FOR 58 POINTS!!!
Angle H is half as large as angle J. Angle J is one fourth as large as angle K. Angle K has a measure of 240 degrees. What is the measure of angle H?

The nth terms of sequence 1 ; 5 ; 11 ; 19  is n² + n + -1   and the nth terms of sequence -2;-3; -6;-11; is -n² + 2n -3  .

The differences (referred to as first differences) between every two successive terms are the same, then it is called an arithmetic sequence (which is also known as a linear sequence). But if the first differences are NOT same, and instead, the second differences are the same, then the sequence is known as a quadratic sequence.

According to the question

The sequence      1   ,   5   , 11  ,   19

First difference :       4      6       8

Second difference:        2     2  

1.1.1>

Now, expression for the nth term of the sequence.

Quadratic equation

ax² + bx + c

at n= 1

a + b + c = 1 -----------------(1)

At n = 2

4a + 2b + c = 5 ------------------(2)

At n = 3

9a + 3b + c = 11 -------------------(3)

solving equation

Subtracting equation (3) from (2)

9a + 3b + c = 11

-4a - 2b - c = -5

5a + b = 6 ----------------------(4)

Subtracting equation (2) from (1)

4a + 2b + c = 5

-a  - b - c = -1  

3a + b = 4 ---------------------------- (5)

Subtracting  equation (5) from  (4)

5a + b = 6

-3a - b = -4

2a = 2

a = 1

Putting value in equation (5)

3a + b = 4

3*1 + b = 4

b = 1

Substituting the value in equation (1)

a + b + c = 1

1 + 1 + c = 1

c = -1

Substituting the value in the quadratic equation

x² + x + -1

For nth term

n² + n + -1  

1.1.2>

Term of the sequence is 2549

Now,

using the nth term

n² + n + -1  = 2549

n (n+1) = 2550

n (n+1) = 50 * 51

n = 50

1.2>  sequence of numbers is given:   -2   ,-3   ,-6   ,-11

                First difference =                       -1     -3    -5

               Second difference =                       -2    -2    

1.2.1 >

Now , expression for the nth term of the sequence.

Quadratic equation

ax² + bx + c

at n= 1  

a + b + c = -2 -----------------(1)

At n = 2

4a + 2b + c = -3 ------------------(2)

At n = 3

9a + 3b + c = -6 -------------------(3)

solving equations  

Subtracting equation (3) and (2)

9a + 3b + c = -6

-4a - 2b - c = 3

5a +b = -3 ----------------(4)

Subtracting equation (2) and (1)

4a + 2b + c = -3

-a - b - c = 2

3a + b = -1 -------------------(5)

Now,

Subtracting equation (5) and (4)

5a +b = -3

-3a - b = 1

2a = -2

a = -1

Putting value of a in equation (5)

3*-1 + b = -1

b = 2

Substituting values in equation (1)

-1 + 2 + c = -2

c = -3

nth term

-n² + 2n -3  

1.2.2>the sequence of numbers will never contain a positive term.  

because its first term is -ve and difference between consecutive term is always -ve. or as per nth term n² is a -ve term .

Hence, the nth terms of sequence 1 ; 5 ; 11 ; 19  is n² + n + -1   and the nth terms of sequence -2;-3; -6;-11; is -n² + 2n -3  .

To know more about Quadratic equation here:

https://brainly.com/question/2263981

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Answer:

33 units²

Step-by-step explanation:

1/2(11 x 6) = 33 units²

Step-by-step explanation:

  [tex]a^{2} + 10a + 24[/tex]

= [tex]a^{2}[/tex] + 6a + 4a + 24

= a(a + 6) + 4(a + 6)

= (a + 6)(a + 4)

Answer:

solution:

[tex] {a}^{2} + 10a + 24[/tex]

a²+6a+4a+24

a(a+6)+4(a+6)

(a+6)(a+4) is your answer

Answer:B

Step-by-step explanation:

Answer:

Soooooo, for Part A I got answer choice D.

I didn't want to overthink it like I normally do with everything else in life so i was like, there are 3 boxes on the side and 4 boxes on the bottom, so 3 times 4= 12.

Now i know that the area of the neighborhood is 12 blocks and 20 blocks equals a mile. 12 is obviously not 20, twelve is actually a little bit over half of twenty or .50%, so the best answer would be D.60%.

Now part B, i dont know bout all that, I can only give you half an answer. Copped out at the mention of the word Density XD. Hope that first part helped tho.

Answer:

18 12

6 22

Step-by-step explanation:

if u understand my handwriting lol

Answer:

$15.65

Step-by-step explanation:

$20 + $20 = $40

$40 - $24.35 = $15.65

Answer:

the first answer maybe?

Step-by-step explanation:

Answer:

c the data shows positive associations with trend line

Answer:

X = 3

Step-by-step explanation:

x= 6 x 1/2

Step-by-step explanation:

{(2)³}⁸×{(2)³}-⁵

2²⁴× 2-¹⁵

2²⁴-¹⁵. ( subtract 24 and 15)

2⁹= 512

So...

8×8×8= 512

hence

8³ Answer

Answer:

[tex]4x {}^{2} - 36 \\ = (2x + 6)(2x - 6) \\ hence \: option \: b \: is \: correct[/tex]

Answer:

20 quarts.

Step-by-step explanation:

Because there are 20 quarts in 5 gallons.

His percent error is 25% because 12 is 75% of 16. 100 - 75 = 25

Answer:

75% correct and 25%error

Step-by-step explanation:

As 12÷16×100=75%

The error =100-75=25%

Answer:

V = 5412 cm^3

Step-by-step explanation:

[tex]v \: = 41 \times 22 \times 6 \\ \\ v = 5412 \: {cm}^{3} [/tex]

I hope that is useful for you :)

Answer:

70 m and 60 m

Step-by-step explanation:

The formula for the area of a rectangle is length ⋅ width.

The area of the pasture of 4200 meters.

70 ⋅ 60 = 4200.

The formula for the perimeter of a rectangle is side + side + side + side.

The perimeter of the rectangle is 260 meters.

70 + 60 + 70 + 60 = 260.

Therefore, the length and width of this pasture are 70 meters and 60 meters.

Answer:

48

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Answer:

22°

Step-by-step explanation:

<1 is a secant-secant angle (it lies outside the circle, created by two lines that cut through the circle). The measure of a secant-secant angle is half the difference of the measures of the intercepted arcs:

<1=(0.5)(98-54)

<1=(0.5)(44)

<1=22°

Answer:

6,0

Step-by-step explanation:

Step-by-step explanation:

don't see any points to pick from however the following would lie on the graph

(0,12)

(1,8)

(2,4)

(3,0)

(4,-4)

Answer:

No

Step-by-step explanation:

To form a proporion, both would need to be a multiple of the same thing, whcih they aren't

Answer:

x = 24.5

Step-by-step explanation:

the angles form a straight line, and a straight line equals to 180°

=> (5x + 8) + (3x - 24) = 180

=> 8x = 196

=> x = 24.5

Answer:

B

Step-by-step explanation:

find slope which is -2 then plug into equation y=mx+b to find constant of 3

Answer:

15 m E. B. C. D. that's why I will be there

Answer:

no she needs $2.20 more

Step-by-step explanation:

2+ 1.10+.05= $3.15

$5.35 - $3.15 = the answer

Answer:

Step-by-step explanation:

(1,5 ) indicates that for every 1 book they make 5 dollars so the point means that for every book they sell they make 5 dollars.