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3 years ago

6x−4=2(3x−2)

Mathematics

2 answers:

Eduardwww [97]3 years ago

8 0

Simply,there is no solution.

sashaice [31]3 years ago

5 0

Answer:

0=0

Step-by-step explanation:

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What is a formula for the nth term of the given sequence? 36, 24, 16...

SpyIntel [72]

Answer:

The formula to find the nth term of the given sequence is 54 · $\frac{2}{3} ^{n}$

Step-by-step explanation:

The formula for nth term of an geometric progression is :

$a_{n} = \frac{a_{1}(r^{n})}{r}$

In this example, we have $a_{1}$ = 36 (the first term in the sequence) and

r = $\frac{2}{3}$ (the rate in which the sequence is changing).

Knowing what the values for r and $a_{1}$ are, now we can solve.

$a_{n} = \frac{a_{1}(r^{n})}{r}$ = $\frac{36 (\frac{2}{3} ^{n}) }{\frac{2}{3} }$ = 54 · $\frac{2}{3} ^{n}$

Therefore, the formula to find the nth term of the given sequence is

54 · $\frac{2}{3} ^{n}$

3 0

3 years ago

Prove that for all n in the naturals, n(n+1)(n+2) is divisible by 3

DerKrebs [107]

By induction:

It's true for $n=1$ , since $1\cdot2\cdot3$ clearly contains a factor of 3.

Suppose it's true for $n=k$ , that $k(k+1)(k+2)$ is divisible by 3. Then

$(k+1)(k+2)(k+3)=\dfrac{k(k+1)(k+2)(k+3)}k=\dfrac{3m(k+3)}k$

where $m$ is an integer. This reduces to

$\dfrac{3m(k+3)}k=3m+9\dfrac mk$

and both terms are clearly multiples of 3. We know that $\dfrac mk$ is an integer since we had set $m=k(k+1)(k+2)$ previously, which implies $m$ is a multiple of $k$ . So the statement is true.

6 0

3 years ago

In 1987 the average price of gasoline was $0.94. Today the price of gas is about $3.00. What is the percent increase from 1987 t

aleksklad [387]

Answer:

219.15% (2DP)

Step-by-step explanation:

The difference between 0.94 and 3 is 2.06

Percentage change = (change in value/ original amount) X100.

(2.06/0.94) X 100

Which equals 219.15%

The price of gas has increased by 219.15%

3 0

3 years ago

Solve the system: -5x+6y=55 4x+3y=34 Write down your solution.

svetlana [45]

Answer:

(1, 10)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

-5x + 6y = 55

4x + 3y = 34

Step 2: Rewrite Systems

4x + 3y = 34

Multiply everything by -2: -8x - 6y = -68

Step 3: Redefine Systems

-5x + 6y = 55

-8x - 6y = -68

Step 4: Solve for x

Elimination

Combine equations: -13x = -13
Divide -13 on both sides: x = 1

Step 5: Solve for y

Define equation: 4x + 3y = 34
Substitute in x: 4(1) + 3y = 34
Multiply: 4 + 3y = 34
Isolate y term: 3y = 30
Isolate y: y = 10

4 0

2 years ago

According to a survey of college students, the use of social media varies widely according to age. Based on the survey, what is

Yanka [14]

Answer:

C. 65

Step-by-step explanation:

The table which shows the results of the survey are attached below.

From the table:

Total Number of non-social media users = 71
Number of non-social media user aged 28 and up = 46

Therefore, the probability that a non-social media user is an older student aged 28 and up

$=\dfrac{\text{ Number of non-social media user aged 28 and up}}{\text{ Total Number of non-social media users}}\\\\=\dfrac{46}{71} \times 100\\\\=64.7\\\\\approx 65\%$

The probability that a non-social media user is an older student aged 28 and up is 65%.

The correct option is C.

4 0

3 years ago