4=2(c-6)-4 solve for c

Find the next term is in the explicit and recursive rule for the in term of the sequence. NO LINKS!!!

BARSIC [14]

9514 1404 393

Answer:

5) 729, an=3^n, a[1]=3; a[n]=3·a[n-1]

6) 1792, an=7(4^(n-1)), a[1]=7; a[n]=4·a[n-1]

Step-by-step explanation:

The next term of a geometric sequence is the last term multiplied by the common ratio. (This is the basis of the recursive formula.)

The Explicit Rule is ...

$a_n=a_1\cdot r^{n-1}$

for first term a₁ and common ratio r.

The Recursive Rule is ...

a[1] = a₁

a[n] = r·a[n-1]

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5. First term is a₁ = 3; common ratio is r = 9/3 = 3.

Next term: 243×3 = 729

Explicit rule: an = 3·3^(n-1) = 3^n

Recursive rule: a[1] = 3; a[n] = 3·a[n-1]

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6. First term is a₁ = 7; common ratio is r = 28/7 = 4.

Next term: 448×4 = 1792

Explicit rule: an = 7·4^(n-1)

Recursive rule: a[1] = 7; a[n] = 4·a[n-1]

7 0

3 years ago

Solve the system of linear equations.<br> 3x + 5y = -2<br> 2x - y = 3

natita [175]

Answer:

3x + 5y = -2 is x= −5 /3 y+ −2 /3

2x - y = 3 is x= 1 /2 y+ 3 /2

Step-by-step explanation:

7 0

2 years ago

A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythag

Sveta_85 [38]

Answer:

$\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

$\displaystyle A_{\text{surface}}=B+\dfrac{1}{2}\times P \times s$

where B stands for Base area

and P for Base Parimeter

so

$\sf\displaystyle \: 144=(8 \times 8)+\dfrac{1}{2}\times (8 \times 4) \times s$

now we need our algebraic skills to figure out s

simplify parentheses:

$\sf\displaystyle \: 64+\dfrac{1}{2}\times32\times s = 144$

reduce fraction:

$\sf\displaystyle \: 64+\dfrac{1}{ \cancel{ \: 2}}\times \cancel{32} \: ^{16} \times s = 144 \\ 64 + 16 \times s = 144$

simplify multiplication:

$\displaystyle \: 16s + 64 = 144$

cancel 64 from both sides;

$\displaystyle \: 16s = 80$

divide both sides by 16:

$\displaystyle \: \therefore \: s = 5$

now we'll use Pythagoras theorem to figure out height

according to the theorem

$\displaystyle \: {h}^{2} + (\frac{l}{2} {)}^{2} = {s}^{2}$

substitute the value of l and s:

$\displaystyle \: {h}^{2} + (\frac{8}{2} {)}^{2} = {5}^{2}$

simplify parentheses:

$\displaystyle \: {h}^{2} + (4 {)}^{2} = {5}^{2}$

simplify squares:

$\displaystyle \: {h}^{2} + 16 = 25$

cancel 16 from both sides:

$\displaystyle \: {h}^{2} = 9$

square root both sides:

$\displaystyle \: \therefore \: {h}^{} = 3$

recall the formula of a square pyramid

$\displaystyle V_{pyramid}=\dfrac{1}{3}\times A\times h$

where A stands for Base area (l²)

substitute the value of h and l:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times \{8 \times 8 \}\times 3$

simplify multiplication:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times 64\times 3$

reduce fraction:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{ \cancel{ 3 \: }}\times 64\times \cancel{ \: 3}$

hence,

$\sf\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

8 0

2 years ago

A rectangle has sides that measure 2 x + 11 units long and 10 x + 1 units long. What is the expression that represents the perim

HACTEHA [7]

Answer:

(24x + 24) units

Step-by-step explanation:

A rectangle is a shape that has four sides in which all angles are equal and opposite sides are equal and parallel to each other. The perimeter of a rectangle is the sum of all its sides. Since opposite sides are equal, the perimeter is given as:

Perimeter = 2(length + width)

Since the sides of the rectangle are 2 x + 11 units long and 10 x + 1 units long. Hence:

Perimeter = 2(2x + 11 + 10x + 1)

Perimeter = 2(2x + 10x + 11 + 1) = 2(12x + 12)

Perimeter = (24x + 24) units

7 0

2 years ago

A rectangular billboard is 9.35 meters wide and 6.82 meters tall. What is the perimeter of the billboard in meters?

White raven [17]

Answer:

32.34 meters

Step-by-step explanation:

All you need to do is label the rectangle with the information given. 9.35 for width, and 6.82 for length.

Next, just fill in the other sides and add. Because it's a rectangle, then you should be able tp label the blank sides.

Next, just add all the sides together and then you'll get your perimeter!

9.35 + 9.35+ 6.82 + 6.82= 32.34

8 0

3 years ago