simplify the fraction

6jk/8k

The functions y = 2 (1/5)^(x) - 5 and y = 2^x are compared as follows

                                 y = 2 (1/5)^x - 5                y = 2^x

Starting value:               2                                    1

base function:        decay function = 1/5         growth function = 2

Transformation:     translation: 5 units down  no transformation

A decay function is a mathematical function that models the decrease or diminution of a value over time and is used in many disciplines including physics, engineering, economics, and machine learning.

It is a sort of function that, as time goes on, approaches zero at a pace proportionate to its current value.

The base function for decay functions is an exponential function, is

0 < k < 1

The growth function, which has values greater than 1, is the reverse of the decay function.

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Answer: B: x ≥ -6

hope this helps

The system of equations that has a solution of approximately (1.8, –0.9) are: x+2y=0 and 6x-5y=15

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Here, we have,

we are given the following equations:

i) x-2y= 4

ii) 4x+5y= 8

iii) 6x-5y=15

iv) x+2y=0

Required:

Which system of equations has a solution of approximately (1.8, –0.9).

To find the approximate equations, substitute x and y for  1.8 and  -0.9 into all the equations respectively and check the resulting values

i) Substitute (1.8, -0.9) in x-2y= 4:

1.8 - 2(-0.9) = 4.

1.8 + 1.8 = 4.

3.6 ≠ 4.

ii) Substitute (1.8, -0.9) in 4x+5y= 8

4(1.8) + 5(-0.9) = 8

7.2 - 4.5 = 8.

2.7 ≠ 8.

iii) Substitute (1.8, -0.9) in 6x-5y=15

6(1.8) - 5(-0.9) = 15.

10.8 + 4.5 = 15

15.3 ≠ 15.

This equation has a solution that is close, therefore it is correct.

iv) Substitute (1.8, -0.9) in x+2y=0

1.8 + 2(-0.9) = 0.

1.8 - 1.8 = 0.

0 = 0.

x + 2 y = 0 has the exact value, therefore it is also correct.

The system of equations that has a solution of approximately (1.8, –0.9) are: x+2y=0 and 6x-5y=15

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The expression equal to 5¹/₃ is ∛5 (option B)

The definition of an expression in math is a statement composed of terms and operations. The terms may be constant (numbers), or variables with coefficients. The operations may be addition, subtraction, multiplication, or division.

Given is an expression, 5¹/₃,

Using indices rule,

b¹/ₐ = [tex]\sqrt[a]{b}[/tex]

Therefore,

5¹/₃, here b = 5, a = 3

Therefore,

5¹/₃ = ∛5

Hence, the expression equal to 5¹/₃ is ∛5 (option B)

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The remaining time of the trip is 3 5/6 hours.

If a trip from Boston to Washington takes 5 3/4 hours and you have traveled 1/3 of the way, the remaining time of the trip can be calculated by subtracting the time traveled from the total time of the trip.

First, we need to convert 5 3/4 hours to a fraction:
5 3/4 = (5 * 4 + 3)/4 = 23/4
Next, we need to calculate the time traveled so far:
23/4 * 1/3 = 23/12
Now we can subtract the time traveled from the total time of the trip:
23/4 - 23/12 = (23 * 3 - 23 * 1)/12 = 46/12 = 3 10/12 = 3 5/6
Therefore, the remaining time of the trip is 3 5/6 hours.
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The triangles ∆ABC and ∆DEF are similar triangles, and ∆ABC ≅ ∆DEF. The values of x and y are 30.6 and 30° respectively.

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

We have that line AC of the triangle ∆ABC corresponds to line BK of the triangle ∆DEF and also angle A of the triangle ∆ABC corresponds to angle D of the triangle ∆DEF.

We can evaluate for the values of x and y as follows:

2y - 5 = 65

2y = 65 - 5 {subtract 5 from both sides}

2y = 60

y = 60/2 {divide through by 2}

y = 30

2x + y = 90.6

2x + 30 = 90.6

2x = 90.6 - 30 {subtract 30 from both sides}

2x = 60.6

x = 60.6/2 {divide through by 2}

x = 30.3

In conclusion, the triangles ∆ABC and ∆DEF are similar triangles, and ∆ABC ≅ ∆BMK. The values of x and y are 30.6 and 30° respectively.

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The point (-2, 1) satisfies both equations y = x + 3 and y = 2x + 5 simultaneously.

What is graph of equation?

Write the equation in the form y = mx + b to determine the slope m and y-intercept (0, b). 2) Next, determine the y-intercept. 3) Depending on whether the slope is positive or negative, go up or down and left or right from the y-intercept.

We are looking for the values of x and y that satisfy both equations simultaneously. We can do this by setting the right-hand sides of the two equations equal to each other:

y = x + 3 (equation 1)

y = 2x + 5 (equation 2)

Setting the right-hand sides equal to each other, we get:

x + 3 = 2x + 5

Simplifying this equation, we get:

x = -2

Now that we have the value of x, we can substitute it into either of the two equations to find the corresponding value of y. Let's use equation 1:

y = x + 3

y = -2 + 3

y = 1

So, the values of x and y that make both equations true are:

x = -2

y = 1

Therefore, the point (-2, 1) satisfies both equations y = x + 3 and y = 2x + 5 simultaneously.

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Answer:

To multiply 0.12 x 0.4, first you need to write the numbers in standard form. 0.12 can be written as 0.120 and 0.4 can be written as 0.400.

Then, multiply the numbers by first multiplying the digits in the ones column, then the digits in the tenths column and finally the digits in the hundredths column.

This is done by multiplying the first digit in the first number (1) with the first digit in the second number (4), then multiplying the second digit (2) with the second digit (0), and finally multiplying the third digit (0) with the third digit (0).

Therefore, the multiplication can be written as:

1 x 4 = 4 2 x 0 = 0 0 x 0 = 0

Adding these three numbers together gives us 0.048, which is the answer to 0.12 x 0.4.

The value of m from the quadratic equation is m = -1/5 or m = 1

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

x² + 4mx + 4m² - m - 1 = 0   be equation (1)

Now , sum of the roots of the equation = -b/a

where b = 4m and a = 1

So , so the sum of the roots = -4m

From the Vieta's formula , we get

-4m = ( -1 - 4m² + m ) / 1

On simplifying the equation , we get

5m² - 4m - 1 = 0

On factorizing the equation , we get

5m² - 5m + m - 1 = 0

5m ( m - 1 ) + 1 ( m - 1 ) = 0

Taking the common terms in the equation , we get

( 5m + 1 ) ( m - 1 ) = 0

when ( 5m + 1 ) = 0

Subtracting 1 and dividing by 5 on both sides , we get

m = -1/5

when ( m - 1 ) = 0

Adding 1 on both sides , we get

m = 1

So , the two values of m are

m = -1/5 and m = 1

Hence , the equation is solved

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The weight 60.5 kg is equal to approximately 133.38 pounds. This conversion was done using the formula 60.5 kg x 2.20462 lbs/kg = 133.37851 lbs.

We know that 1 kg is equivalent to 2.20462 pounds, which means that we can convert kilograms to pounds by multiplying the weight in kilograms by the conversion factor 2.20462.

So to convert 60.5 kg to pounds, we can use the following formula:

60.5 kg x 2.20462 lbs/kg = ? lbs

Multiplying 60.5 by 2.20462 gives us:

60.5 x 2.20462 = 133.37851

Therefore, 60.5 kg is equivalent to 133.37851 pounds.

Finally, we can round this result to two decimal places to get:

60.5 kg is approximately equal to 133.38 pounds.

So the final answer is that 60.5 kg is equivalent to approximately 133.38 lbs.

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The solution of the Equation is x=1  and y= -3.

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. LHS = RHS is a common mathematical formula.

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:

-3x + 7y = -18...........(1)

4x - 4y = 8.................(2)

Solving equation (1) and (2) we get

-12x + 28y = -72

12x - 12y = 24

____________

16y =  -48

y= -48/ 16

y = -3.

and, -3x + 7(-3) = -18

-3x = 3

x= -1

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The amount of money that he earned in interest is given as follows:

$420.

The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

P is the value of the initial deposit.

r is the interest rate, as a decimal.

The interest accrued is given as follows:

I(t) = Prt.

The parameters for this problem are given as follows:

P = 7000, r = 0.02, t = 3.

Hence the total interest is of:

I(3) = 7000 x 0.02 x 3

I(3) = $420.

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The general solution for the non-homogeneous equation is the sum of the homogeneous solution and the particular solution::

y(x) = c1 * cos(√-17i * x) + c2 * sin(√-17i * x) + (3/64) * e^8x

where c1 and c2 are arbitrary constants.

The method of undetermined coefficients is used to find a particular solution for a non-homogeneous linear ordinary differential equation of the form:

dy/dx + p(x)y = g(x)

where p(x) and g(x) are known functions. To use this method, we first find the general solution of the corresponding homogeneous equation:

dy/dx + p(x)y = 0

The general solution of this homogeneous equation can be written as:

y = c1 * y1(x) + c2 * y2(x)

where c1 and c2 are arbitrary constants and y1(x) and y2(x) are the linearly independent solutions of the homogeneous equation.

Next, we guess a particular solution yp of the non-homogeneous equation of the form:

yp = A * f(x)

where A is an unknown constant and f(x) is a function of x that matches the form of the forcing function g(x).

For the given equation: y'' + 17y = 3e^8x

The corresponding homogeneous equation is: y'' + 17y = 0

The characteristic equation is: r^2 + 17 = 0

The roots are: r = ±√-17i

So the general solution of the homogeneous equation is:

y = c1 * cos(√-17i * x) + c2 * sin(√-17i * x)

where c1 and c2 are arbitrary constants.

For the non-homogeneous equation, we guess a particular solution of the form:

yp = A * e^8x

where A is an unknown constant. Substituting this into the non-homogeneous equation, we have:

yp'' + 17yp = A * 8^2 * e^8x = A * 64e^8x

Comparing the right-hand sides of the two equations, we see that yp'' + 17yp = A * 64e^8x = 3e^8x, so A = 3/64.

Therefore, a particular solution for the non-homogeneous equation is:

y = yp = (3/64) * e^8x

The general solution for the non-homogeneous equation is the sum of the homogeneous solution and the particular solution:

y = c1 * cos(√-17i * x) + c2 * sin(√-17i * x) + (3/64) * e^8x

where c1 and c2 are arbitrary constants.

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The number of cubes that have just one red face is 25.

A solid three-dimensional shape called a cube contains six square faces, eight vertices, and twelve edges.

Given:

Meg paints the whole outside of a 5 x 5 x 5 cube red and then cuts it up into 1 x 1 x 1 cube.

The surface area of the cube with dimensions 5 x 5 x 5,

= 6 x 5 x 5

= 150 square units.

The surface area of the cube with dimensions 1 x 1 x 1,

= 6 square units.

The number of cubes that have just one red face is,

= 150/6 = 25

Therefore, 25 is the required number.

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Answer:

Each person will receive 12 ounces

Step-by-step explanation:

84 ounces divided by 7 people

84 / 7 = 12

The two zeros of the equation are -3,8.

The zeros of any equation lie on the x axis.On x axis y=0.The zeros can be found by substituting y=0 and finding the corresponding y values.

here, we have,

The given equation is :

f(x) = x² - 5x - 24

Comparing it with quadratic equation

y = ax^2+bx+c

We have a=1,b=-5,c=-24.

To find the zeros we substitute y=0.

x² - 5x - 24= 0

WE need to find two numbers which on multiplication will give us ac that is 1(-24)=-24.The same numbers on addition should give us b=-5.

The two numbers are -8 and 3.-8 times 3=-24 and -8+3=-5.

The factors of the equation are (x+8)(x-3)=0

making  both factors =0 we have:

x+8=0 and x-3=0

Solving for x

x=-8 and x=3.

Hence, The two zeros of the equation are -3,8.

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Answer:

Division

7n=21

7n÷7=21÷7

n=3

Step-by-step explanation:

Answer:

the answer is 3

Step-by-step explanation:

7n=21

divide both sides by 7

n=3

The formula for calculating percent recovery is

Percent recovery = (mass of purified compound obtained / mass of original compound) x 100

Percent recovery is an important parameter used in recrystallization to determine the efficiency of a purification process. It refers to the percentage of the original material that is recovered after the recrystallization process.

To calculate percent recovery, first, the mass of the original sample is measured before the recrystallization process. After the process is completed, the mass of the purified compound is measured, which is obtained from the recrystallization.

The mass of the purified compound is then divided by the mass of the original compound and multiplied by 100 to get the percent recovery. A high percent recovery indicates that the recrystallization process was successful in separating the target compound from the impurities, and the final product is relatively pure.

A low percent recovery may indicate that the recrystallization process was not efficient in separating the target compound from impurities, or that some of the target compound was lost during the process. Thus, percent recovery is a crucial parameter that determines the success of a recrystallization process.

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Complete question is:

How do you calculate percent recovery during recrystallization?

The statement, When two events are disjoint, they are also independent is false.

In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)

Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:

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

=> P(B ∩ A) = P(B) × P(A) --(2)

(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.

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The number of signature on the petition in the first week is 6

A double is a number or an amount that is twice as large as the given number or amount. So, if we multiply a number by 2 or if we add a number to itself, we say that the number is doubled.

Since the signature doubles every week

represent the initial signature by x

p(o) = x

second week =2 x

third week =4 x

fourth week = 8x

fifth week =16 x

sixth week = 32x

32x = 192

x = 192/32

x = 6

therefore the number of signature on the petition in the first week is 6

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The equations that represent nonlinear functions include the following:

C. m(x) = 8^x

F. f(x) = 8x^2 + 8x.

In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, a linear function has the same slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.

In conclusion, m(x) = 8^x represents an exponential function while f(x) = 8x^2 + 8x represents a quadratic function.

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Yes, it is True that The sensitivity range for an objective function coefficient (range of optimality) is the range of values over which the current optimal solution point (product mix) will remain optimal.

The sensitivity range for an objective function coefficient, also known as the range of optimality, is the range of values over which the current optimal solution (product mix) will remain optimal. This range represents the tolerance for changes in the objective function coefficients without causing the optimal solution to change.

The range of optimality is determined by analyzing the linear programming model and checking how changes in the objective function coefficients affect the optimal solution. If a change in an objective function coefficient falls within the sensitivity range, it means that the current optimal solution will still be optimal, even with the change. However, if the change falls outside the sensitivity range, it will cause the optimal solution to change.

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Answer:

24

Step-by-step explanation:

Write 10% as 10/100

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have 10/100 of 240 = 10/100×240

Therefore, the answer is 24

The price of the sweater after the discount is 0.72P.

A reduction made from the gross (see gross entry 1 sense 3b) amount or value of something.

Since the price P would represent 100% and the price was discounted by 10%, you can calculate 10% of 100% and subtract that amount, which would be:

100× 10%=10

100-10=90%

The price paid would be 90% of P.

Then, the statement says that the price was discounted by another 20%. Now let us calculate 20% of the price and subtract that amount from the price:

90×20%=18

90-18=72%

Hence, the price of the sweater after the discount is 0.72P.

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Answer:B

Step-by-step explanation:

-7+5.25n-4.5n=-7+0.75n