please help this is a hard question and i just cant figure it out

The [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex] .

Quadratic sequences are sequences that include  [tex]nth[/tex]  term. They can be identified by the fact that the differences between the terms are not equal, but the second differences between terms are equal.

Quadratic sequence [tex]=an^2+bn+c[/tex]

Here [tex]a,b,c[/tex] are constant and [tex]n[/tex] is the position of term.

First difference [tex]= 3a+b[/tex]

Second difference [tex]=2a[/tex]

We have,

Quadratic sequence [tex]8,16,26,38,52,68,86,....[/tex]

Quadratic sequence [tex]=an^2+bn+c[/tex]

so,

For [tex]n=1[/tex];

[tex]8=an^2+bn+c[/tex]

[tex]8=a+b+c[/tex]   [tex]........(i)[/tex]

For [tex]n=2[/tex];

[tex]16=4a+2b+c[/tex]    [tex]........(ii)[/tex]

For [tex]n=3[/tex];

[tex]26=9a+3b+c[/tex]    [tex]........(iii)[/tex]

Now,

Subtract equation [tex](i)[/tex] from [tex](ii)[/tex]

we get,

[tex]8=3a+b[/tex]    [tex]........(iv)[/tex]

Subtract equation [tex](ii)[/tex] from [tex](iii)[/tex] we get,

[tex]10=5a+b[/tex]    [tex]........(v)[/tex]

Subtract equation [tex](iv)[/tex] from [tex](v)[/tex] we get,

[tex]2=2a[/tex]  (This is second difference mentioned above)

[tex]a=1[/tex]

Putting [tex]a=1[/tex]  in [tex](iv)[/tex]

⇒[tex]b=5[/tex]

Now putting values of [tex]a[/tex] and [tex]b[/tex] in equation [tex](i)[/tex]

[tex]8=1+5+c[/tex]

[tex]c=2[/tex]

Now, putting values of [tex]a[/tex] , [tex]b[/tex] and [tex]c[/tex] in,

Quadratic sequence [tex]=an^2+bn+c[/tex]

we get,

[tex]nth[/tex] term rule [tex]=n^2+5n+2[/tex]

Hence, we can say that the [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex].

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Answer:

B is the answer I'm pretty sure

Answer:

0.6x30=18

Step-by-step explanation:

18 miles would be how far it ran.

You didn't give us any answer choices for which equation, so I would say the equation I wrote could work.

Answer:

0.6 × 30 = 18

Step-by-step explanation:

You multiply the two values to get 18:

0.6 * 30 = 18

Hope that helps! :)

Answer:

[tex]-2x^{2} -7x-6[/tex]

Step-by-step explanation:

(2x + 3) (-x - 2)

distribute first term, to the second term:

2x(-x) + 2x(-2) + 3(-x) + 3(-2)

multiply:

[tex](-2x^{2})[/tex] + (-4x) + (-3x) + (-6)

[tex]-2x^{2} -4x-3x-6[/tex]

combine the like terms:

[tex]-2x^{2}[/tex] - 4x - 3x - 6

             -7x

[tex]-2x^{2}[/tex] - 7x - 6

final answer :

[tex]-2x^{2}[/tex] - 7x - 6

hope this helped !!

mark me brainliest :D

Hi there! :)

A geometric sequence is a sequence where we use multiplication or division to get to the next term.

We use multiplication in the third sequence (we multiply by -5)

So the answer is Option C

Hope it helps

~Just a gloomy teen who misses her best friend

#CarryOnLearning

[tex]SilentNature[/tex]

Answer:

1 juice boxes = 153 millimeters

459 ?

3 juice boxes = 459 millimeters

Step-by-step explanation:

Answer:

35°

Step-by-step explanation:

As we know vertically opposite angles are equal . So ,

x + 90= 125

x = 125-90 = 35°

Answer:

35

Step-by-step explanation:

125 + 90(APC) + DPA + EPB + x = 360

215 + DPA + EPB + x = 360

DPA = 180 - 125 = 55

EPB = DPA

EPB = 55

X = 90(EPC) - EPB

X = 90 - 55

X = 35

OR easy way

DB is a straight line so angels on it add up to 180

EPB = 180 - 125

EPB = 55

X = 90(EPC) - EPB

X = 90 - 55

X = 35

(BC + AD) / 2 = 17

(2x + 1 + 3x + 8) / 2 = 17

5x + 9 = 34

5x = 25

x = 5

Answer:

12 and 16

Step-by-step explanation:

Turn it into algebra.

Make one of the pieces x. So x+4 is the piece that is 4 feet longer and x is the piece that it is 4 feet longer than.

So x+4+x=28, which is the total length, and if you simplify it, it makes 2x+4=28.

Then you just solve it, so do 28-4=24, and then divide that by 2, which gets 12.

Then you substitute 12 where x has been substituted for the pieces.

One piece is x feet, so that just stays 12, and another piece is x+4, so 12+4 which is 16.

To make sure it's correct, you can check it by doing 16-12=4 and add 12 and 16 together which gets the correct total of 28.

Answer:

x2 - x - a2 - 3a - 2

Step-by-step explanation:

STEP 1

 ((x2) -  x) -  (a + 1) • (a + 2)

STEP 2

Final result :

 x2 - x - a2 - 3a - 2

Answer:

$3.75 every 8 oz bags.

Step-by-step explanation:

7.5 divided by 2 to get 3.75. 1 LB is equal to 16 oz so 8 is half of 16.

Answer:

6 or 3 because my is the opposite of yx so I would think it'll be 6 or 3

Answer:

Step-by-step explanation:

26. -14

27. -4.732050808

Answer:

26.  (-14)

27.  −4.732050808

Step-by-step explanation:

26.  [tex](\sqrt{2}+4)(\sqrt{2}-4)[/tex]

Multiplication can be transformed into difference of squares using the rule:

(a − b) (a + b) = a² - b²

[tex](\sqrt{2} ^{2} ) - 4^{2}[/tex]

The square of √2 is 2.

[tex]2 - 4^{2}[/tex]

Calculate 4 to the power of 2 and get 16.

2 - 16

Subtract 16 from 2 to get −14.

27.  [tex](\sqrt{3} +2)(\sqrt{3} -3)[/tex]

Apply the distributive property by multiplying each term of √3 + 2 by each term of √3 - 3.

[tex]\sqrt{3} ^{2}-3\sqrt{3} +2\sqrt{3} -6[/tex]

The square of √3 is 3.

[tex]3-3\sqrt{3} +2\sqrt{3} -6[/tex]

Combine -3√3 and 2√3 to get -√3.

[tex]3-\sqrt{3} -6[/tex]

Subtract 6 from 3 to get −3.

-3 - √3

Answer:

$14.80

Step-by-step explanation:

You just have to 0.8 * 18.50 becuase the new price is 80% of the old price. That would result in 14.80.

Answer:

a) she will become used to it, knowing everyone must go.

b) i guess most children can intuit their loss of childhood's freedom on that first day of school.

Explanation: i took the quiz

Answer:

Yes

Step-by-step explanation:

It is a function because the x value doesnt repeat itself. The x value is the input

Answer:

Slope: -3/2

Y-Intercept: (0,-9)

Step-by-step explanation:

Answer:

14.28

Step-by-step explanation:

I think the answer is 20+40...

Hello there! :)

8x+20y=-120

We want to put this equation into slope-intercept form (y=mx+b)

First, let's move 8x to the right side:

20y=-120-8x

Now, we divide both sides by 20 to isolate y:

y=-8/20-6

Simplify the fraction:

y=-2/5-6

Hence, that's our equation. Hope it helps you! (:

If you have any queries, feel free to ask me! :)

~A smiley teen who adores helping others

[tex]MagicalNature[/tex]

Answer:

can't be simplified or you can add you get the answer

the answer is 1/6 bbbbbbbbb

Step-by-step explanation:

bring both fractions to the same denominator (bottom number). then we can readily compare our add or subtract them.

what is the snaked common multiple of 2 and 3 (the smallest number that can be divided without remainder by both numbers)?

it is 6 (in case of doubt simply multiply both numbers and use the result as common denominator).

so, we need to bring both to fractions in the form .../6.

2/3 = 4/6

1/2 = 3/6

so,

4/6 - 3/6 = 1/6

and that is the answer to the original question.

=》The answer is -61/3 = -20.333

Steps are in the attachment.

Note :-

=》The LCM is 3.

_______

Hope it helps ⚜ :))

[tex]\text{Given that ,}\\\\f(x) = 4x+3\\\\g(x) = x^2 -3\\\\g(4) = 4^2 - 3 = 16-3=13\\\\f (g(4)) = f(13) = 4\times 13 + 3 = 55[/tex]

Answer:

1*4 = 4 in^2

Step-by-step explanation:

The area for this shape is calculated by multiplying width and length:

1*4 = 4 in^2

Answer:

yes, the question is proportional. if you multiply 9.50 by 2 you get 19 and so on and so forth. the constant rate is 9.50