6, 11, 16, 21, ________, ________, _______, Write the next 3 terms below

The value of R(x) term is 36.

We are given that;

The equation x³ + 2x² - 72x - 28

Now,

We divide the first term, 8x, by the first term of d(x), which is x. This gives us 8, which is the third term of Q(x). We write 8 above the division bar and multiply it by d(x), which gives us 8x - 64. We subtract this from the new dividend, which gives us 36.

Since we cannot divide 36 by x-8 any further, we stop here and write 36 as the remainder R(x).

   x² + 10x + 8

  _______________

x-8 | x³ + 2x² - 72x - 28

    - (x³ - 8x²)

    -------------

        10x² - 72x

      - (10x² -80x)

      -------------

             8x -28

           - (8x -64)

           ----------

                36

Q(x) = x² + 10x + 8 and R(x) = 36.

Therefore, by the equation the answer will be R(x) = 36.

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Therefore, there are 4,084,710,000 distinct strings of 20-decimal digits with the given conditions.

To determine the number of strings of 20-decimal digits with the given conditions, we will use the concept of permutations. Here's the explanation:
There are 20 positions in the string for placing the digits. We will calculate the number of ways we can arrange the digits in the string.
1. Place two 0s: Choose 2 positions out of 20, which can be done in C(20, 2) ways.
2. Place four 1s: Choose 4 positions out of the remaining 18, which can be done in C(18, 4) ways.
3. Place three 2s: Choose 3 positions out of the remaining 14, which can be done in C(14, 3) ways.
4. Place two 3s, two 4s, two 5s, and two 7s: There are 8 positions left, and we can arrange the remaining digits in 8!/(2! * 2! * 2! * 2!) ways (as each digit appears twice).
5. Place three 9s: This will be done automatically, as there are 3 positions left for the three 9s.
Now, to find the total number of strings, multiply the number of ways for each step:
Total strings = C(20, 2) * C(18, 4) * C(14, 3) * [8!/(2! * 2! * 2! * 2!)].
Therefore, there are 4,084,710,000 distinct strings of 20-decimal digits with the given conditions.

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Answer:

arithmetic sequence: 24, 42, 66, 90, 114; y = 24x - 30

geometric sequence: -54, 162, -486, 1458, -4374; y = -6(-3)^(x - 1)

Step-by-step explanation:

Arithmetic sequence:

-6, 18, ...

18 - (-6) = 24

18 + 24 = 42

42 + 24 = 66

66 + 24 = 90

90 + 24 = 114

y = -6 + 24(x - 1)

y = -6 + 24x - 24

y = 24x - 30

Geometric sequence:

-6, 18, ...

18/(-6) = -3

18 * (-3) = -54

-54 * (-3) = 162

162 * (-3) = -486

-486 * (-3) = 1458

1458 * (-3) = -4374

y = -6(-3)^(x - 1)

The next 5 terms in the arithmetic sequence are 42, 66, 90, 114, 138.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

Given that, the first 2 terms of the sequence -6, 18,....

Here, a=-6 and common difference = 18-(-6) =24

So, the next 5 terms in the arithmetic sequence are

18+24=42, 42+24=66, 66+24=90, 90+24=114, 114+24=138

42, 66, 90, 114, 138

The function is aₙ= -6+(n-1)24

= -6+24n-24

= 24n-30

The next 5 terms in the geometric sequence are

Here, a=-6 and common ratio = 18/(-6) =-3

Now, 18×(-3)=-54, -54×(-3)=162, 162×(-3)=-486, -486×(-3)=1458, 1458×(-3)=-4374

The function is \(a_n=-6(-3)^{n-1}\)

Therefore, the next 5 terms in the arithmetic sequence are 42, 66, 90, 114, 138.

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Answer:

7y=-91

Step-by-step explanation:

-2x + 2y = 8 (multiply the second equation by 2)

12x + 2y = 22

Adding the two equations, we get:

10x = 30

Therefore, x = 3.

Substituting x = 3 into the second equation, we get:

6(3) + y = 11

Simplifying, we get:

y = -13

Finally, we can find the value of 7y:

7y = 7(-13) = -91

Angle b = 31

b=8

c=13

not 100% sure

To minimize the total area of an equilateral triangle and square, the side length of the square should be 2.167 and the side length of the triangle should be 3.833.

To find the dimensions that minimize the total area, we can set up equations based on the given information. Let's denote the side length of the square as 's' and the side length of the equilateral triangle as 't'. The perimeter of the square is 4s, and the perimeter of the equilateral triangle is 3t. Given that the combined perimeter is 13, we have the equation 4s + 3t = 13.

To minimize the total area, we need to consider the formulas for the areas of the square and equilateral triangle. The area of the square is given by A_square = \(s^2\), and the area of the equilateral triangle is given by A_triangle = (\(\sqrt{(3)}\)/4) *\(t^2\).

To find the values that minimize the total area, we can substitute s = (13 - 3t)/4 into the equation for A_square and solve for t. By finding the derivative of the total area with respect to t and setting it equal to zero, we can find the value of t that minimizes the area.

Similarly, to find the dimensions that maximize the total area, we follow the same process but this time maximize the total area by finding the value of t that maximizes the area.

Performing the calculations, we find that to minimize the total area, the side length of the square is approximately 2.167 and the side length of the triangle is approximately 3.833. To maximize the total area, the side length of the square is approximately 4.333 and the side length of the triangle is approximately 1.667.

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Answer:

0

Step-by-step explanation:

Here, given the function f(x), we want to calculate f(1)

Mathematically, this means we shall substitute 1 for the value of x in that function.

Thus, given F(x) = 1-x

Then F(1) would be = 1-1 = 0

Step-by-step explanation: The solution to this system of equations will be where the two lines on the graph intersect with each other.

Notice that both of them intersect to the left of the y-axis which means our x - coordinate must be negative.

They also intersect above the x-axis so our y-coordinate must be positive.

So the only option with a negative x-coordinate

and a positive y-coordinate is (-1/4, 3/4).

Answer:

a=4

Step-by-step explanation:

Hope this helps! Plz give brainliest!

Answer:

Subtract 6a6a from both sides.

12a-6a=24

12a−6a=24

2 Simplify 12a-6a12a−6a to 6a6a.

6a=24

6a=24

3 Divide both sides by 66.

a=\frac{24}{6}

a=

6

24

​

4 Simplify \frac{24}{6}

6

24

​

to 44.

a=4

a=4

Step-by-step explanation:

Answer:

what function

Step-by-step explanation:

the answer is either (2,8) or [2,8}

The accurate solution is that the probability of the proportion of nearsightedness of at least 0.09 is approximately 0.0324 or 3.24%.

There are a few steps to answer this question about probability with the proportion of nearsightedness:

1. Define the variable: Let p be the true proportion of children with nearsightedness.

2. Check the conditions for using the normal approximation to the binomial distribution: np = 356 × 0.09 = 32.04 and n(1 - p) = 356 × 0.91 = 323.96, both greater than or equal to 10.

3. Calculate the z-score using the formula: z = (x - np) / √(np(1 - p)), where x = 0.09 × 356 = 32.04.

4. Find the probability using a calculator.

The probability that 356 randomly selected children will have a proportion of nearsightedness of at least 9% is approximately 0.0324, or 3.24%.

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The value of the [f(x+h)-f(x-h)]/2 will be 2[2h - xh].

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

Given the function   f(x)=4x-x²,

Now,

f(x+h) = 4(x + h) - (x+h)²

f(x+h) = 4x + 4h - x² - h² - 2xh

Now,

f(x-h) = 4(x -h) - (x - h)²

f(x-h) = 4x - 4h - x² - h² + 2xh

Now,

[f(x+h)-f(x-h)]/2 = [8h - 4xh]/2

[f(x+h)-f(x-h)]/2 = 2[2h - xh]

Hence "The value of the [f(x+h)-f(x-h)]/2 will be 2[2h - xh]".

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Answer:

  see below

Step-by-step explanation:

For a vertical scale factor of 'b', and a translation by (h, k) in the (right, up) direction, the transformed function is ...

  g(x) = b·f(x -h) +k

For a scale factor of 1/2 and translation left 3 and down 2, the transformed function is ...

  g(x) = (1/2)f(x +3) -2

  g(x) = (1/2)5^(x +3) =2 . . . . matches the 2nd choice

Answer:

Step-by-step explanation:

not sure 2

Answer:

-21. -19.-17

Step-by-step explanation:

Let x be the smallest

x+2 next smallest

x+4 be the largest

4*(x) = 18+6(x+4)

Distribute

4x = 18+6x+24

Combine like terms

4x = 42+6x

Subtract 6x from each side

-2x = 42

Divide by -2

-2x/-2 = 42/-2

x = -21

x+2 = -19

x+4 = -17

Answer:

- 21, - 19, - 17

Step-by-step explanation:

Let y be the smallest no.

& y + 2 next smallest no.

& y + 4 be the largest no.

= 4 * (y) = 18 + 6 * (y + 4)

4y = 18 + 6y + 24

4y - 6y = 42

- 2y = 42

= - 21

The other 2 numbers are:

y + 2

= - 19

y + 4

= - 17

Hope this helps!

Answer: 1/1

Step-by-step explanation: if you drawn imaginary line that kind of averages all of the Bluepoints you get for every one time it goes up it goes to the side one time

To factor the expression 4x² - 8x + 4 completely, we can use the factoring method.
The expression 4x² - 8x + 4 can be factored as (2x - 2)(2x - 2).

Explanation:
1. First, we look for common factors, but in this case, there are none.
2. Next, we try to factor the quadratic trinomial. We can do this by finding two numbers that multiply to give the product of the coefficient of x² (which is 4) and the constant term (which is 4) and add up to the coefficient of x (which is -8).
  - In this case, the product of 4 and 4 is 16, and the sum of -4 and -4 is -8.
3. We rewrite the expression as 4x² - 4x - 4x + 4.
4. Now, we group the terms and factor by grouping:
  - Factor out 4x from the first two terms: 4x(x - 1).
  - Factor out -4 from the last two terms: -4(x - 1).
  - We can see that both terms have a common factor of (x - 1).
5. Factoring out (x - 1) from both terms, we get:
  - (x - 1)(4x - 4).
6. Finally, we can simplify further by factoring out 4 from the second term:
  - (x - 1)(4(x - 1)).
7. Combining like terms, we have:
  - (x - 1)(4x - 4) = (2x - 2)(2x - 2).

So, the expression 4x² - 8x + 4 can be factored completely as (2x - 2)(2x - 2).

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Answer:

A: $188.75

B: $566.25

Step-by-step explanation:

To find the amount of the discount you can either multiply the original price ($755) by 1/4 or you can divide by 4.

Either way will get you $188.75. This is a quarter of the original price and is what is subtracted from the original sale price ($755). To find the sale price after the discount you do:

755-188.75=$566.25.

To check this you can do 755 × 3/4.

Hope this helps.

Please Mark Brainliest!!!

Answer:

What he said

Step-by-step explanation:

Answer:

u think its A if not sorry

Step-by-step explanation:

Answer:

3.777777777777777777777777777777777777 and it goes on

The statement that "the tribe is the οldest sοciοpοlitical type; the tribe predates the state" is a widely accepted view in anthrοpοlοgy and archaeοlοgy.

It suggests that human sοcieties evοlved frοm smaller, kinship-based grοups knοwn as tribes befοre transitiοning tο larger, centralized fοrms οf pοlitical οrganizatiοn knοwn as states.

Tribes are characterized by a clοse-knit sοcial structure based οn kinship ties, with members sharing cοmmοn ancestry and οften living in smaller, decentralized cοmmunities. Tribal sοcieties typically have egalitarian sοcial structures, with leadership based οn kinship οr achieved status rather than fοrmal hierarchical systems.

As human sοcieties evοlved, sοme tribes eventually develοped intο states, which are characterized by centralized pοlitical authοrity, fοrmal legal systems, and defined territοrial bοundaries. States οften have mοre cοmplex sοcial hierarchies, specialized institutiοns, and a mοnοpοly οn the use οf fοrce.

The transitiοn frοm tribes tο states is believed tο have οccurred gradually οver thοusands οf years, as human pοpulatiοns grew and interactiοns between grοups increased. The emergence οf agriculture, surplus prοductiοn, and the need fοr larger-scale gοvernance are οften cited as factοrs cοntributing tο the develοpment οf states.

While the specific timeline and prοcesses οf this transitiοn are still subjects οf οngοing research and debate, it is generally accepted that tribal sοcieties predate the develοpment οf states in human histοry.

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Answer:

\( \frac{x}{4} + \frac{1}{2} = \frac{1}{8} \)

\( \frac{x}{4} = - \frac{3}{8} \)

\(x = - \frac{3}{2} = - 1 \frac{1}{2} \)

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.

x/4 + 1/2 = 1/8

Take the 1/2 term on the other side,

x/4=1/8 - 1/2

Taking the LCM on the Right side,

x/4 = (1-4) / 8

x/4 = -3/8

Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,

x = ( -3/8) * 4

x = -3/2

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

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The parabola appears wider when |a| >1, the parabola appears thinner

When a is positive, the parabola opens upwards, but when a is negative parabola opens downwards

Step-by-step explanation:

brainliest?

Step-by-step explanation:

Step 1:  Convert degrees into radians

\(\frac{degrees}{1}*\frac{\pi }{180}\)

\(\frac{52}{1}*\frac{\pi}{180}\)

\(\frac{52\pi}{180}\)

\(\frac{13\pi}{45}\)

Step 2:  Find the arc length

\(S = r\theta\)

\(S=(3)(\frac{13\pi}{45})\)

\(S = \frac{39\pi}{45}\)

\(S=\frac{13\pi}{15}\)

Answer: Option B

When the radius is 10 inches and the height is 20 inches

(a) rate change of the volume of the cylinder is 5340.7 inch²/min.

(b) rate of change of the surface area of the cylinder is 1068.14 inch²/min.

Volume and surface area of the closed cylinder both increase with time.

Let r be the Radius and h be the height of the cylinder in inches at time t.

\(\frac{dr}{dt} =5\) inch/min and \(\frac{dh}{dt} =-3\) inch/min

Let V be the volume of the cylinder then

Differentiating with respect to t,

\(\frac{dV}{dt} =2\pi r(\frac{dr}{dt} )h+\pi r^{2} \frac{dh}{dt}\)

At r=10 inch and h=20 inch,

\(\frac{dV}{dt} =1700\pi =\) 5340.7 inch²/min ≈ 5000 inch²/min

Thus, it is increasing with time as it has a positive sign.

Let S be the surface area of a closed cylinder

\(\frac{dS}{dt} =2\pi r(\frac{dr}{dt} )h+2\pi r(\frac{dr}{dt} )+4\pi (\frac{dr}{dt} )r\)

At r=20 inch and h=20 inch

\(\frac{dS}{dt} =340\pi =\) 1068.14 inch²/min ≈ 1000 inch²/min

It is also increasing with time as it is also having a positive sign.

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To calculate the ratio strength of a medication, we compare the amount of active ingredient (lorazepam in this case) to the total volume of the medication.

In this case, the lorazepam injection contains 4 mg of lorazepam per milliliter.

Therefore, the ratio strength can be calculated as:

Ratio Strength = Amount of Active Ingredient / Total Volume

In this case, the amount of active ingredient is 4 mg, and the total volume is 1 mL.

Ratio Strength = 4 mg / 1 mL

Thus, the ratio strength of the lorazepam injection is 4:1 (4 to 1) or 4.

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To solve this problem, we can use algebra. Let's call one of the positive numbers "x" and the other positive number "y".

From the problem, we know that:

- The difference between the two positive numbers is 24, so we can write an equation:

   x - y = 24

- The product of the two positive numbers is 1620, so we can also write an equation:

   xy = 1620

Now we can use algebra to solve for x and y.

One way to do this is to use substitution. We can solve the first equation for one of the variables (let's solve for x):

x - y = 24

x = y + 24

Now we can substitute this expression for x into the second equation:

xy = 1620

(y + 24)y = 1620

Expanding the left side:

y² + 24y = 1620

Subtracting 1620 from both sides:

y² + 24y - 1620 = 0

Now we have a quadratic equation in terms of y. We can use the quadratic formula to solve for y:

y = (-24 ± sqrt(24² - 4(1)(-1620))) / (2(1))

y = (-24 ± sqrt(3936)) / 2

y = (-24 ± 4sqrt(246)) / 2

y = -12 ± 2sqrt(246)

Since we are looking for two positive numbers, we can discard the negative solution and only use:

y = -12 + 2sqrt(246)

Now we can use this value of y to find x:

x = y + 24

x = (-12 + 2sqrt(246)) + 24

x = 12 + 2sqrt(246)

Therefore, the two positive numbers that satisfy the given conditions are approximately:

x ≈ 12 + 2sqrt(246)

y ≈ -12 + 2sqrt(246) (discard)

To summarize:

- The positive numbers are approximately x ≈ 12 + 2sqrt(246) and y ≈ -12 + 2sqrt(246) (discard).
- The difference between the two positive numbers is 24.
- The product of the two positive numbers is 1620.

We used algebra to set up equations based on the given information, solved for one variable in terms of the other, substituted into the other equation, and solved for the remaining variable using the quadratic formula. We then discarded the negative solution and found the positive numbers that satisfied the conditions.

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Answer:

Your answer would be C

Step-by-step explanation:

Trust it's c and if it's not I am sorry but trust me.