in a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b what is the value of b, if c=13, a=12?

Answer:

Please check the explanation.

Step-by-step explanation:

(a) What is the recursive rule for the sequence?

Given the sequence

6, 18, 54, 162,...

Please note that each successive term is 3 times the previous term.

i.e. 18 = 6×3, 54 = 18×3, 162 = 54×3

Here, r = 3 is the common multiplier

In other words, every next term can be obtained by multiplying the previous term by a number 'r', using the recursive formula

[tex]a_n=a_{n-1}\times r[/tex]

Here, aₙ is r times the previous term aₙ₋1.

For example, in order to determine the 2nd term a₂, just put n=2 in the recursive formula

[tex]a_n=a_{n-1}\times r[/tex]

so substituting r = 3, and n = 1 in the recursive formula

[tex]a_2=a_{2-1}\times 3[/tex]

[tex]a_2=a_1\times \:3\:\:\:\:\:\:[/tex]

as

a₁ = 6

so

[tex]a_2=6\times \:3\:\:\:\:\:\:[/tex]

[tex]a_2=18[/tex]

(b) What is the iterative rule for the sequence?

Given the sequence

6, 18, 54, 162,...

A geometric sequence has a constant ratio 'r' and is defined as

[tex]a_n=a_1\cdot r^{n-1}[/tex]

[tex]\frac{18}{6}=3,\:\quad \frac{54}{18}=3,\:\quad \frac{162}{54}=3[/tex]

The ratio of all the adjacent terms is the same and equal to, so

r = 3

as

a₁ = 6

so substituting r = 3 and a₁ = 6 in the nth term of the sequence

[tex]a_n=a_1\cdot r^{n-1}[/tex]

[tex]a_n=6\cdot \:3^{n-1}[/tex]

Thus, the iterative rule for the sequence is

a) The recursive rule for the sequence is [tex]a_n=3a_{n-1}[/tex]

b) The iterative rule for the sequence is [tex]a_n=2(3^n)[/tex]

The given sequence is:

6, 18, 54, 162, …

The common ratio, r = 18/6

r  =  3

Let the last term be [tex]a_n[/tex]

Let the preceding term be [tex]a_{n-1}[/tex]

The recursive rule for the sequence is given as:

[tex]a_n=a_{n-1}r\\\\a_n=3a_{n-1}[/tex]

b) The iterative rule is gotten by using the formula:

[tex]a_n=ar^{n-1}[/tex]

Substitute a = 6 and r = 3 into the formula above

[tex]a_n=6(3)^{n-1}\\\\a_n=\frac{6}{3}(3^n )\\\\a_n=2(3^n)[/tex]

Learn more on sequence here: https://brainly.com/question/6561461

Answer:

a. always positive

Step-by-step explanation:

Alex learning?

Answer:

4.24

Step-by-step explanation:

By geometric mean property

[tex] {x}^{2} = 6 \times 3 \\ \\ {x}^{2} = 18 \\ \\ x = \pm\sqrt{18} \\ \\ x = \pm 4.24264069 \\ \\ \because \: x \: can \: not \: be \: - ve \\ \\ \therefore \: x = 4.24 \: units \\ [/tex]

Answer:

Option (a) [tex]\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}[/tex]

Step-by-step explanation:

The given expression is :

[tex]\dfrac{3}{1{\cdot} 2}+\dfrac{3}{2{\cdot} 3}+\dfrac{3}{3{\cdot} 4}+\dfrac{3}{4{\cdot} 5}+....[/tex]

We need to rewrite the sum using sigma notation.

The numerator is 3 in all terms.

At denominator, in first term (1)(2), in second term (2)(3) and so on.

A general term for the denominator is k(k+1).

Sigma notation is :

[tex]\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}[/tex]

Hence, the correct option is (A).

Answer:

1) the probability that he wins the second game is 0.45

2) the probability he wins the first game given that he won the second game is 0.333  

3) Expected Value is $ 1.5 and the variance is 0.75

Step-by-step explanation:

Given the data in the question;

Let Win1 represent first game victory

and Loss1 represent first game loss

Let Win2 denote second game victory

and Loss2 denote second game loss

now from the Tree diagram of Daniel;

P ( Win1 ) = 0.6

P ( Loss1 ) = 0.4

P ( Win2 | Win1 ) = 0.25

P ( Loss2 | Win1 ) = 0.75

P ( Win2 | Loss1 ) = 0.75

P ( Loss2 | Loss1 ) = 0.25

1) probability that he wins the second game will be;

P ( Win2 )  =  [P ( Win1 ) × P ( Win2 | Win1 )] + [P ( Loss1 ) × P ( Win2 | Loss1 ) ]

we substitute

= [0.6 × 0.25] + [0.4 * 0.75] = 0.45

Therefore the probability that he wins the second game is 0.45

2)

If he wins the second game, what is the probability that he also won the first game  will be;

{From Bayes' Theorem}

P ( Win1 | Win2 )  =  P ( Win1 ) × P ( Win2 | Win1 ) / P ( Win2 )

= 0.6 × 0.25 / 0.45 = 0.333  

Therefore the probability he wins the first game given that he won the second game is 0.333  

c)

winnings       probability

$0                  0.4 × 0.25 = 0.1

$1                   0.6 × 0.75 = 0.45

$2                  0.4 × 0.75 = 0.3

$3                  0.6 × 0.25 = 0.15

so Expected Value = ∑( winnings × individual win probability)

=  (0 × 0.1) + (1 × 0.45) + (2 × 0.3) + (3 × 0.15)

= 0 + 0.45 + 0.6 + 0.45

= $ 1.5

Variance = ∑( X² ) - (∑(X))²

∑( X² ) = Summation of ( Winnings² × Probability of Each Win )

so

Variance = 0 × 0 × 0.1 + 1 × 1 × 0.45 + 2 × 2 × 0.3 + 3 × 3 × 0.15 - ( 1.5 )²

Variance = 0 + 0.45 + 1.2 + 1.35 - 2.25

Variance = 3 - 2.25

Variance = 0.75

Therefore Expected Value is $ 1.5 and the variance is 0.75

Answer:

$90

Step-by-step explanation:

To find the original price, divide 63 by 0.7:

63/0.7

= 90

So, the original price is $90

Answer:

$90.00

Step-by-step explanation:

First of all let x be the price of the pair of shoes that you are trying to find.

next since we have 30percent off that price we have

x - 0.30x = 0.70x

which in turn is equal to 63 dollars

so our expression is

0.70x = $63

x = 63 / 0.70

= $ 90.00

Answer:

-54+17=    -37  LESS

35+(-61)=  -26

Step-by-step explanation:

plz mark B R A I N L I E S T :P

Answer:

5

Step-by-step explanation:

To find the slope of a line, you need to find the [tex]\frac{rise}{run}[/tex] between two points. I will be calculating the slope using the two points (2, 10) and (3, 15).

Slope = [tex]\frac{rise}{run}[/tex]

          = [tex]\frac{15-10}{3-2}[/tex]

          = 5

Answer:

The ratio of that is 2:1

Step-by-step explanation:

Thats all

Answer:

The answer is (-3X+6i)(x+2i)

Step-by-step explanation:

You can do this by plugging in the answers in the equations and get that (-3x+6i)(x+2i) equals the following expression.

Answer: I think your answer should be x=7, please mark me as brainliest! :D

Step-by-step explanation:

Answer:

70 < x < 105 and 0 < y ≤ 60

Step-by-step explanation:

The constraints that represent this real-world problem are; 70 < x < 105 and 0 < y ≤ 60 where x is the temperature and y is the number of people on your trip.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

Given:

The Range of temperature is between 70 and 105 degrees.

So, x lies between these two temperatures so x must be greater than 70 degrees but less than 105 degrees.

Therefore, x > 70and x < 105.

On combining these two inequalities we get,

70 < x < 105

Now, number of people that can come for the trip is 60.

y represents the number of people for the trip. So, y can be at most 60.

Or, y ≤ 60 must be less than or equal to 60 and is given as:

Hence, the constraints are:

70 < x < 105 and 0 < y ≤ 60

The constraints that represent this real-world problem are; 70 < x < 105 and 0 < y ≤ 60 where x is the temperature and y is the number of people on your trip.

Learn more about inequality ;

brainly.com/question/14164153

#SPJ2

Answer:

3.2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

s

Step-by-step explanation:

Answer:

17/70

Step-by-step explanation:

First use PEMDAS which is the order to solve questions like these.

Parenthesis

Exponents

Multiplication

Division

Addition

and Subtraction

There is one parenthesis which has a (-1/4) so let's start with that, we know that when there is a negative and a positive sign the negative out rules the positive

3/5-1/4 divided by 7/10      (Sorry I don't have the division sign on my device)

There are no exponents or multiplication but there is division

-1/4 divided by 7/10 is -5/14

3/5-5/14 is 17/70

Thus, our answer is 17/70

Answer:

W=−5

r=3

hope this helps!!

Answer:

11

Step-by-step explanation:

32.50-7.50=25

225/25=11

Answer:

Step-by-step explanation:

Given

Need to complete square on the left side of equation

The square should be in the form of:

We see a = x therefore

So the missing constant term is 9/64

Answer:

No, it cannot.

Step-by-step explanation:

When you multiply a factor 1 or greater, the product gets larger. However, when you are multiplying decimals, the product gets smaller. (Ex. When you multiply 0.1 [or 0.10], you are making the product ten times as small.)

Answer:

the points are not joined hence not a function

Answer:

Imma say its option 2 thats the only one that makes any sense good luck

Step-by-step explanation:

Answer:

415 ÷ 3.4 = 122.058

Step-by-step explanation:

Answer:0.1072

Step-by-step explanation:

Siri

Answer:

All Of The Number At The Top

Step-by-step explanation:

Like Said, The Tables Functions f

So, Basically It's A Challenge,

All Of The Numbers In Row X From Above Table

I Hope You Found This Answer Helpful

Good Day

You'll Get 100% Don't Stress It✨

By: LocalLesMara

Answer:

720

Step-by-step explanation:

600*.2=120

120+600

720

Answer:

720 dollars

Step-by-step explanation:

find 20% of 600 dollars

[tex]\frac{20}{100} * 600[/tex]

= 120 dollars

600 + 120

= 720

I hope this helped!

please mark me as brainliest