Find w=a+bi=, where a and b are real numbers
√-8+6i

The solutions to the equations are:

x = 6, x = 4, x = 7.

1. 8x² + 11 = 191 + 3x²

Rearranging the equation:

8x² - 3x² = 191 - 11

5x² = 180

Dividing both sides by 5:

x² = 36

Taking the square root of both sides:

x = ±6

Checking the solution:

8(6)² + 11 = 191 + 3(6)²

288 + 11 = 191 + 108

299 = 299

The solution x = 6 satisfies the equation.

2. 7x² - 15 = 49 + 3x²

Rearranging the equation:

7x² - 3x² = 49 + 15

4x = 64

Dividing both sides by 4:

x² = 16

Taking the square root of both sides:

x = ±4

Checking the solution:

7(4)² - 15 = 49 + 3(4)²

112 - 15 = 49 + 48

97 = 97

The solution x = 4 satisfies the equation.

3. 14x² - 157 = 333 + 4x²

Rearranging the equation:

14x² - 4x^2 = 333 + 157

10x² = 490

Dividing both sides by 10:

x² = 49

Taking the square root of both sides:

x = ±7

Checking the solution:

14(7)² - 157 = 333 + 4(7)²

686 - 157 = 333 + 196

529 = 529

The solution x = 7 satisfies the equation.

Therefore, the solutions to the equations are:

x = 6, x = 4, x = 7.

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The solution to the inequality 2x + 7 > 27 is x > 10

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

2x + 7 > 27

Subtract 7 from both sides of the inequality

So, we have

2x > 20

Divide both sides by 2

x > 10

Hence, the solution to the inequality 2x + 7 > 27 is x > 10

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An example of an extension of a function f is adding additional input-output pairs beyond the original domain and range of f.

The extension of a function f means new function that preserves the properties and behavior of the original function on its domain while adding new values or expanding its domain.

For example, we will consider the function f(x) = x^2 defined on the interval [0, 1]. An extension of this function could be g(x) = x^2 for x in [0, 1] and g(x) = 0 for x outside [0, 1].

This extension maintains the quadratic behavior of f on [0, 1] while assigning a constant value of 0 to points outside that interval.

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The solution to the equation 3x = 8 - 2x is x = 1.6.

To solve the equation 3x = 8 - 2x by graphing, we can plot the two sides of the equation as functions of x and find the point(s) where they intersect. Here's a step-by-step explanation:

Express the equation in the form of y = f(x). Rearrange the equation:

3x + 2x = 8

5x = 8

x = 8/5 or 1.6

Graph the functions y = 3x and y = 8 - 2x on the same coordinate plane. The line represented by y = 3x is upward sloping, and the line represented by y = 8 - 2x is downward sloping.

Plot the points (1.6, 3(1.6)) and (1.6, 8 - 2(1.6)) on the graph.

The point of intersection represents the solution to the equation. In this case, the lines intersect at (1.6, 4.8).

Therefore, the solution to the equation 3x = 8 - 2x is x = 1.6.

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There were 600 downloads of the standard version.

An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign.

Let x represents the number of downloads of the standard version.

Given:

Size of the standard version = 2.4 MB

Size of the high-quality version = 4.2 MB

Total download size = 4716 MB

Total downloads = 1380

We will set up the following equation:

2.4x + 4.2(1380 - x) = 4716

2.4x + 5796 - 4.2x = 4716

-1.8x + 5796 = 4716

-1.8x  = 4716 - 5796

-1.8x = -1080

x = 600

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The instantaneous rate of change of y = √x at x = 2 is √2 / 2.

To find the instantaneous rate of change of y = √x at x = 2, we need to calculate the derivative of the function with respect to x and evaluate it at x = 2.

Taking the derivative of y = √x using the power rule for differentiation, we have:

dy/dx = (1/2) × x^(-1/2)

Now, substituting x = 2 into the derivative expression:

dy/dx = (1/2) × 2^(-1/2)

= (1/2) × √2

= √2 / 2

Therefore, the instantaneous rate of change of y = √x at x = 2 is √2 / 2.

None of the provided options (-1/2, -1/4, -1) are the correct instantaneous rate of change at x = 2.

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The solution of the given equation is x = -10.

We are given that;

The equation 1/27^{4-x}=9^{2x-1}

Now,

This is an exponential equation that can be solved by using the properties of exponents and logarithms. Here are the steps to solve it:

Rewrite both sides of the equation using the same base. Since 27 and 9 are both powers of 3, we can use 3 as the base. We have:

(3(-3))(4-x) = (32)(2x-1)

Apply the power rule of exponents to simplify the expressions. The power rule states that (ab)c = a^(bc). We have:

3^(-12+3x) = 3^(4x-2)

Since the bases are equal, we can set the exponents equal to each other and solve for x. We have:

-12 + 3x = 4x - 2 -10 = x

Therefore, by the given equation the answer will be x = -10.

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Dependent variable: Total cost of riding the trolley

Independent variable: Number of times Henry rides the trolley.

In this scenario, the dependent variable is the total cost of riding the trolley, and the independent variable is the number of times Henry rides the trolley.

The dependent variable, the total cost of riding the trolley, depends on the independent variable, which is the number of times Henry rides the trolley. As Henry rides the trolley multiple times, the total cost will vary based on the number of rides.

The independent variable, the number of times he rides, determines the value of the dependent variable, the total cost.

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Answer:

1.58 ish

Step-by-step explanation:

For a logx y = z, x^z = y
So here, log4 9= 1.58 or so
1.5849625007

Answer:

5(5y - 3z)

Step-by-step explanation:

25y - 15z ← factor out common factor of 5 from each term

= 5(5y - 3z)

The sum total by the given data is equals to $658,880.

We are given that;

Percent=15%

Amount= $98,880

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

To divide by a percentage, we can convert it to a decimal by moving the decimal point two places to the left. This gives us:

15% = 0.15

To divide by 0.15, we can multiply by its reciprocal, which is 1/0.15. This gives us:

$98,880 / 0.15 = $98,880 x 1/0.15

To multiply by 100, we can move the decimal point two places to the right. This gives us:

$98,880 x 1/0.15 x 100 = $658,880

Therefore, by the percentage the answer will be $658,880.

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Answer:

1,000 grams

noun. a unit of mass equal to 1,000 grams: the basic unit of mass in the International System of Units (SI). Up until 2019 the kilogram was defined as equal to the mass of an international prototype, a platinum-iridium cylinder kept in Sèvres, France.

Among the mean, mode, and median, the unique one is the b. mode.

The mode is the data value that occurs many times more than other data values.

Unlike the mean that shows the average value of all the data values, the mode occurs more.  While we compute the mean by dividing the total data value by the number of data items, the mode is not computed but found as the most frequent data value.

Similarly, the median can be computed when two values occur as the middle values.

Thus, among the three measures of central tendency, the mean, the median, and the mode, the mode is the most unique since it is not computed.

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The amount of debt per person in the small country is approximately $2,439. This means that, on average, each person in the country would be responsible for around $2,439 of the national debt.

To calculate the amount of debt per person in the small country, we divide the total national debt by the population and round the result to the nearest whole number. Let's perform the calculation.

The population of the small country is 2.457 million, which is equivalent to 2,457,000 people. The national debt is $5.99 billion.

To find the debt per person, we divide the national debt by the population:

$5.99 billion / 2,457,000 = $2,439.05 (rounded to two decimal places)

Since we want the answer in whole numbers, we round the result to the nearest whole number:

Debt per person = $2,439 (rounded to the nearest whole number)

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An equation to represent this situation is y = 60x

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, we can logically deduce that the cheetah was clocked running 60 miles per hour over a 50-yard distance. This ultimately implies that, an equation that models this situation is given by:

y = 60x

Where:

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Answer:$0.25

Step-by-step explanation:

To find the expected value of playing the game, we need to multiply the payoff for each possible outcome by its probability and then add up all the values.

Let's first find the probabilities of each outcome:

- Probability of spinning1:1/6

- Probability of spinning2:1/6

- Probability of spinning3:1/6

- Probability of spinning4:1/6

- Probability of spinning5 or6:2/6( or1/3)

Now let's calculate the expected value:

Expected value=(1/6*$1)+(1/6*$3)+(1/6*$5)+(1/6*$7)+(1/3*-$1.25)

Expected value=$0.25

So the expected value of playing the game is$0.25 per spin.

In the long run, Scott can expect to gain money since the expected value is positive. However, this doesn't guarantee that he will actually win money every time he plays the game, as there is still a certain degree of randomness involved in each spin.

The frequency distribution table would be:

Class ______ Freq ___ Midpoint __R/Freq__ C/Freq

0 - 9 _______ 4 ______ 4.5 ______ 0.2 _____ 4

10-19 _______ 5 ______ 14.5 _____0.25 _____9

20-29 ______ 4 ______ 24.5_____ 0.2______ 13

30-39_______3 ______ 34.5 _____0.15______ 16

40-49_______4 ______ 44.5 _____ 0.2 _____ 20

The data ranges from 0 - 49 . we had to use a class interval of 10 since we were interested in having just 5 classes.

The midpoint is the average value of the upper and lower class.

Relative frequency is the ratio of the class frequency to the total number of data in the distribution.

Cumulative Frequency is the running sum of frequencies in the distribution table.

Therefore, the frequency distribution captures all the information required.

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The simplified form of the rational expression is 1/(2[tex]x^5[/tex]).

To simplify the rational expression (7x)/(14[tex]x^6[/tex]), we can reduce the numerator and denominator by their greatest common factor.

In this case, the greatest common factor is 7x.

Dividing both the numerator and denominator by 7x, we get:

(7x)/(14[tex]x^6[/tex]) = (7x)/(7x × 2[tex]x^5[/tex])

Canceling out the common factor of 7x, we have:

= 1/(2[tex]x^5[/tex])

Therefore, the simplified form of the rational expression is 1/(2[tex]x^5[/tex]).

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Answer:

An improper fraction for 1 3/4 is 7/4.

Step-by-step explanation:

[tex]\frac{7}{4}[/tex]

To find the improper fraction of a mixed number fraction. You first have to remove the whole number from the fraction (the big one bending the fraction)

Do this by multiplying the denominator (4) by the whole number (1)

4 x 1 = 4

Then add this number with the numerator (top number) which is 3.

4+3 = 7

Seven is our new numerator, our denominator stays the same (4)

So our new improper fraction is:

[tex]\frac{7}{4}[/tex]

Answer:

The approximate user base of the social media site 10 months from now would be approximately 52,374.

Step-by-step explanation:

To calculate the approximate user base of the social media site 10 months from now, considering a 4% increase per month, we can use the following steps:

1. Calculate the monthly growth factor: 1 + (4% / 100) = 1 + 0.04 = 1.04

2. Apply the growth factor to the current user base for each month:

  Month 1: 35,930 * 1.04 = 37,387.2 (approx.)

  Month 2: 37,387.2 * 1.04 = 38,868.49 (approx.)

  ...

  Month 10: Previous Month * 1.04

By repeating this calculation for each month, we can determine the approximate user base 10 months from now.

Month 1: 37,387.2

Month 2: 38,868.49

Month 3: 40,391.33

Month 4: 41,957.61

Month 5: 43,569.34

Month 6: 45,228.24

Month 7: 46,936.32

Month 8: 48,695.44

Month 9: 50,507.45

Month 10: 52,374.40 (approx.)

Therefore, the approximate user base of the social media site 10 months from now would be approximately 52,374.

Answer:

Step-by-step explanation:

You have to use the quadratic formula

x = -b +/- [tex]\sqrt{(b^{2} -4ac)/2a[/tex]

and then you can simplify both answers so the first one would be -13/2 and the second would be -27/2

you usually have to reject an answer but since there is no equal sign in the question, you should be fine

For an item with a marked price of Rs. 26,600 and a 10% discount, the discount price is Rs. 2,660. Therefore, the customer will pay Rs. 23,940 after applying the discount.

To calculate the amount of discount on an item with a marked price of Rs. 26,600 and a discount percentage of 10%, we can follow a simple formula.

First, let's calculate the discount amount. The discount percentage is 10%, which means we can find the discount amount by multiplying the marked price by the discount percentage:

Discount amount = Marked price × Discount percentage

= Rs. 26,600 × 10/100

= Rs. 2,660

So, the discount amount for the item is Rs. 2,660.

Now, let's understand what this means. A discount is a reduction in the original price of an item. In this case, the discount amount of Rs. 2,660 is the amount by which the price of the item is reduced. Therefore, after applying the discount, the customer would only need to pay Rs. 26,600 - Rs. 2,660 = Rs. 23,940.

It's important to note that the discount amount is not the final price the customer pays. The final price is the marked price minus the discount amount. So, in this scenario, the customer will receive a discount of Rs. 2,660, and they will pay Rs. 23,940 for the item.

Understanding how discounts work can be helpful when making purchasing decisions or comparing prices. It allows customers to evaluate the value they are receiving and make informed choices based on their budget and preferences.

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Probable question:

What is the amount of the discount if the marked price of an item is Rs. 26,600 and the discount percentage is 10%?

In a case whereby Darren says that more students hands are 4 2/4 inches longer than 4 and 5 1/4 inches combined, he is wrong

[tex]4\frac{2}{4}[/tex] that was given in the question can be seen as mixed fraction, we can expressed this as improper fraction so that it will be easier to handle.

[tex]4\frac{2}{4} = \frac{16+4}{2}[/tex]

=[tex]\frac{18}{4}[/tex]

Then [tex]4 + 5\frac{1}{4} = \frac{16}{4} +\frac{20+1}{4} \\\\=\frac{37}{4}[/tex]

Then after expressing the given fractions as improper fraction we can now compare them so that e will know may be Darren is right or wrong, then here we can see that [tex]\frac{18}{4}[/tex] is less than [tex]\frac{37}{4}[/tex] Hence, Darren is wrong.

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The roots of the function F(x) = x³ + 2x² + 4x + 8 are given as follows:

B. 1 real root and 2 complex roots.

The function in this problem is defined as follows:

F(x) = x³ + 2x² + 4x + 8.

The function is of the third degree, hence the total number of zeros of the function is of 3.

From the graph, the function has only one x-intercept, which is given as follows:

x = -2.

Hence the two remaining roots are the complex roots, meaning that option B is the correct option for this problem.

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a. It will take 7 months to pay off the credit card.

b. it will take 4 months to pay off the credit card.

Since, APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance.

We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

n = log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

n = 6.18

Therefore, it will take 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

n = log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

n = 3.43

Therefore, it will take 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

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