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The given identity (P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1) is proven below

Given the following equation

(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)

We start by simplifying the left-hand side of the equation:

(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)= [(P²+1)/(P(P-1))] + [(P²+1)/(P(P+1))] - [(P²-1)/((P+2)P)] - [(P²+1)/((P-2)P)]

Next, we have the following steps to simplify the expression

= [(P³ + P² + P + 1)/(P(P²-1))] - [(P³ - 3P)/(P(P²-4))]

= [(P³ + P² + P + 1)(P²-4) - (P³ - 3P)(P²-1)]/[(P(P²-1))(P(P²-4))]

= [(P⁵ - 3P³ + P³ - 3P² + P² - 4P + P² - 4P - 4 + P³ - 3P)/(P⁴ - 5P² + 4)]

= [P⁵ - 2P³ - 6P² - 8P - 4]/[(P²-4)(P²-1)]

= -4(2p² + 1)/(p²-4) (p² - 1)

Hence, the given identity is proven.

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Step-by-step explanation:

m ∠WXY = 72°

m ∠ 1 = m ∠ 2 + 6°

m ∠WXY = m ∠ 1 + m ∠ 2

72° = (m ∠ 2 + 6°) + m ∠ 2

72° = 2 × (m ∠ 2) + 6°

2 (m ∠ 2) = 72° - 6°

2 (m ∠ 2) = 66°

(m ∠ 2) = 33°

a) The formula relating y to t is: y = 45.1 * e^(-0.693/19 * t) b) there will be approximately 30.1 mg of the substance present after 9 minutes.

(a) The general formula for exponential decay is y = y0 * e^(-kt), where y is the amount at time t, y0 is the initial amount, k is the decay constant, and e is Euler's number.

To find the decay constant, we can use the fact that the half-life is 19 minutes. The formula for half-life is t1/2 = ln(2) / k, where ln(2) is the natural logarithm of 2.

Substituting t1/2 = 19 and ln(2) = 0.693 into the formula gives:

19 = 0.693 / k

k = 0.693 / 19

So the formula relating y to t is:

y = 45.1 * e^(-0.693/19 * t)

(b) To find how much will be present in 9 minutes, we can plug t = 9 into the formula we found in part (a):

y = 45.1 * e^(-0.693/19 * 9) ≈ 30.1 mg

So, there will be approximately 30.1 mg of the substance present after 9 minutes.

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[tex]\sf Length\, of\,the\,field=\boxed{\sf 104(m)}}.[/tex]

A conversion factor is just a fraction that contains an equivalence. We make the numerator be the unit we want to have as a result and the denominator is the current unit that we have.

The problem states that 0.5 cm equals 8 m, and we want to convert from cm to m, therefore, a conversion factor for this problem is:

[tex]\sf \dfrac{8(m)}{0.5(cm)}[/tex]

To use the conversion factor, just multiply each measure by the fraction:

[tex]\sf 6.5(cm) \dfrac{8(m)}{0.5(cm)}[/tex]

Here the centimeters (cm) cancel out each other and the ending answer is expressed in meters:

[tex]\sf 6.5(cm) \dfrac{8(m)}{0.5(cm)}=\boxed{\sf 104(m)}.[/tex]

For the other measure:

[tex]\sf 3.25(cm) \dfrac{8(m)}{0.5(cm)}=\boxed{\sf 52(m)}.[/tex]

So a soccer field, as you may already know, is always longer than it is wide, therefore, the greatest measure (104m) should be the length of the field.

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The Surface area of the composite figure is calculated as approximately: 234 sq. cm

The surface area of the composite figure is the area surrounding the faces of the solid as a whole. Therefore, we have:

Surface area (SA) = Surface area of the square prism + surface area of the square pyramid - 2(area of base)

Area of base = area of square = 6 * 6 = 36 sq. cm.

Surface area of the square prism = 2a² + 4ah

a = 6 cm

h = 4 cm

Plug in the values:

Surface area of the square prism = 2(6²) + 4*6*4

= 72 + 96

= 168 sq. cm.

Surface area of the square pyramid = 2bs + b²

b = side length = 6 cm

s = slant height = √(8² + 3²) = 8.5 cm

Plug in the values:

Surface area of the square pyramid = 2 * 6 * 8.5 + 6² = 138 sq. cm.

Surface area of the composite figure = 168 + 138 - 2(36) = 234 sq. cm

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Answer:

Assuming you meant to write "x^2 - 4x - 12", there are a few equivalent forms that you could use to represent this expression. One common form is:

(x - 6)(x + 2)

Step-by-step explanation:

This is the factored form of the expression, which shows that it can be written as a product of two linear factors. To see why this is true, you can use the distributive property to expand the product:

(x - 6)(x + 2) = x(x + 2) - 6(x + 2) = x^2 + 2x - 6x - 12 = x^2 - 4x - 12

Step-by-step explanation:

[tex](x + 3)(x - 2) = 2x\\ {x}^{2} + x - 6= 2x \\ {x}^{2} - x - 6 = 0 \\ (x - 3)(x + 2) = 0 \\ x = 3 \: or \: x = - 2[/tex]

The value of the variable a in the equation is 5 from the calculation here.

We need to square of a number is described as a number that when multiplied by itself give the original number.

Also, index forms are described as those mathematical forms that are used to represent numbers that are too large or small.

From the information given, we have the equation;[tex]a^2[/tex]=25

find the square root of value of 25,

We have;25 = [tex]5^2[/tex]

Substitute the value, we get;[tex]a^2[/tex] =  [tex]5^2[/tex]

Take out the similar factor, this is their exponents.

We then have;

a = 5

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Complete question;

Find the value of a in the equation;a² = 25

Answer:

angle 5 is 120 since there is Z shape with angle 3

Answer:

Simple interest= PRT/100

parameters

price =300

Rate=6%

Time=4years

300*6*4/100

7200/100

=72

Answer:

$2,631.55

Step-by-step explanation:

To find the total amount in the account after 6 years, we can use the compound interest formula.

[tex]\boxed{\sf A=P\left(1+\dfrac{r}{n}\right)^{nt}}[/tex]

where:

Given values:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=2000\left(1+\dfrac{0.046}{4}\right)^{4 \cdot 6}[/tex]

[tex]\implies \sf A=2000\left(1+0.0115\right)^{24}[/tex]

[tex]\implies \sf A=2000\left(1.0115\right)^{24}[/tex]

[tex]\implies \sf A=2000\left(1.3157739...\right)[/tex]

[tex]\implies \sf A=2631.54794...[/tex]

Therefore, the total amount after 6 years is $2,631.55 rounded to the nearest cent.

Answer:

51/4 quarters

Step-by-step explanation:

To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator for 4 and 2 is 4x2=8.

So we need to convert both fractions to have a denominator of 8:

31/4 = (31/4) x (2/2) = 62/8

41/2 = (41/2) x (4/4) = 164/8

Now we can add the fractions:

62/8 + x/4 = 164/8

Subtracting 62/8 from both sides:

x/4 = 102/8

Simplifying:

x = 51/4

Therefore, we need to add 51/4 quarters to 31/4 to get 41/2

The surface area of the rectangular prism is 210 in²

An equation is an expression that shows the relationship between numbers and variables using mathematical operators.

The surface area of a rectangular prism is the sum of each area for the surface.

Hence:

Surface area = 2(8 in * 5 in) + 2(5 in * 5 in) + 2(8 in * 5 in) = 210 in²

The surface area of the prism is 210 in²

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Answer:

x=38.6

Step-by-step explanation:

x=b/cos(alpha)

x=30/cos(39⁰)

x=38.602

Answer:

The correct answer is C, Graph D.

x^2 - 4x + 4 = (x - 2)^2.

When the product of a fraction and a factor is greater than the factor, it means that the fraction is greater than 1.

Due to the principles of multiplication, when multiplying a value greater than 1 with a given amount, the product will be larger than the original number. To provide an example, if we multiply 5 by 2, the result will be 10, which is greater than 5.

By extension, if we multiply a fraction with a factor that's greater than 1, the resulting product will be greater in size as compared to the initial quantity. For instance, when we calculate 1/2 multiplied by 3, the outcome is 3/2, which surpasses the worth of 1/2. Hence, it can be deduced that any result which exceeds its own source was obtained through multiplication by value greater than 1.

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The value of the 3 × f( - 4 ) - 3 × g( - 2 ) is 40

Given the following expression 3 × f( - 4 ) - 3 × g( - 2 ), to find the required values, we can assume that;

f( - 4 ) = 15

g( - 2 ) = 5

Substitute the given parameters into the expression to have:

3 × f(- 4 ) - 3 × g(- 2) = 3 × 15 - 3 × 5

= 45 - 5

= 40

Hence the value of the 3 × f( - 4) - 3 × g( - 2) is 40

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the solution to the original rational equation is: [tex]x = 4.678[/tex] (rounded to three decimal places)

A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. In other words, it is a number that can be written in the form of a/b, where a and b are integers and b is not equal to zero

There are two equal signs in the equation, which is incorrect. Assuming you meant to write:

[tex]2/(x-2) + 3/(x-4) = 1/(x^2 + 6x + 8)[/tex]

We can start by finding a common denominator for the left-hand side of the equation:

[tex]2/(x-2) + 3/(x-4) = 1/[(x+2)(x+4)][/tex]

Multiplying both sides of the equation by (x-2)(x-4)(x+2)(x+4), we get:

[tex]2(x-4)(x+2)(x+4) + 3(x-2)(x+2)(x+4) = (x-2)(x-4)[/tex]

Expanding and simplifying, we get:

[tex]5x^3 - 19x^2 - 39x + 56 = 0[/tex]

This polynomial equation does not factor nicely, so we can use the rational root theorem or numerical methods to find approximate solutions. Using a calculator or computer, we find that there is one real solution to the equation:

[tex]x \approx 4.678[/tex]

Therefore, the solution to the original rational equation is:

[tex]x = 4.678[/tex] (rounded to three decimal places)

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The measure of angle JKM is 26°

The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the opposite angles in the triangle.

Also the sum of angle in a triangle is 180°

Therefore ;

3x+64 = 5x+4

collecting like terms

5x -3x = 64-4

2x = 60

x = 60/2

x = 30

since x = 30

value of the exterior angle = 5x+4

= 5×30+4

= 150+4 = 154

therefore angle JKM = 180-( 154)

= 26°

Therefore the measure of angle JKM is 26°

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The amount of grams that is equivalent to 3/10 of a kg is given as follows:

300 grams.

The amount of grams that is equivalent to 3/10 of a kg is obtained applying the proportions in the context of the problem.

The amount of kg is 3/10 of a kilogram is given as follows:

3/10 = 0.3kg.

(conversion of a fraction to decimal, divide the numerator by the denominator).

Each kg is composed by 1000 grams, hence the amount of grams in 0.3 kg is given as follows:

0.3 x 1000 = 300 grams.

(proportion applied to obtain the conversion).

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In linear equation, 9 is the constant of variation k.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.

given x varies inversely with y then

xy = k ← k is the constant of variation

to find k use the condition x = - 4 when y = - 9, hence

k = -4 × -9 = 36

 x = 36/y

 when x = 4 , then  y = 36/4

                                  x = 9

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Answer:

2(4x-3)

Step-by-step explanation:

Find common numbers between 8 and 6, which is 2. 2x4= 8 2x3=6

x is only on 8 so you can't put x on the outside of the bracket. so you put it with the 4 so it comes out correct

18. C

(m / 2) - 6 = (m / 4) + 2

---Multiply everything by the LCM of the denominators

---LCM = 4

2m - 24 = m + 8

m - 24 = 8

m = 32

19. A

k / 12 = 25 / 100

---We can simplify 25/100

---We want to simplify enough to where the denominator of 25/100 is a multiple or factor of 12

k / 12 = 1 / 4

---4 x 3 = 12, 1 x 3 = 3

k = 3

20. A

9 / 5 = 3x / 100

---Cross multiply and solve algebraically

(5 * 3x) = (9 * 100)

15x = 900

x = 60

Hope this helps!

The value of side c to the nearest tenth is 4.2.

The law of cosines signifies the relation between the lengths of sides of a triangle with respect to the cosine of its angle.

It is expressed as:

c² = a² + b² - ( 2ab × cosC )

From the diagram:

a = 7

b = 8

Angle C = 32 degrees

Plug these values into the above formula and solve for c.

c² = a² + b² - ( 2ab × cosC )

c = √( a² + b² - ( 2ab × cosC ) )

c = √( 7² + 8² - ( 2 × 7 × 8 × cos32 ) )

c = √( 49 + 64 - ( 112 × cos32 ) )

c = √( 113 - 94.98 )

c = √18.02

c = 4.2

Therefore, the value of c is 4.2.

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Thus, the probability for the outcome of either purple or orange: P(purple or orange) = 57/97.

a choice that is made at random (entirely by chance, with no predictability). Every person in the population under study need to have an equal probability of getting chosen. Every person who is under investigation has an equal probability of being chosen at random for the sample.

Given bag with balls:

probability = favourable outcome / total outcome

P(purple) = 28/97

P(orange) = 29/97

Thus,

P(purple or orange) = 28/97 + 29/97

P(purple or orange) = 57/97

Thus, the probability  for the outcome of either purple or orange ball : P(purple or orange) = 57/97.

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The side that corresponds to uv is LK

The scale factor is 3 : 1

To solve for the scale factor between two geometric figures, follow these steps:

Identify corresponding sides or corresponding lengths between the two figures.

Choose one pair of corresponding sides and write a proportion using the lengths of those sides.

Solve for the scale factor by simplifying the proportion.

The shape in UV occupies the space of 6 boxes

The space in LK is made of 2 boxes

Hence we have 6 : 2

= 3 : 1

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The amount of water that the plastic container can hold is -p + 3.

To determine the amount of water that can be held, we will first assume that the container can hold x quantity of water.

So, the glass jug can hold:

p + 6 - x

2 glass jugs and 2 plastic containers can hold 6p quarts of water.

= 2(p + 6 - x) - 2x = 6p

2p + 12 - 2x -2x = 6p

2p + 12 -4x = 6p

12 - 4x = 6p - 2p

-4x = 6p -2p - 12

-4x = 4p -12

x = 4p - 12/-4

x = -p - 3

or -p + 3

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Answer:

The correct statement is "The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela".

The correct answer option is option A

How to solve ratio?

Mangos Used Smoothie Size

Angela 1 9 oz

Kim 3 27 oz

Bri 4 36 oz

Check the given options to determine which statement is correct;

The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela.

Kim = 27 : 3 = 9 : 1

Angela = 9 : 1

True

The ratio of smoothie size to mangos used for Kim is 1:9, and the ratio of smoothie size to mangos used for Bri is 4:27.

Kim = 27 : 3 = 9 : 1

Bri = 36 : 4 = 9 : 1

False

The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.

Angela = 9 : 1

Kim = 27 : 3 = 9 : 1

False

The ratio of smoothie size to mangos used for Bri is 9:1, and the ratio of smoothie size to mangos used for Angela is 4:36.

Bri = 36 : 4 = 9 : 1

Angela = 9 : 1

False

Therefore, Kim and Angela has equal ratio of smoothie size to mangoes used.

Answer:

23.375 in^2

Step-by-step explanation:

To find the area of a rectangle or square, you need to multiple the length by the width.

The length: 8.5

Width: 11

8.5*11 = 93.5

Now we divide by 4

93.5/4

23.375