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3 years ago

What is the nth term rule of the linear sequence below? 15 , 7 , − 1 , − 9 , − 17 , . . .

Mathematics

1 answer:

Doss [256]3 years ago

7 0

You can see that you're constantly subtracting 8 to get the next number. So, we have

$a_1 = 15$

$a_2 = a_1-8$

$a_3 = a_2-8 = (a_1-8)-8=a_1-2\cdot 8$

$a_4=a_1-3\cdot 8$

$a_5=a_1-4\cdot 8$

So, as you can see, to get the n-th term we must subtract (n-1) times 8 from the original number.

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I don’t understand this assignment!!

Rashid [163]

Answer:

Equation of the Line: y = 1.25x + 5

Equation in Standard Form: 5x - 4y = -20

Step-by-step explanation:

y = mx + b

$\frac{17.5 - 22.5}{10 - 14}$ = $\frac{-5}{-4}$ = $\frac{5}{4}$ or 1.25

y = 1.25x + 5

Ax + By = C (A must be positive, and no fractions or decimals)

y = 1.25x + 5

-1.25x + y = 5

times -4

5x - 4y = -20

7 0

3 years ago

What is 2160 minus 1600 long way

lilavasa [31]

Hey there, Lets solve this problem together.

The First step is to line up the numbers.

$= 2160

- 1600$

$\mathrm{Subtract\:each\:column\:of\:digits,\:starting\:from\:the\:right\:and\:working\:left}$

We calculate $0-0$ the result of which is $0$ 

We calculate $6-0$ the result of which is $6$ .

Since we get a negative number in the next column, we must take 1 from the next column and carry it over to this column. Now the number will be changed to 10.

We calculate $10+1-6$ , and the result is $5$ .

We calculate $2-1-1$ the result of which is $0$ .

Therefore,

$2160 - 1600 = 0560$

8 0

3 years ago

Is (3, 2) a solution of -8x – 2y < 6?

zzz [600]

Answer:

yes

Step-by-step explanation:

To determine if the point is a solution, substitute the coordinates into the left side of the inequality, evaluate and compare with right side.

- 8(3) - 2(2) = - 24 - 4 = - 28 < 6

Thus (3, 2) is a solution

5 0

3 years ago

Read 2 more answers

What does rename mean

schepotkina [342]

It means to give a new name to someone or something.

7 0

3 years ago

The coordinates of polygon ABCD are A(-4,-1), B(-2,3), C(2,2), and D(4,-3). Use these coordinates to complete the sentences belo

PolarNik [594]

Answer:

The perimeter of polygon ABCD, to the nearest thousandth units is

22.227 units

The perimeter of polygon ABCD', to the nearest thousandth, would be 20.980 units

The area of polygon ABCD' is 19.5 units²

Step-by-step explanation:

The coordinates forming the polygon are

A (-4,-1), B(-2,3), C(2,2), and D(4,-3)

The perimeter then is given by the sum of the length of the sides as follows;

Length of line between two X and Y points distance, xi and yj apart is

length XY = $\sqrt{x^2+y^2}$

Therefore, the length between points AB is

length AB = $\sqrt{(-4 - (-2))^2+(-1-3)^2}$

= $\sqrt{(-4 +2)^2+(-4)^2} = \sqrt{-2^2+-4^2} = \sqrt{20}$ = 4.472 units

Similarly, length BC is given by

Length BC = $\sqrt{(-4)^2+1^2} = \sqrt{17}$ = 4.123 units

Length CD = $\sqrt{(-2)^2+5^2} = \sqrt{29}$ = 5.385 units

Length DA = $\sqrt{(8)^2+(-2)^2} = \sqrt{68}$ = 8.246 units

The perimeter is equal to;

length AB + Length BC + Length CD + Length DA

= 4.472 + 4.123 + 5.385 + 8.246 = 22.227 units

If the point D is moved up 2 units and left 1 unit we have

D' = x-1, y+2 where x and y are the coordinates of point D

D(4, -3) → D'((4-1), (-3+2)) = D'(3, -1)

The length D'A = $\sqrt{(7)^2+(0)^2} = \sqrt{49}$ =7 units

The perimeter of polygon ABCD'

length AB + Length BC + Length CD + Length D'A

= 4.472 + 4.123 + 5.385 + 7 = 20.980 units.

The area is given by the determinant of the 3 by 3 matrix using Cramer's Rule as follows

$S_{\bigtriangleup}$ = $(\frac{1}{2})|x_1y_2+x_2y_3+x_3y_1-x_1y_3-x_2y_1-x_3y_2|$

= $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

Triangle ABC we have

A(-4,-1)

B(-2,3)

C(2,2)

$S_{{\bigtriangleup}ABC}$ = $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

$=(\frac{1}{2})|(-4)(3-2)+(-2)(2-(-1)) +2((-1)-3)|$

= $=(\frac{1}{2})|-4-6 -8|= 9 units^2$

Triangle ACD'

A(-4,-1)

C(2,2)

D'(3, -1)

$S_{{\bigtriangleup}ACD'}$ = $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

$=(\frac{1}{2})|(-4)(2+1)+(2)(-1+1) +3((-1)-2)| = \frac{21}{2}$ = 10.5 units²

Area of polygon = $S_{{\bigtriangleup}ABCD'}$ = $S_{{\bigtriangleup}ABC}$ + $S_{{\bigtriangleup}ACD'}$ = (9 + 10.5) units²

Area of polygon ABCD' = 19.5 units².

8 0

3 years ago