Find the value of the 100th and 1000th term in the sequence { 3,-5,7,-9,...}

Answer:

[tex]\\ 6x^{\frac{3}{4}} = 6\sqrt[4]{x^{3}}[/tex]

Step-by-step explanation:

When a number is raised to a rational number like [tex]\\ {\frac{3}{4}}[/tex], that is, a fraction, the denominator represents the index of the radical (or commonly known as the root nth of the radical), and the numerator represents the number to which the radicand (the part of the expression inside the radical sign) is about to be raised.

Looking at [tex]\\ 6x^{\frac{3}{4}}[/tex], the index (root) of the radical is 4 and the numerator raises the value of x to the third power, that is,  [tex]\\ x^{3}[/tex]. That explains the answer: six (6) times [tex]\\ \sqrt[4]{x^{3}}[/tex]. The six (6) only multiplies the expression.

Likewise, a radical of index 5, with a radicand [tex]\\ (x + 8)[/tex] raised to the ninth power is represented by  [tex]\\ \sqrt[5]{(x + 8)^{9}}[/tex], which is equivalent to [tex]\\ (x+8)^{\frac{9}{5}}[/tex].

By the way, a particular case is when the index is 2, that is, [tex]\\ x^{\frac{1}{2}}[/tex]. Here, the number 2 is omitted from the radical symbol and is represented by [tex]\sqrt{x}[/tex].

Using the knowledge of fractions, the number of 1/6-pound servings in 2 pounds of fudge is: 12.

Fractions are numbers that represent part of a whole number. They have a denominator and a numerator.

The fraction of a pounds servings is given as 1/6.

Therefore, number of 1/6 pound servings in 2 pounds of fudge would be:

2 ÷ 1/6 = 2 × 6/1 = 12.

Learn more about fractions on:

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1/10.

Hope this helps!

Paul will pay approximately $529.47 each month for his new car.

To calculate how much Paul will pay each month for his new car, we need to divide the total car loan amount by the number of monthly payments. In this case, the car loan is $19,061 and the number of payments is 36. So, the monthly payment can be calculated as:

Monthly payment = Car loan amount / Number of payments

Substituting the given values, we get:

Monthly payment = $19,061 / 36

Running this calculation, we find that Paul will pay approximately $529.47 each month for his new car, rounded to the nearest cent.

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To find the distance from the wall to the base of the ladder, use the Pythagorean theorem. The distance is 6 feet.

To find the distance from the wall to the base of the ladder, we can use the Pythagorean theorem. The ladder, the ground, and the wall form a right triangle. Let's call the distance from the wall to the base of the ladder x. According to the Pythagorean theorem, the square of the ladder's length (10 feet) is equal to the sum of the squares of the distances from the base of the ladder to the wall (x) and the height of the window (8 feet).

x^2 + 8^2 = 10^2

Simplifying the equation, we get:

x^2 + 64 = 100

Subtracting 64 from both sides:

x^2 = 36

Taking the square root of both sides:

x = 6

Therefore, the distance from the wall to the base of the ladder is 6 feet.

The maximum amount of hours the DJ will play at the dance is 4 hours.

To find the maximum amount of hours the DJ will play at the dance, we need to set up an inequality. Let x represent the number of hours the DJ will play. The total cost is given by $125 per hour plus $55 for an assistant, so the cost function is C(x) = 125x + 55. We want the total cost to be less than or equal to $555, so the inequality is 125x + 55 ≤ 555.

To solve this inequality, we need to isolate x. First, subtract 55 from both sides to get 125x ≤ 500. Then, divide both sides by 125 to get x ≤ 4. Therefore, the maximum amount of hours the DJ will play at the dance is 4 hours.

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Answer:

The domain and range values are a) -3.8 b) -2.6 C) 1.7 D) 4.4 E) 1.0

Step-by-step explanation:

Consider the provided table:

The domain of the function becomes the range of the inverse function and the range of the function becomes the domain of the inverse function.

Now consider Figure 1:

The x value of table 1 becomes the y value of table 2 and the y value of table 1 becomes the x value of table 2.

Therefore, the domain and range values are a) -3.8 b) -2.6 C) 1.7 D) 4.4 E) 1.0

Answer:

This was a little confusing. I had trouble getting the right answer, but it is all there. It was (a+3) *(b+2) for me.

Thanks BenjaminG123