The Laplace Transform of 9t -3t f(t) = 6 + 2e = is ____ =

Answer:

  x = 9

Step-by-step explanation:

You want the value of x that satisfies 6/40 = x/60.

This equation can be solved in one step: multiply by the inverse of the coefficient of x.

The coefficient of x is 1/60. Its inverse is 60/1 = 60. Multiplying the equation by 60 gives ...

  60(6/40) = 60(x/60)

  360/40 = x

  9 = x

__

Additional comment

Often, you will be advised to "cross multiply" as the first step in solving a proportion. Doing this would give you ...

  6(60) = 40(x)

Now, you would need to divide by the coefficient of x (or multiply by its inverse).

  6(60)/40 = (40x)/40

  360/40 = x = 9

This accomplishes in two steps what we did above in one step.

Answer:

(-2,4] and [7,α)

Step-by-step explanation:

the domain is open at -2 but closed at 4 and also closed at 7 but open till infinity..

The domain of the given function is (-2,4] U [7, ∞), which is the correct option (B).

A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).

The graph is given in the question, as shown

f(x) = x²+1 if (-2,0]

This the sub-function define between the interval (-2,0].

f(x) = -1 if (0, 4]

This the sub-function define between the interval (0, 4].

f(x) = -(x-7)² if [7, ∞)

This the sub-function define between the interval [7, ∞).

Thus, the domain of the given function is (-2,4] U [7, ∞).

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Answer:

the vertex is (0,3)

Step-by-step explanation:

using vertex form: y=a(x-h)^2+k    you can find the vertex

h: the horizontal <----------->

and

k: the vertical       |      

so, there is no h, but there is a k, which is 3, so the answer is (0,3) I believe

Significant figures with representation of x are a) 14.8 m = 14.x m. b) $10.25 = 10.2x. c) 0.05 L = 0.0x L. d) 1.000 g/mL = 1.00x g/mL. e)  6200cm = 6200x cm. f)  403 kg = 40x kg.

a) 14.8m has 3 significant figures. Representation with x in place of estimated digit: 14.x m. b) $10.25 has 4 significant figures. Representation with x in place of estimated digit: 10.2x. c) 0.05 L has 1 significant figure. Representation with x in place of estimated digit: 0.0x L. d) 1.000 g/mL has 4 significant figures. Representation with x in place of estimated digit: 1.00x g/mL. e) 6200cm has 2 significant figures. Representation with x in place of estimated digit: 6200x cm. f) 403 kg has 3 significant figures. Representation with x in place of estimated digit: 40x kg. Significant figures are the digits in a measurement that are reliable and accurate. They provide an indication of the precision of a measurement, and allow us to communicate the level of certainty we have in a particular value. When determining the number of significant figures in a measurement, we typically follow a set of rules. Non-zero digits are always significant, zeros between non-zero digits are significant, and trailing zeros to the right of the decimal point are significant. Zeros at the beginning of a number or to the left of a non-zero digit are not significant. The use of significant figures is important in science and engineering to ensure accurate and reliable measurements. When performing calculations with measurements, the result should be reported with the same number of significant figures as the least precise measurement used in the calculation. In addition, when rounding a number, the last digit should be rounded to the nearest value consistent with the number of significant figures being used. Understanding significant figures is an important part of scientific and mathematical communication, and can help to ensure accuracy and consistency in the reporting of data and calculations.

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Answer:

x = 9

FGH = 5x-3 = 42°

HGI = FGH = 42°

FGI = 42+42= 84°

Step-by-step explanation:

5x - 3 = 6x - 11

x = 9

1/2 is the probability that the number will add up to more than 4. Option C is correct

Probability is defined as the likelihood or chance that an event will occur.

Probability = Expected/Total

From the given spinner, the total outcome is expressed according to the permutation

For orange spin

3P2 = 3!
3P2  = 6

For green spin

4P2 = 4!/2!
4P2 = 12

If they are both spinned, the probability that the sum will be more than 4 are:

Expected (orange) = {(2,3)}

Expected (green) = {((1, 3), (3, 4) (2, 4), (2,3)}

Pr(number added is 4) = 1/6 + 4/12

Pr(number added is 4)  = 2+4/12

Pr(number added is 4)  = 1/2

Hence the probability that the number will add up to more than 4 is 1/2

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The equations are

a) Julie can type 25 words in 1 minute and Debbie can type 20 words in 1 minute

b) Julie can type 1500 words in 1 hour and Debbie can type 1200 words in 1 hour

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

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 number of words typed by Julie be = J

Let the number of words typed by Debbie be = D

a)

Now ,

Julie can type 50 words in 2 minutes

So , the number of words Julie can type in 1 minute = 50 / 2

Number of words Julie can type in 1 minute = 25 words

And ,

Debbie can type 300 words in 15 minutes

So , the number of words Debbie can type in 1 minute = 300 / 15

Number of words Debbie can type in 1 minute = 20 words

b)

1 hour = 60 minutes

The number words Julie can type in 1 hour = Number of words Julie can type in 1 minute x 60

Substituting the values in the equation , we get

The number words Julie can type in 1 hour = 25 x 60

The number words Julie can type in 1 hour = 1500 words

And ,

The number words Debbie can type in 1 hour = Number of words Debbie can type in 1 minute x 60

Substituting the values in the equation , we get

The number words Debbie can type in 1 hour = 20 x 60

The number words Debbie can type in 1 hour = 1200 words

Hence , the number of words per hour for Julie and Debbie are 1500 and 1200 respectively

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the polynomial is: \(f(x) = (x + 2)^2(x - 2)^2x^3.\)

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Since -2 and 2 are zeros of multiplicity 2, we know that the factors \((x + 2)^2 and (x - 2)^2\) must be in the polynomial. Since 0 is a zero of multiplicity 3, we know that the factor \(x^3\) must also be in the polynomial. Therefore, we can write:

\(f(x) = k(x + 2)^2(x - 2)^2x^3\)

where k is some constant. To find k, we can use the fact that f(-1) = 27:

\(27 = k(-1 + 2)^2(-1 - 2)^2(-1)^3\)

27 = 27k

k = 1

So the polynomial is:

\(f(x) = (x + 2)^2(x - 2)^2x^3\)

To sketch the graph of f, we can start by plotting the zeros at x = -2, x = 2, and x = 0. Since the degree of the polynomial is 7, we know that the graph will behave like a cubic function as x approaches infinity or negative infinity. Therefore, we can sketch the graph as follows:

As x approaches negative infinity, the graph will go downward to the left.

As x approaches -2 from the left, the graph will touch and bounce off the x-axis.

As x approaches -2 from the right, the graph will touch and bounce off the x-axis.

Between -2 and 0, the graph will be shaped like a "W", with three local minima and two local maxima.

At x = 0, the graph will touch and bounce off the x-axis.

Between 0 and 2, the graph will be shaped like a "U", with one local minimum and one local maximum.

As x approaches 2 from the left, the graph will touch and bounce off the x-axis.

As x approaches 2 from the right, the graph will touch and bounce off the x-axis.

As x approaches infinity, the graph will go upward to the right.

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Answer:

Step-by-step explanation:

Let one number = x

Let the other number = y

x + y = 124

You can't go any further than that without more information.

The good news is that no number is excluded.

x = 248

y = -124 for example

functions can't be with exponents -

the correct answers are b,c,d

Answer:

These 3:

y = 2, y = 1/2x + 5, y = x

Step-by-step explanation:

Y can't be squared that would give a sideways function, that doesn't pass the vertical line test

Answer:

x = 2.25

Step-by-step explanation:

-3x + 10 = 5x - 8

add 3 to 5x, add 8 to 10

18 = 8x

divide 18 by 8

x = 18/8 = 2.25

Ally will be able to cover 285 miles for the trip

Ally wants to rent the car for one day

The rents costs $35 and $0.35 per mile

Ally has $134.75 to spend for the trip

The number of miles Ally can drive for the trip can be calculated as follows

134.75 - 35

= 99.75

99.75/0.35

= 285

Hence Ally will be able to drive 285 miles for the trip  

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Answer:

show us the graph

Step-by-step explanation:

The figure that shows KLMN is dilated by a scale factor of 0.2 with the original as the center of dilation to produce K’ L’ M’ N is attached.

The Center of Dilation is described as a reference point used to appropriately scale the dilation of a figure.

From the image Square KLMN has a side length of 16 units and after dilation the sides of square K'L'M'N' will be (1/8)*16 = 2 units length.

In conclusion,  we find that the area of of square K'L'N'M' is 2² = 4 square units.

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The term is called an identity element. In multiplication, the identity element is one because any number multiplied by one results in the same number. In addition, the identity element is zero because any number added to zero results in the same number.

The term in mathematics for the operation or number that leaves others unchanged when combined with them is called the identity element.

It is also known by the name of neutral element.

In multiplication, the identity element is one (1) because when you multiply a number by one the result remains the same as the original number. For any number a,

a1=1a=a.

While in addition, the identity element is zero (0) because when you add zero to a number, the result remains the same as the original number. For any number a,

a+0=0+a=a.

There is no identity element for subtraction, and division only has an identity element for certain sets.

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Answer:

2x^2 + 19x + 9

Step-by-step explanation:

Using the FOIL method (ask me via comments if you don't know what it is), we expand it to 2x^2 + 18x + x + 9, then we add like terms, equal to 2x^2 + 19x + 9.

The trinomial expression for (2x + 1)(x + 9) is \(2x^2 + 19x + 9\).

To express (2x + 1)(x + 9) as a trinomial, you need to perform the multiplication.

Distribute each term from the first parenthesis to each term in the second parenthesis:

(2x + 1)(x + 9) = 2x * x + 2x * 9 + 1 * x + 1 * 9

Now, simplify the expression:

\(= 2x^2 + 18x + x + 9\)

Finally, combine like terms:

\(= 2x^2 + 19x + 9\)

So, (2x + 1)(x + 9) expressed as a trinomial is \(2x^2 + 19x + 9.\)

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Answer:

y' = y

Step-by-step explanation:

The slopes are independent of x.  So the only possible answer is y' = y.

Answer:

The solution of the equation f(x) = g(x) is the set of all x for which the graphs of f and g intersect.

Step-by-step explanation:

Answer:

Para dividir un número decimal como 0.1 en 10 se debe adicionar un 0 del lado derecho del punto, es decir, del lado de los decimales.

Step-by-step explanation:

Dado que, si para dividir un número por 10 le debo suprimir a ese número la última cifra, como por ejemplo 120/10 es igual a 12, o 122/10 es igual 12 y me sobran 2, para dividir un número decimal como 0.1 en 10 se debe adicionar un 0 del lado derecho del punto, es decir, del lado de los decimales. Esto se comprueba al realizar dicha división:

0.1 / 10 = 0.01

0.01 / 10 = 0.001

The Fourier-sine transform of f(x) = x + x^3 can be calculated as follows:

To find the Fourier-sine transform of f(x) = x + x^3, we need to evaluate the integral:

F_s[f(x)] = ∫[0,∞] (x + x^3) sin(kx) dx

We can split this integral into two parts:

F_s[f(x)] = ∫[0,∞] x sin(kx) dx + ∫[0,∞] x^3 sin(kx) dx

Using integration by parts for the first integral, and then simplifying the resulting expression, we can find the transform:

F_s[f(x)] = [-x cos(kx) / k]∣[0,∞] + [2/k^3 - 2cos(kx)/k^3 - 2x^2sin(kx)/k]∣[0,∞]

The first term in the result is zero because of the boundary conditions. For the second term, when we substitute the upper limit (∞), the cosine term goes to zero, and the sine term becomes oscillatory. Hence, we have:

F_s[f(x)] = 2/k^3

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As the interest rate increases from 10 percent to 11 percent, the present value of the bond decreases from $1,074.47 to $1,058.31. Conversely, when the interest rate decreases to 9 percent, the present value increases to $1,091.19. This is because the discount rate used to calculate the present value is inversely related to the interest rate, meaning that as the interest rate increases, the present value decreases, and vice versa.

To compute the present value of a five-year, 10 percent coupon bond with a face value of $1,000, we need to discount the future cash flows (coupon payments and face value) by the appropriate interest rate.

Step 1: Calculate the present value of each coupon payment.
Since the bond has a 10 percent coupon rate, it pays $100 (10% of $1,000) annually. To calculate the present value of each coupon payment, we need to discount it by the interest rate.

Using the formula: PV = C / (1+r)^n
Where PV is the present value,

C is the cash flow,

r is the interest rate, and

n is the number of periods.

At an interest rate of 10 percent, the present value of each coupon payment is:
PV1 = $100 / (1+0.10)^1 = $90.91

Step 2: Calculate the present value of the face value.
The face value of the bond is $1,000, which will be received at the end of the fifth year. We need to discount it to its present value using the interest rate.

At an interest rate of 10 percent, the present value of the face value is:
PV2 = $1,000 / (1+0.10)^5 = $620.92

Step 3: Calculate the total present value.
To find the present value of the bond, we need to sum up the present values of each coupon payment and the present value of the face value.
Total present value at an interest rate of 10 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,074.47

When the interest rate goes to 11 percent, we would repeat the above steps using the new interest rate.
Total present value at an interest rate of 11 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,058.31

When the interest rate goes to 9 percent, we would repeat the above steps using the new interest rate.
Total present value at an interest rate of 9 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,091.19

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Part A: Sydney made $21.50 at her yard sale by selling lemonade by the cup. She earned a $8 gratuity from a neighbor after selling each cup for $0.50. Here is an equation to illustrate: 0.5x + 8 = 21.50

Part B: Daria sold lemonade and earned $21.00. She earned a $7 gratuity from a neighbor for selling her lemonade for $1 per cup, but she also had to pay $0.20 for each plastic cup she used. A suitable equation is: 1.0y + 7 - 0.2y = 21.00

Part A:

Let x be the number of cups of lemonade Sydney sold.

Then the amount of money she made by selling cups of lemonade is given by:

0.5x + 8

And we know that she made $21.50 in total, so we can write:

0.5x + 8 = 21.50

The equation that captures the scenario is as follows.

Part B:

Let y be the number of cups of lemonade Daria sold.

Then the amount of money she made by selling cups of lemonade is given by:

1.0y + 7

But she also had to buy plastic cups for $0.20 each, so her expenses are given by:

0.2y

Therefore, her profit is:

1.0y + 7 - 0.2y

And we know that her profit was $21.00, so we can write:

1.0y + 7 - 0.2y = 21.00

Simplifying this equation, we get:

0.8y + 7 = 21.00

This is the equation that represents the situation.

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Triangle KVM is similar to triangle BVG because angle M = angle G = 90° and angle V is common to both triangles.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio.

For two triangles to be similar, the corresponding angles must be congruent i.e equal.. Also the ratio of the corresponding sides of similar triangles are equal.

angle M and G are both 90° , this means they are equal.

angle KVM = BVG

therefore angle K = angle B

Since all the corresponding angles are equal, we can say triangle KVM is similar to triangle BVG

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Answer:

Step-by-step explanation:

Assumed the question is how many pages are in each chapter.

Let it be x: