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Answer:

Step-by-step explanation:

The possible values of a and the corresponding values of b are; a= -3, 2 and b= -18, 12.

Expanding the left-hand side of the equation:

(a + 3√5)² + a - b√5 = a² + 6a√5 + 45 + a - b√5

Combining like terms:

2a² + (2a - b)√5 + 45 = 51

Simplifying further:

2a² + (2a - b)√5 = 6

Now, since √5 is irrational, the only way the left-hand side can equal 6 is if both the rational and irrational parts are equal to 0. Therefore two equations:

2a² + 2a - b = 0 (Equation 1)

2a - b = 0 (Equation 2)

Solving Equation 2 for b:

b = 2a

Substituting this into Equation 1:

2a² + 2a - 2a = 0

Simplifying:

2a² = 0

Thus, a = 0 is a solution. However, a = 0 does not satisfy the original equation, since the left-hand side would be 45, which is not equal to 51. Therefore, we can divide both sides of Equation 1 by 2a to get:

a + 1 - b/2a = 0

Multiplying both sides by 2a:

2a² + 2a - b = 0

Substituting b = 2a:

2a² + 2a - 2a = 0

Simplifying:

2a² = 0

Thus, a = 0 is a solution. However, as noted above, a = 0 does not satisfy the original equation. Therefore, we must consider the case where a ≠ 0. Dividing both sides of Equation 2 by 2:

a - b/2 = 0

Solving for b:

b = 2a

Substituting into the original equation:

(a + 3√5)² + a - 2a√5 = 51

Expanding:

a² + 6a√5 + 45 + a - 2a√5 = 51

Combining like terms:

a² + 7a√5 - 6 = 0

Using the quadratic formula:

a = (-7√5 ± √(7²√5² - 4(1)(-6))) / 2(1)

Simplifying:

a = (-7√5 ± 13) / 2

Therefore, the possible values of a are -3 and 2. For each value of a, we can use b = 2a to find the corresponding value of b. Thus, the possible values of b are -18 and 12.

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Answer:

12

Step-by-step explanation:

You simply add the coefficients together.
3 + 4 + 5 = 12

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

The answer is (x + 10)

Step-by-step explanation:

(9x + 6) - (8x - 4)

9x + 6 - 8x + 4

Rearrange it

9x - 8x + 6 + 4

Combine like terms

x + 10

Thus, The answer is (x + 10)

Answer: inside width, length and heights may be smaller

Step-by-step explanation. Walls of box have certain thickness, assume 0.1 inches. Then inner measures would be 2.8 in, 4.3 in and 4.8 in. You need to reduce thickness of wall from both sides.

Answer:

(Sorry this is a late response) This fraction 6 3/5 would equal 6.6 so 6 3/5=6.6 Then you will do 6.6 times 15.38=101.508 or 101.5

Step-by-step explanation:

You would divide 3 and 5 or 5 and 3 because 3 and 5 equals the fraction 3/5. The dividend is 3 and the 5 is the divisor. The quotient of this is 0.6. So the next step would be to add the 6 from 6 3/5 so this is the whole number so add it in front of 0.6 so it would turn into 6.6. The last step is to multiply the weight of the orange by the mg of vitamin C/oz that is 15.38 so multiply 6.6 by 15.38 this would equal 101.508 so you would just round this to a better answer and that would make it 101.5. I hope this helps :0

The solution is Option A.

The coordinate of the triangle after the translation is given by A' ( 0 , -3 ) with 4 units right and 4 units down

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the coordinate of the triangle be represented as A

Now , the coordinate A = A ( -4 , 1 )

Now , the coordinate of the triangle after translation is A' ( 0 , -3 )

when there is a translation of the coordinate A by 4 units to the right , we get

A to 4 units right = A ( -4 + 4 , 1 )

The new coordinate of A = A ( 0 ,  1 )

Now , A to 4 units down , we get

The coordinate of A' = A' ( 0 , 1 - 4 )

The coordinate of A' = A' ( 0 , -3 )

Hence , the translated coordinate is A' ( 0 , -3 )

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Answer:

Step-by-step explanation:

Given:

Sale percent is:

Answer: Area = l × w

= 3.5 × 2.8

= 9.8 meters2

Step-by-step explanation:

\( \: \: \: \: \large\bf\implies \: 4.32\)

\( \longrightarrow \bf \: 1.42 - ( - 2.9) \\ \longrightarrow \bf \: 1.42 + 2.9 \\ \longrightarrow \bf \: 4.32\)

First of all we know that to do this type of question that is ↓

Answer:

24,241 people

Step-by-step explanation:

To determine the attendance at the festival in the fifth year, we need to calculate the cumulative increase in attendance over five years.

1st year: 20,000

2nd year: 20,000 * 1.05 = 21,000 (5% increase from the first year)

3rd year: 21,000 * 1.05 = 22,050 (5% increase from the second year)

4th year: 22,050 * 1.05 = 23,127.50 (5% increase from the third year)

5th year: 23,127.50 * 1.05 = 24,241.38 (5% increase from the fourth year)

So, in the fifth year the festival will be attended by approximately 24,241 people.

The inequality represented by the graph is given as follows:

y > 3x - 4.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -4, hence the intercept b is given as follows:

b = -4.

When x increases by 1, y increases by 3, hence the slope m is given as follows:

m = 3.

Hence the equation of the line is:

y = 3x - 4.

The inequality is composed by the values to the right (greater) of the line, and has an open interval due to the dashed line, hence:

y > 3x - 4.

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Answer:

X ( - 1, 1/2)

Step-by-step explanation:

4 - 2x > 3

4 - 2x < 6

Then solve the inquality for x

X< 1/2

X > - 1

Then u get the answer x ( - 1, 1/2)

Note: [ 1/2 is 1 over 2]

Step-by-step explanation:

3<4-2x 4-2x<6

-1<-2x -2x<2

1/2>x x>-1

x<1/2

the graph shown in pic

The most likely be included in the magazine article that follows this introduction is A. examples of radio programs

A radio program, radio programme, or radio show is a piece of content designed for radio broadcast. It could be a one-time production or part of a recurring series.

Headphones are ubiquitous! People are trapped in their downloaded music worlds, relying on their personal music libraries for entertainment. They are thus ignoring a diverse world of radio offerings that could enrich and entertain them. Local radio stations broadcast music and news, whereas National Public Radio (NPR) broadcasts debate and entertainment for people of all ages.

Based on the information given, it should be noted that after the introduction, the next thing is to simply give the examples of the radio shows. This is important in order to buttress the introduction.

In conclusion, based on the information, the correct option is A.

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Answer:

Step-by-step explanation:

a  i was told by my teacher

The percentage of drivers who are at least 45 is 62%

From the question, we have the following parameters that can be used in our computation:

The table of values

From the table, we have

Age 45 = 62 percentile

When represented properly

So, we have

Age 45 = 62%

This means that the percentage of drivers who are at least 45 is 62%

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The amount of water the farmer can put in the tank increase when the larger tank is built is 106.33%.It takes 4days for the horses to drink all the water in the larger tank.

Percentage is a way of expressing a proportion or a fraction out of 100. It represents the number of parts per hundred of a quantity.

Dimension refers to a measurable aspect of an object or a system, such as length, width, height, depth, volume, area, or mass. In mathematics, dimension also refers to the number of coordinates required to specify a point in a space. For example, a two-dimensional shape like a square has two dimensions, length and width, while a three-dimensional object like a cube has three dimensions, length, width, and height.

To find the percentage increase in the amount of water the farmer can put in the larger tank, we need to calculate the volume of the original tank and the volume of the larger tank, and then compare the two.

The original tank has dimensions of 2 4/5 ft, 2 2/5 ft, and 2 1/2 ft. We can convert these mixed numbers to improper fractions for easier calculations:

2 4/5 ft = (2 x 5 + 4)/5 ft = 14/5 ft

2 2/5 ft = (2 x 5 + 2)/5 ft = 12/5 ft

2 1/2 ft = (2 x 2 + 1)/2 ft = 5/2 ft

The volume of the original tank is then:

Volume = Length x Width x Height = 14/5 ft x 12/5 ft x 5/2 ft

Now, the farmer plans to increase measurement  by 25%. To do this, we multiply each measurement by 1.25.

The dimensions of the larger tank would be:

Length = 14/5 ft x 1.25 = 3.5 ft

Width = 12/5 ft x 1.25 = 3 ft

Height = 5/2 ft x 1.25 = 3.125 ft

The volume of the larger tank is then:

Volume = Length x Width x Height = 3.5 ft x 3 ft x 3.125 ft

To find the percentage increase, we can compare the two volumes:

Percentage increase = ((Volume of larger tank - Volume of original tank) / Volume of original tank) x 100

Plugging in the values we found:

Percentage increase = ((3.5 ft x 3 ft x 3.125 ft - 14/5 ft x 12/5 ft x 5/2 ft) / (14/5 ft x 12/5 ft x 5/2 ft)) x 100

After calculating the above expression, we find that the percentage increase is approximately 106.33%. So, the amount of water the farmer can put in the larger tank will increase by approximately 106.33% when the larger tank is built.

Now, to find how many days it will take the horses to drink all the water in the larger tank, we can assume that the rate at which the horses drink water remains constant. Since the volume of the larger tank is approximately 106.33% more than the original tank, it will take the horses approximately the same amount of time to drink all the water in the larger tank, which is 4 days.

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The food will last for 48 meals.

\(\frac{36}{\frac{3}{4} }\)

\(36*\frac{4}{3} =\\ \\\frac{36*4}{3}= \\\\48\)

The food will last for 48 meals.

Answer:

A

Step-by-step explanation:

because

Answer: One factor is positive and one is negative, so the product will be negative.

Answer:

One factor is positive and one factor is negative, so the product will be negative

Step-by-step explanation:

If you see there (-15)3 so -15 is a negative number and 3 is a positive and when you multiple a negative number with a positive number it becomes negative.

There will be 90 grams of the element remaining after the 5.3 minute

From the question, we have the following parameters that can be used in our computation:

Mass of element = 430 grams

Rate of decay = 25.4% per minute

The above implies that the decay follows an exponential path

An exponential function that represents a decay function is represented as

A(n) = a * (1 -r)ⁿ

Where

A(n) = remaining amount at the nth minute

a = Initial amount = 430

r = rate of decay = 25.4%

So, we have

A(n) = 430 * (1 -25.4%)ⁿ

Evaluate the difference

A(n) = 430 * (0.746)ⁿ

When there are 90 grams, we have

430 * (0.746)ⁿ = 90

This gives

(0.746)ⁿ = 0.21

So, we have

n = log(0.21)/log(0.746)

Evaluate

n = 5.3

Hence, the number of minutes is 5.3

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The complete  table will be:

Fraction      Decimal       Percent

39/100            0.39           39%

82/100            0.82           82%

22/100           0.22          22%

3/4                   0.75          75%

80/100           0.8             80%

The percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the following example:

\(\frac{25}{100} =0.25*100=25%\)

The percentage is considered a math tool with several applications and areas, for example: medicine, engineering, investments, supermarkets, drugstores,banks  etc.

Fraction      Decimal       Percent

39/100            0.39           0.39*100=39%

Fraction      Decimal       Percent

82/100            0.82         0.82*100=82%

Fraction      Decimal       Percent

22/100           0.22        22%

Fraction      Decimal       Percent

3/4                 0.75        0.75*100=75%

Fraction      Decimal       Percent

80/100           0.8         0.80*100=80%

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Answer:

133 m^2

Step-by-step explanation:

to find are of a circle it’s r^2 times pi

6^2 x pi

36 pi

113 m^2

Hopes this helps please mark brainliest

Answer:

Answer C is correct

Step-by-step explanation:

The formula to find the area of a circle is:

A = πr²

Here,

r => radius = 6m

Let us find the area of the circle.

A = πr²

A = 3.14 × 6 × 6

A = 113.04 m²

Approx. = 113m²

The probability that all 4 computers with the critical file fail in this incident

P(x=4)=0.00085

This is further explained below.

Generally,  is  mathematically given as

\($H \rightarrow(n, m)$\)

p.d.F. of Hyper Geometric distribution

given, $N=39, n=4, M=8, x=4$

\(\begin{aligned}P(x=4) &=\frac{8}{4} \frac{39}{39} \\&=\frac{70 \times 1}{82251}\end{aligned}$$\)

\(\begin{aligned}&P(x=4)=8.5106 \times 10^{-4} \\&P(x=4)=0.00085\end{aligned}\)

In conclusion, P(x=4)=0.00085

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Answer:

156.6

Step-by-step explanation:

Sorry for the messy handwriting.

Hope this helps!

Answer:

0.6

Step-by-step explanation:

Answer:

\(m=-2\)

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Simply plug in the 2 coordinates into the slope formula to find slope m:

\(m=\frac{-1-3}{-1-(-3)}\)

\(m=\frac{-4}{-1+3}\)

\(m=\frac{-4}{2}\)

\(m=-2\)

Answer:

hope it helps you..........

Answer:

60

Step-by-step explanation:

g(x)= x^2 +8x - 24

Substitute x for 6 in the equation

g(6)= 6^2 + 8(6) - 24

= 36+48-24

= 60

The required reverse Euclidean algorithm is the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

Given that (5*x) mod 91 =32.

To solve the modular equation (5*x) mod 91 =32 using reverse Euclidean algorithm is to find the modular inverse of 5 modulo 91.

Consider  (5*x) mod 91 =32.

5x = 32(mod 91)

Apply the Euclidean algorithm to find GCD of 5 and 91 is

91 = 18 * 5 + 1.

Rewrite it in congruence form,

1 = 91 - 18 *5

On simplifying the equation,

1 = 91 (mod 5)

The modular inverse of 5 modulo 91 is 18.

Multiply equation by 18 on both sides,

90x = 576 (mod91)

To obtain the smallest positive  solution,

91:576 = 6 (mod 91)

Divide both sides by the coefficient of x:

x = 6 * 90^(-1).

Apply the Euclidean algorithm,

91 = 1*90 + 1.

Simplify the equation,

1 + 1 mod (90)

The modular inverse of 90 modulo 91 is 1.

Substitute the modular inverse in the given question gives,

x = 6*1(mod 91)

x= 6 (mod91)

Therefore, the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

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Answer: 34,650 permutations