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3 years ago

Which set of numbers could represent the side lengths of a right triangle?

Mathematics

1 answer:

sveticcg [70]3 years ago

8 0

Answer: D) 8, 15, 17

<u>Step-by-step explanation:</u>

In order for three side lengths to represent a right triangle, they must satisfy the Pythagorean Theorem: a² + b² = c² where c is the largest side.

A) 2² + 3² = 4²

4 + 9 = 16

13 = 16 FALSE

B) 4² + 5² = 6²

16 + 25 = 36

41 = 36 FALSE

C) 6² + 9² = 12²

36 + 81 = 144

117 = 144 FALSE

D) 8² + 15² = 17²

64 + 225 = 289

289 = 289 TRUE!

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We say that an integer a is a type 0 integer if there exists an integer n such that a = 3n. An integer a is a type 1 integer if

Delicious77 [7]

Answer:

<em>Proof below</em>

Step-by-step explanation:

Let's assume a is a type 1 integer. By definition, it means we can find an integer n such that

a=3n+1

We need to prove $a^2$ is a type 1 integer

Expanding

$a^2=(3n+1)^2=9n^2+6n+1$

If $a^2$ is a type 1 integer, then we should be able to find an integer m such as

$a^2=3m+1$

Equating

$a^2=3m+1=9n^2+6n+1$

solving for m

$m=3n^2+2n$

Since we know n is an integer, then the expression of m gives an integer also. Having found the required integer m, the assumption is proven

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3 years ago

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The temperature in the late afternoon was -7.5° it dropped 5° by early evening and then dropped another 85° by midnight what was

dalvyx [7]

Step-by-step explanation:

i think you missed a decimal place for 8.5°

when temperatures drop it means minus

-7.5-5-8.5= -21°

6 0

3 years ago

(easy)

Andreyy89

Answer:

<h2>9 weeks</h2>

Step-by-step explanation:

Sol had $1535 in his savings

has been spending $30 each week for guitar lessons.

If his current balance is $1265

find:

how many weeks has he been taking lessons?

$1535 - $1265 = $270

<u> $270 </u> = 9 weeks

$ 30 per week

7 0

3 years ago

the population of woodstock, Ga is about 23,896 people,and the city encompasses 11.3 square miles. What is the population densit

aev [14]

The population density of Woodstock is 2114.7 people per square mile

Step-by-step explanation:

Population density is the number of people per square kilometer or per square mile

Given

Number of people = 23896

Area = 11.3 square miles

The population density is given by the formula:

$Population\ density=\frac{Number of People}{Area}\\=\frac{23896}{11.3}\\=2114.69=>2114.7\ people\ per\ square\ mile$

Hence,

The population density of Woodstock is 2114.7 people per square mile

Keywords: Population density, Area

Learn more about population density at:

#LearnwithBrainly

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3 years ago

What games do you play ?

kherson [118]

Mario Cart
What about you?

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2 years ago

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