For the following geometric sequence, find the recursive formula.
{-80, 20, -5, ...}

f(x) = 7x-5

 find f(-10)

 replace x with -10

 so you have 7(-10)-5

7*-10=-70 - 5 = -75

 so f(-10) = -75

f(x) = 7x-5

find f(-10)

replace x with -10

so you have 7(-10)-5

7*-10=-70 - 5 = -75

so f(-10) = -75

The set of complex numbers is indeed closed under subtraction because the subtraction of any two complex numbers always results in another complex number.

The set of complex numbers being closed under subtraction is indeed true. In mathematics, a set is said to be closed under a particular operation if performing that operation on members within the set always results in a member that is also within that set.

In the case of complex numbers, if we subtract one complex number from another, the result is a complex number. For example, if we have two complex numbers, (a + bi) and (c + di), and we subtract the latter from the former, the result will be a complex number (a - c) + (b - d)i.

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Final answer:

The framer can make at most 4 complete picture frames from the usable length of the board, after deducting the scratched section, and each frame using 1 2/3 feet of the board.

Explanation:

The picture framer has a board that is 10 1/12 feet long. However, part of this board is unusable due to scratches, and that section is 2 3/8 feet. Therefore, the usable length of the board is 10 1/12 feet - 2 3/8 feet. Each picture frame requires 1 2/3 feet of this board. To find out how many complete picture frames can be made, we need to divide the usable length of the board by the length required for each frame.

First, convert the mixed numbers to improper fractions:

Total length of the board: 121/12 feet

Scratched section: 19/8 feet

Frame length: 5/3 feet

After subtracting the scratched section from the total length, we have:

(121/12) - (19/8) = (968/96) - (228/96) = 740/96 feet

Now we divide the usable length by the frame length:

(740/96 feet) / (5/3 feet) = (740/96) * (3/5) = 740/160 = 4.625

Since we cannot have a partial frame, the framer can make at most 4 complete picture frames.

By substituting '12' into the given linear equation 'y = 10x - 18', we find that figure 12 in this tile pattern would be 102.

The given pattern follows the linear equation y = 10x - 18. To find the value of figure 12, smaller 'x' with '12' in the equation: y = 10 * 12 - 18 = 102. Therefore, figure 12 in this tile pattern would be 102.

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The correct equation for the given scenario is 38m + 150 = 3,000. Solving this equation, we find that it will take Paula approximately 75 minutes to finish her essay.

The question involves calculating how much time Paula needs to complete her essay based on her typing speed and desired essay length. Paula needs to write 3,000 words, but she already has 150 written. Therefore, she needs to write 3,000 - 150 = 2,850 more words. If she types at a rate of 38 words per minute, the number of minutes, represented as m, can be found using the equation 38m = 2,850. Therefore, the correct equation from the options is 38m + 150 = 3,000. Solving this equation for m gives m = 2,850 / 38 ≈ 75 minutes. Thus, option c) 38m + 150 = 3,000; m = 75 minutes is the correct answer.

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Answer:

6 People in a round table can be seated in (6 - 1) ! ways = 120. Now we need to subtract the number of cases when one of those is sitting next to 2 of the other 5. We can consider as if 5 people are sitting in a row because it is round table.

Answer:

[tex]g = \frac{48}{4}[/tex]

Step-by-step explanation:

[tex]Average = \frac{\text{Sum of all observations}}{\text{No. of observations}}[/tex]

[tex]Average = \frac{\text{Total score}}{\text{Total no. of games}}[/tex]

Since we are given that Dylan scored a total of 48 points in first 4 games of the basketball season.

So,[tex]Average = \frac{48}{4}[/tex]

Let the average be g

So, [tex]g = \frac{48}{4}[/tex]

Hence The equation can be used to find g, the average number of points he scores per game is [tex]g = \frac{48}{4}[/tex]

So we know that the three boys are friends – Sam, Ryan and Daniel.

We also know that Daniel is Ryan’s brother and Ryan is Sam’s brother.

But the question here is why does Sam is not Daniel’s brother.

Because the answer here is Sam is a girl which makes her a sister of Daniel, not a brother.

Answer:

Average change per day since then = $0.72

Step-by-step explanation:

Stock listing for Enam Telecom is given as

52 wk high    52 wk low   Symbol       Div.      Close      Net change

  122.866          64.77          ENM        3.45       99.14          4.74          

The lowest price $64.77 occurred 48 days ago.

Today's close for the stock was $99.14.

Now we have been asked to tell the approximate average change per day since then.

Therefore Average change per day = (closing value for today - closing value 48 days ago) ÷ (number of days)

Since closing value 48 days ago = 52 week low = $64.77

Now average change = [tex]\frac{(99.14-64.77)}{48}=0.72[/tex]

Therefore answer is $0.72 is the average change per day.

The approximate average change per day since the lowest price occurred is approximately $0.72, option B is correct.

To find the approximate average change per day since the lowest price occurred 48 days ago, we need to calculate the total change and divide it by the number of days.

The lowest price in the past year was 64.77, and the current price is 99.14.

The change in price is the difference between these two values:

Change = 99.14 - 64.77

= 34.37

Now, we divide the total change by the number of days:

Average Change per Day = Change / Number of Days

Average Change per Day = 34.37 / 48

Average Change per Day = 0.716

Hence, the approximate average change per day since the lowest price occurred is approximately $0.72.

Therefore, the correct option is b. $0.72.

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To graph the parabola [tex]f(x) = -1/3x^2 + 4/3x - 16/3[/tex], plot the vertex at (2, -4), note the axis of symmetry at x = 2, and create a downward-opening parabolic shape on a coordinate plane.

To graph the parabola given by the function [tex]f(x) = -1/3x^2 + 4/3x - 16/3[/tex], follow these steps:

1. Identify the vertex: The vertex of a parabola in the form of [tex]y = ax^2 + bx + c[/tex] is given by (-b/2a, f(-b/2a)). In this case, a = -1/3 and b = 4/3. Calculate the x-coordinate of the vertex using -b/2a:

  x-coordinate of the vertex = -b / (2a) = -(4/3) / (2 * (-1/3)) = 2.

  Now, find the corresponding y-coordinate by plugging the x-coordinate back into the function:

[tex]f(2) = (-1/3)(2)^2 + (4/3)(2) - 16/3 = (-4/3) + (8/3) - 16/3 = -12/3 = -4.[/tex]

  So, the vertex is at (2, -4).

2. Find the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex. In this case, it's the vertical line x = 2.

3. Calculate additional points: To create a more accurate graph, you can choose additional x-values and calculate their corresponding y-values. For instance, you can select x-values to the left and right of the vertex.

  - For x = 0:

    [tex]f(0) = (-1/3)(0)^2 + (4/3)(0) - 16/3 = -16/3.[/tex]

  - For x = 4:

    [tex]f(4) = (-1/3)(4)^2 + (4/3)(4) - 16/3 = -64/3 + 16/3 - 16/3 = -64/3.[/tex]

4. Plot the points: Plot the vertex (2, -4) and the additional points you calculated on a coordinate plane.

5. Draw the parabola: Connect the points smoothly to form the parabolic shape. Since the leading coefficient (-1/3) is negative, the parabola opens downward.

6. Label the axis of symmetry: Label the vertical line x = 2 as the axis of symmetry.

Your graph of the parabola f(x) = -1/3x^2 + 4/3x - 16/3 should resemble a downward-opening parabola with the vertex at (2, -4) and the axis of symmetry at x = 2.

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The given expressions need to be solved.

[tex]b[/tex] will include all numbers less than but not equal to [tex]0[/tex].

[tex]b[/tex] will include greater than but not equal to [tex]2[/tex].

The given expression is

[tex]6b-1<-7\\\Rightarrow 6b<-7+1\\\Rightarrow 6b<-6\\\Rightarrow b<-1[/tex]

So, [tex]b[/tex] will include all numbers less than but not equal to [tex]-1[/tex].

[tex]2b+1>5\\\Rightarrow 2b>5-1\\\Rightarrow 2b>4\\\Rightarrow b>\dfrac{4}{2}\\\Rightarrow b>2[/tex]

[tex]b[/tex] will include all numbers greater than but not equal to [tex]2[/tex]

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Final answer:

To simplify an expression involving division of exponential terms with the same base, subtract the exponents of those terms. Numerical coefficients are divided normally while applying the subtraction rule to the exponents.

Explanation:

When simplifying the expression that involves division of exponentials, the correct action is to subtract the exponents. This rule applies when the bases of the exponential terms are the same. For example, when dividing [tex]a^m[/tex] by [tex]a^n[/tex], you would calculate a^(m-n). If we have numerical coefficients in front of the terms, we divide those normally, then apply the rule for exponents. An example is 4.5 × [tex]10^9[/tex] / [tex]10^6[/tex] = 4.5 × [tex]10^(9-6)[/tex] = 4.5 × [tex]10^3[/tex].

Answer:

1/5

Step-by-step explanation:

5y = x - 3

To find the slope of a line, we need to get the equation in the form y= mx+b where m is the slope and b is the y intercept

5y = x - 3

Divide each side by 5

5y/5   = x/5 - 3/5

y = 1/5 x - 3/5

The slope is 1/5 and the y intercept is -3/5

Answer:

1/5

Step-by-step explanation: