if you borrow $1000 for a year with a credit card that charges 27.9% annual interest, how much interest will you pay for the year?

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  .

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Answer:

The hight written in digital is 14286

Answer:

48

Step-by-step explanation:

6x8=48

6 baked a cake for the 8

                          --------48-------

Answer:

$7.85

Step-by-step explanation:

Per pound = 1

Ratios:

[tex]\frac{4.71}{0.6} =\frac{x}{1} \\\\0.6x=4.71\\x=7.85[/tex]

Answer:

66 in

Step-by-step explanation:

Answer:

i dont know because you have not really explained it

Step-by-step explanation:

The quotient of the division of 145413 by 321 is 453.

Division is one of the operation in mathematics where number is divideD into equal parts as that of a definite number.

We are using long division method here.

For that dividend is 145413 and divisor is 321.

First take the first some digits of dividend which is greater than 321.

That is the first four digits, 1454.

The multiple of 321 closest to 1454 is 1284 which is equal to 4 × 321

So the first digit of quotient is 4.

1454 - 1284 = 170

Now 170 is less than 321.

Add the next digit of the dividend to 170.

It becomes 1701.

Multiple of 321 closest to 1701 is 1605 which is equal to 5 × 321.

The next digit of the quotient is 5.

1701 - 1605 = 96

Again since 96 less than 321, take the next digit of the dividend and the number becomes 963.

Now 963 is a multiple of 321, where 963 = 3 × 321

So the next digit of the  quotient is 3.

Quotient = 453

Hence the quotient of the given division is 453.

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Answer:

2,100,000

Step-by-step explanation:

Just round

J.

x represents the minutes and y shows how many gallons over that time.

The correct table for best represents the situation is shown in Table J.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

A standard bathtub holds 60 gallons of water.

And, A full tub drains 12 gallons per minute.

Now, From table J;

Rate of change is,

⇒ (24 - 12) / (2 - 1)

⇒ 12 / 1

⇒ 12 gallons per minutes

Which is given in situation.

Thus, The correct table for best represents the situation is shown in Table J.

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Answer:

QUESTION:

which one is it?

ANSWER:

Okay, so everyone knows that a straight angle/ full triangle equals up to the sum of 180°, right?

So you take the 180° and subtract the 51°. And you should be getting 129°.

But, since this is a right triangle all I did was subtract 51° from 90° (a right triangle). In the end, the final answer is 39°

Step-by-step explanation:

Hope that this helps you out! :)          

If you have any questions please put them in the comment section below this answer.          

Have a great rest of your day/night!          

Please thank me on my profile if this answer has helped you.

Answer:

14

Step-by-step explanation:

im so sorry that the other people's comments are making you feel uncomfortable :(

there are 14 marbles in total since:

5 marbles+3 marbles+6 marbles = 14 marbles

each marble has one chance of being pulled out, therefore, there are 14 different outcomes.

Answer:

B

Step-by-step explanation:

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

Answer:

10. Area = 72 units²

Step-by-step explanation:

10. The shape in number 10 is a trapezoid.

Area of trapezoid = ½(a + b)*h

Where,

a = 6

b = 12

h = 8

Area = ½(6 + 12) * 8

Area = ½(18)8

Area = 72 units²

Answer:

Radius: R = 12 in

Diameter: D = 24 in

Circumference: C = 75.4in

Area: A = 452.39 in²

Step-by-step explanation:

Solutions:

Diameter d= 2r

D = 2 × 12

D = 24

Circumference

C = 2πr

C = 2 × π × 12

C = 24π

C = 75.3982237

Area:

A = πr²

A = π × 12²

A = 144π

A = 452.389342

Answer:

Area = 346.2yd²

Perimeter = 72.1yd

Step-by-step explanation:

AREA

Split it into three shapes: (1) the semi-circle, (2) the triangle, and (3) the rectangle. Find the area of each and then add them together for the area of the whole shape.

Area₁ = πr² = (6²)π = 36π = 113.1 yd²

Area₂ = (1/2)bh = (1/2)(11.3)(14) = 79.1 yd²

Area₃ = lw = (11)(14) = 154 yd²

154 + 79.1 + 113.1=346.2yd²

PERIMETER

The perimeter consists of the length of the curve on the semi-circle, the top , the right side, the bottom, and the slanted line.

length of the curve on the semi-circle = half the cicumference of circle with radius 6 = (2π(6))/2 = 6π = 18.8

the top = 22.3

the right side = 14

the bottom = 11

the slanted line = the hypotenuse of triangle(2) - the diameter of circle(1) = (√(11.3²+14²))-12= (√(323.69))-12=18-12=6

18.8+22.3+14+11+6=72.1yd

Answer:

x = 7

z = 85

Step-by-step explanation:

For x:

8x + 39 = 95

8x = 56

x = 7

For z:

95 + 95 + z + z = 360

190 + 2z = 360

2z = 170

z = 85

Check work:

DOES 85 + 85 + 95 + 95 = 360 ? Yes. Answer is correct.

I would appreciate Brainliest, but no worries.

Answer:

1. ∠CFD = 28°

2. ∠RPQ = 53°

Step-by-step explanation:

For the first one:

∠CFD and ∠DFE are angles on a straight line

Angles on a straight line add up to equal 180

That being said we can find the missing angle (∠CFD) by subtracting the given angle measure (152°) from 180

so ∠CFD = 180 - 152

180 - 152 = 28

Hence, ∠CFD = 28°

For the second one:

Complementary angles have a sum of 90°

If ∠RPQ and ∠SPR are complementary angles we can find the missing angle ( ∠RPQ in this case ) by subtract the given angle measure ( 37° ) from 90

so ∠RPQ = 90 - 37

90 - 37 = 53

Hence , ∠RPQ = 53°

Answer:

divergent

Step-by-step explanation:

just took it

Answer:

Solution given:

<6+24=180[co- interior angle]

<6=180-24=156°

<6=156°

Using the Central Limit Theorem, it is found that the approximate standard error of the mean for a sample size of 300 is given by:

B. 0.46

It states that the sampling distribution of sample means of size n from a population with standard deviation [tex]\sigma[/tex] has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

In this problem, we have that the parameters are [tex]\sigma = 7.89, n = 300[/tex], hence the standard error is given by:

[tex]s = \frac{7.89}{\sqrt{300}} = 0.46[/tex]

Hence option B is correct.

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Answer:

There are thousands of different combinations possible.

Step-by-step explanation:

Answer:

Can you do it in english? I can't read in spanish sorry.

Answer: 600 sq cm

Step-by-step explanation: Each side is 100 cm^2, and there are a total of 6 sides. 100•6=600.

Hope this helps!

Answer:

SA = 600

Step-by-step explanation:

A cube has six sides.

The formula to find the SA of a cube is 6a^2

6 x 10^2 = 6 x 100 = 600

Answer: 2 is the y intercept

Step-by-step explanation:

Slope is rise over run and in this problem our y intercept is 2 because it is defined as the y. Negate your 9 and put it over the y intercept to make into a fraction to represent slope. This makes it y = mx + b form now.

y = - 9/2x + 2