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3 years ago

What is the length of the unknown leg in the right triangle?

Mathematics

1 answer:

ankoles [38]3 years ago

6 0

Answer:

Step-by-step explanation:

The Pythagorean Theorem can be used to determine an unknown side of a right triangle when two sides are known.

It states that a^2+b^2=c^2.

This is where a and b are the legs of the triangle, and c is the hypotenuse.

If you're unclear on this, you can draw a diagram to help you visualize it.

Hence, we can plug the given information into this formula.

a^2+8^2=(√73)^2

Simplify.

a^2+64=73

Subtract 64 from both sides.

a^2+64-64=73-64

a^2=9

Find the square root of both sides.

a=3

The length of the unknown leg in the right triangle is 3 units.

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The sequence shown: 28, 22, 16, 10...)

noname [10]

Recursive formula: $a_n = a_{n-1} -6$

Explicit Formula: $a_n = 34-6n$

35th term: -176

Sum of first 35 terms: -2590

Step-by-step explanation:

Given sequence is:

28, 22, 16, 10

First of all, we have to determine if this is an arithmetic sequence or geometric sequence. for this purpose we will find the common difference.

Here

$a_1 = 28\\a_2 = 22\\a_3 = 16$

$d = a_2-a_1 = 22-28 =-6\\d = a_3-a_2 = 16-22 = -6$

As the common difference is same the sequence is an arithmetic sequence

Recursive Formula:

Recursive formula is the formula that uses the previous term and common difference to find the next term

As the common difference is -6

The recursive formula will be:

$a_n = a_{n-1} +(-6)\\a_n = a_{n-1} -6$

Explicit formula:

The explicit formula for an arithmetic sequence is:

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

Putting the value of d and a_1

$a_n = 28 + (n-1)(-6)\\= 28 -6n+6\\= 34-6n$

35th term of the sequence:

To find the 35th term, putting n = 35

$a_{35} = 34-6(35)\\a_{35} = 34 - 210\\a_{35} = -176$

Sum:

$a_1 = 28\\a_{35} = -176$

The formula for sum of finite arithmetic sequence is:

$S_n = \frac{n}{2} (a_1+a_n)$

As we have to find sum of 35 terms, the formula will be:

$S_{35} = \frac{35}{2}(28-176)\\S_{35} = 17.5 (-148)\\=-2590$

Hence,

Recursive formula: $a_n = a_{n-1} -6$

Explicit Formula: $a_n = 34-6n$

35th term: -176

Sum of first 35 terms: -2590

Keywords: Arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

5 0

3 years ago

Help me in math aaaaaaa

Dominik [7]

Answer:

105

Step-by-step explanation:

180 - 140 = 40

180 - 145 = 35

35+ 40 = 75

180 - 75 = 105

a = 5

5 0

3 years ago

Read 2 more answers

Nadeem has 160 bottle caps in his bottle cap collection. He has 32 times more bottle caps in his collection then Benson. How man

anygoal [31]

Answer:

Benson has 5,120 bottle caps.

Step-by-step explanation:

160x32

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Answer:

The answer is All of the above

Step-by-step explanation:

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Round 6.8 to nearest hundredth

Andrej [43]

Answer:

6.8

Step-by-step explanation:

The number is already rounded to the nearest tenth and hundredth.

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