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2 years ago

Fill in the gaps in this sequence: -8, -19, -30, _ , _. (Geometric and arithmetic sequences)

Mathematics

1 answer:

gavmur [86]2 years ago

6 0

-8, -19, -30, -49 , -60

Step-by-step explanation:

Here we have the following sequence :

-8, -19, -30, _ , _

First term of sequence is -8 .
Second term of sequence is -19 : $-8-11 = -19$
Third term of sequence is -30 : $-19-11 = -30$
Fourth term of sequence is : $-30-11 = -49$
Fifth term of sequence is : $-49-11 = -60$

Following sequence was an AP( Arithmetic Progression ) with first term as -8 i.e. $a = -8$ and common difference $d = -11$ having general equation as : $-8 -11n$ .

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How do I use the subtraction theorem to write equivalent expressions?

Andreas93 [3]

The subtraction theorem states that for all real numbers, $a$ and $b$ , $a-b=a+(-b)$ .
(To subtract, we can add the inverse.)
Thus, we can have the these two equivalent expressions.

$3 - 2 = 3 + (-2) = 1\\ \\ 5 - (-2) = 5 + 2 = 7$

3 0

2 years ago

6,859^1/3 can be written as

zloy xaker [14]

Answer:

∛6859 ( = 19).

Step-by-step explanation:

6,859^1/3 = ∛6859 (the cube root of 6859).

Using a calculator we see that this = 19.

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2 years ago

Solve the equation X³+2X²-5X -6

Natali [406]

Answer: x = {-1, -3, 2}

Step-by-step explanation:

x³ + 2x² - 5x - 6 = 0

Use the rational root theorem to find the possible roots: ±1, ±2, ±3, ±6

Use Long division, Synthetic division, or plug them into the equation to see which root(s) work (result in a remainder of zero).

I will use Synthetic division. Let's try x = 1

1 | 1 2 -5 -6

| ↓ 1 3 -2

1 3 -2 -8 ← remainder ≠ 0 so x = 1 is NOT a root

Let's try x = -1

- 1 | 1 2 -5 -6

| ↓ -1 -1 6

1 1 -6 0 ← remainder = 0 so x = -1 is a root!

The coefficients of the reduced polynomial are: 1, 1, -6 --> x² + x - 6

Factor: x² + x - 6

(x + 3)(x - 2)

Set those factors equal to zero to solve for x:

x + 3 = 0 --> x = -3

x - 2 = 0 --> x = 2

Using Synthetic Division and Factoring the reduced polynomial, we found

x = -1, -3, and 2

6 0

2 years ago

If each cube has edges .5 inches long, what is the volume of the prism?

Gre4nikov [31]

.20 is the correct answer

6 0

2 years ago

Read 2 more answers

David inherited some money from his uncle. He invested half of the money with Bernie

ValentinkaMS [17]

Given:
Let x be the whole amount inherited.
1/2 * x - invested with Bernie Madoff
1/3 * x - lost due to identity theft
1/8 * x - lost in casino
40,000 - remainder

x - x/2 - x/3 - x/8 = 40,000

LCM:
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
3: 3, 6, 9, 12, 15, 18, 21, 24
8: 8, 16, 24,

x * 24/24 = 24x / 24
x/2 * 12/12 = 12x / 24
x/3 * 8/8 = 8x / 24
x/8 * 3/3 = 3x / 24
40,000 * 24/24 = 960,000 / 24

24x/24 - 12x/24 - 8x/24 - 3x/24 = 960,000/24
(24x - 12x - 8x - 3x)/24 = 960,000/24
x/24 = 960,000/24
24 * x/24 = 24 * 960,000/24
x = 960,000

x = 960,000 initial inheritance
x/2 = 960,000/2 = 480,000 invested with Bernie Madoff
x/3 = 960,000/3 = 320,000 lost due to identity theft
x/8 = 960,000/8 = 120,000 lost in the casino
40,000 - remaining amount.

960k - 480k - 320k - 120k = 40k
40k = 40k

3 0

2 years ago