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krok68 [10]
3 years ago
7

In a geometric sequence, the ratio between consecutive terms is...

Mathematics
1 answer:
Leokris [45]3 years ago
6 0
<h3>Answer: The same or equal</h3>

========================================================

Explanation:

Consider an example like 3, 6, 12, 24, 48, ...

The ratio between consecutive terms is

  • 6/3 = 2
  • 12/6 = 2
  • 24/12 = 2
  • 48/2 = 2

Each time we divide any given term over its previous one, we get the same ratio 2. We call this the common ratio. In terms of notation, the variable r is used for the common ratio, so r = 2 in this case.

As another example, the geometric sequence 5, 50, 500, 5000, ... has r = 10 as the common ratio because we multiply each term by 10 to get the next one. Moving forward has us multiply by r, moving backward and we divide by r. The value of r cannot be zero, but it can be negative.

An example with r being negative would be something like

1, -1, 1, -1, 1, -1, ....

we just bounce back and forth between those two values. In this case, r = -1.

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20 POINTS! + BRAINLIEST!
g100num [7]

Answer:

= x^4 -x^3 -4x^2 -3

Step-by-step explanation:

f(x) = x^4 -x^2 +9

g(x) = x^3 +3x^2 +12

We want to find f-g

(f-g) (x) = x^4 -x^2 +9 - (x^3 +3x^2 +12)

Distribute the minus sign

(f-g) (x) = x^4 -x^2 +9 - x^3 -3x^2 -12

            = x^4 -x^3 -4x^2 -3

3 0
3 years ago
Read 2 more answers
If h(x)=(f o g) (x) and h(x)= ∛x+3, find g( x) if f(x)= ∛x+2 (picture attached)
Aleksandr-060686 [28]

Answer:

g(x) = x+1

Step-by-step explanation:

Informally, you can see that the function h(x) takes the root of a value that is 1 more than the value under the same radical in f(x). This suggests that adding 1 to x in f(x) will give you h(x). That is, ...

h(x) = f(x+1) = f(g(x))

so

g(x) = x+1

_____

More formally, you can apply the inverse of the function f(x) to the equation ...

h(x) = f(g(x))

f^-1(h(x)) = f^-1(f(g(x))) . . . inverse function applied

f^-1(h(x)) = g(x) . . . . . . . . . simplified

Now f^-1(x) can be found by solving for y in ...

x = f(y)

x = ∛(y+2) . . . . . . . . . definition of f(y)

x^3 = y+2 . . . . . . . . . cube both sides

x^3 -2 = y = f^-1(x) . . . subtract 2 from both sides

So, f^-1(h(x)) is ...

f^-1(h(x)) = g(x) = (∛(x+3))^3 -2 = x+3 -2

g(x) = x+1

5 0
3 years ago
Suppose that y varies directly with x. Given x=4 when y=20.<br> Find y when x = 3
scoray [572]

Answer:

y = 15

Step-by-step explanation:

Given: y varies directly with x, x=4 when y=20

To find:  y when x = 3

Solution:

As y varies directly as x, it means that as x increases, y also increases by the same factor.

As y varies directly with x,

y=kx

Here, k is a constant

As x = 4 when y = 20,

20=4k\\k=\frac{20}{4}=5\\\Rightarrow y=5x

Put x = 3

y= 5(3) = 15

4 0
2 years ago
How many times larger is a 10pound dog from a hamster weighing 5/8 pound
lutik1710 [3]
 it would be 16 times larger
6 0
3 years ago
For a party, the family bought 24 pizzas for $12.50 each and 36 bottles of soda for $1.20 each. How much did the family spend on
xxTIMURxx [149]

Answer:

1) The amount the family spent on pizza is $300

2) The amount the family spent on soda is $43.2

3) The amount the family spent in all is $343.2

Step-by-step explanation:

The number of pizzas bought by the family = 24

The price of each pizza = $12.50

The number of bottles of soda the family bought = 36

The price of each bottles of soda = $1.20

1) The amount the family spent on pizza = 24 × $12.50 = $300

2) The amount the family spent on soda = 36 × $1.20 = $43.2

3) The amount the family spent in all = The amount the family spent on pizza + The amount the family spent on soda

∴ The amount the family spent on soda = $300 +$43.2 = $343.2.

7 0
2 years ago
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