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2 years ago

What equation is equivalent to 9^x - 3 = 729?

Mathematics

1 answer:

swat322 years ago

6 0

Answer: 9^(x-3) = 9^3

Step-by-step explanation:

Realizing that 729 = 9^3, we can rewrite the equation ...

9^(x -3) = 729

as ...

9^(x -3) = 9^3 . . . . . . matches the second selection

Recognizing that 9 = 3^2, a couple of other equivalent forms can be made.

(3^2)^(x -3) = (3^2)^3

3^(2x-6) = 3^6

or, taking the square root, ...

3^(x -3) = 3^3

None of these forms match any answer choices.

_____

The solution will be found by matching exponents:

x -3 = 3

x = 6

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A group of students is arranging squares into layers to create a project. The first layer has 5 squares. The second layer has 10

True [87]

Answer:

Recursive formula:

$a_1=5;a_n=5+a_{n-1},n>0$

Explanation:

All the shown formulae in the choice list are recursive formulae instead of explicit formulae.

Explicit formulae that represent arithmetic sequences are of the form:

$a_n=a_1+(d-1)n$

That kind of formula permits to determine any term knowing the first term, the number of the term searched, and the common difference (d).

On the other hand, the recursive formulae let you to calculate one term knowing the previous term and the difference.

In this case, the difference in the number of squares of two consecutive terms is:

differece = number of squares in the second layer - number of squares in the first layer.

d = 10 - 5 = 5

Then, the recursive formula is:

$a_1=5;a_n=5+a_{n-1},n>0$

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2 years ago

$34,300 loan at 3.5% for 4 months.

cestrela7 [59]

keeping in mind that 4 months is not even a year, since there are 12 months in a year, 4 months is then 4/12 years.

let's assume is simple interest.

$\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$34300\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years\to \frac{4}{12}\dotfill &\frac{1}{3} \end{cases} \\\\\\ A=34300\left[ 1+(0.035)\left( \frac{1}{3} \right) \right]\implies A= 34300(1.011\overline{6})\implies A=34700.1\overline{6}$

5 0

2 years ago

Enter the decimal equivalent of 6/8

ikadub [295]

Answer:

.75

Step-by-step explanation:

6/8 can be simplified to 3/4, if that helps.

3 0

2 years ago

Square root 2x-1+2=5 what is x equal to?

KATRIN_1 [288]

Because your question isn't specific or formatted exactly, I cannot guarantee that my answer is what you expect.

√2x - 1 + 2 = 5
√(2x + 1)² = 5²
2x + 1 = 25
2x = 24
/2 /2
x = 12

Therefore x = 12.
Proof:

√2x - 1 + 2 = 5
√2(12) - 1 + 2 = 5
  √24 - 1 + 2 = 5
  √25 = 5
5 = 5

8 0

2 years ago

Help me<br> didn’t have enough

kobusy [5.1K]

Answer:

h=0.344

Step-by-step explanation:

4.52-5h=2.8

Subtract 4.52 from both sides

-5h=-1.72

Divide -5 from both sides

h=0.344

4 0

2 years ago