, so we can use this to determine the lower bound for y. To prove this, we can examine the case when x = 2 and y = 3. Since 3 is greater than 2, the statement is true.

(b) ∃y∀x(y ≤ 0 ∨ x > 0)

This statement can be read as: There exists a y such that for all x, y is less than or equal to 0 or x is greater than 0.

This statement states that there exists a y such that for all x, either y is less than or equal to 0 or x is greater than 0. To calculate this, we can look at the inequalities in both directionsTo prove this, we can examine the case when y = -1 and x = 1. Since 1 is greater than 0, the statement is true.

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