Find a solution to the linear equation 13x + y = 26 by filling in the boxes with a valid value of x and y.

Find the sixth term of the sequence 1/2, -3/8, 9/32

sukhopar [10]

Answer:

The sixth term is -243/2048 ⇒ answer B

Step-by-step explanation:

* Lets explain the geometric sequence

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)

# 5000 , 1000 , 200 , 40 , …………………………(÷5)

* General term (nth term) of a Geometric sequence:

# U1 = a , U2 = ar , U3 = ar² , U4 = ar³ , U5 = ar^4

# Un = ar^(n-1), where a is the first term , r is the constant ratio

between each two consecutive terms and n is the position of the

number in the sequence

- Ex: U5 = ar^4 , U7 = ar^6 , U10 = ar^9 , U12 = ar^11

- Lets solve the problem

∵ The sequence is 1/2 , -3/8 , 9/32

- Lets find the constant ratio r

∵ The first term is a = 1/2

∵ The second term is U2 = ar

∵ The second term U2 = -3/8

∴ ar = -3/8

∴ 1/2 r = -3/8 ⇒ multiply both sides by 2

∴ r = -3/4

- Lets find the sixth term

∵ a = 1/2 and r = -3/4

∵ n = 6

∴ U6 = ar^5

∴ U6 = 1/2 (-3/4)^5 = 1/2 × -243/1024 = -243/2048

* The sixth term is -243/2048

8 0

3 years ago

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Priscilla’s grandmother’s fruit salad recipe calls for one part apple, one part orange, four parts strawberry, two parts cherry,

Anvisha [2.4K]

Answer:

Step-by-step explanation:

There are 11 parts of fruit: 4-strawberry, 3- grape, 2, cherry, 1- apple, 1-orange

4/11 from the entine quantity of fruits- strawberry

3/11-grapes

2/11- cherries

1/11- apples

1/11- oranges } ⇒ the quantity of oranges and apples are equal

The biggest part of the fruit- 4/11 - are strawberries

4/11>3/11>2/11>1/11

the smallest part of the fruit- apples and oranges

5 0

2 years ago

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. At a historical la

Alborosie

Answer:

The number of candles will hold 2 candles

And large candle holder will hold 6 candles.

Step-by-step explanation:

Let the number of candles small candle holder have x

And the number of candles large candle holder have y

So, according to the information given in the question:

17 small candle holders means 17 x

and 2 large candle holders means 2y

using a total of 46 candles means $17x+2y=46$ (1)

Similarly, 8 small candle holders and 2 large candle holders, for a total of 28 candles gives:

$8x+2y=28$ (2)

We will solve equation (1) and (2) by elimination method:

Subtractijng the two equations we get:

$9x=18$

$\Rightarrow x=2$

Substitute x=2 in equation(2) we get: $8(2)+2y=28$

$2y=12$

$\Rightarrow y=6$

So, the number of candles will hold 2 candles

And large candle holder will hold 6 candles.

7 0

3 years ago

A rectangular play area is 8 yards long. The expression 56+8x represents the area of the play area in square yards. What express

VikaD [51]

Answer:

w = 7 + x

Step-by-step explanation:

The formula for the area of a rectangle is

A = lw

56 + 8x = 8w

Divide both sides by 8

w = 7 + x

4 0

3 years ago

ABC Car Share Inc. offers car sharing for a $199 yearly fee plus $14/hr for the use of its car share. What equation models the t

Katarina [22]

Total cost equals the yearly fee price plus $14 times number of hours.

T= total cost
n= number of hours

Equation:
T= $199 + $14n

Hope this helps! :)

6 0

3 years ago

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