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3 years ago

Is 5, 12, 14 a pythagorean triple ? Show why or why not?

Mathematics

2 answers:

Ket [755]3 years ago

3 0

Answer:

Step-by-step explanation:

Let's test these values using the Pythagorean Theorem.

a^2+b^2=c^2

where a and b are the legs and c is the hypotenuse.

a and b are the legs, or the shorter sides. 5 and 12 are the shorter sides, so they are a and b.

c is the hypotenuse, or the longest side. 14 is the longest side, so it is c.

5^2+12^2=14^2

Evaluate all the exponents

25+144=196

Add 25 and 144

169=196

169 $\neq$ 196

169 is not equal to 196, so 5, 12 and 14 cannot be a Pythagorean Triple

-Dominant- [34]3 years ago

3 0

Answer:

Step-by-step explanation:

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Each of the six letters stands for a different number, 1 through 9. Using the three clues, can you deduce the number represented

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Answer:

A = 9

B = 2

C = 5

D = 1

E = 8

F = 7

Step-by-step explanation:

A 9 B 2 C 5 = 16

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3 years ago

Is 73 a prime number

lora16 [44]

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3 years ago

Dwayne drove 18 miles to the airport to pick up his father and then returned home. On the return trip he was able to drive an av

Nesterboy [21]

Answer:

30 mph

Step-by-step explanation:

Let d = distance (in miles)

Let t = time (in hours)

Let v = average speed driving to the airport (in mph)

⇒ v + 15 = average speed driving from the airport (in mph)

Using: distance = speed x time

$\implies t=\dfrac{d}{v}$

Create two equations for the journey to and from the airport, given that the distance one way is 18 miles:

$\implies t=\dfrac{18}{v} \ \ \textsf{and} \ \ t=\dfrac{18}{v+15}$

We are told that the total driving time is 1 hour, so the sum of these expressions equals 1 hour:

$\implies \dfrac{18}{v} +\dfrac{18}{v+15}=1$

Now all we have to do is solve the equation for v:

$\implies \dfrac{18(v+15)}{v(v+15)} +\dfrac{18v}{v(v+15)}=1$

$\implies \dfrac{18(v+15)+18v}{v(v+15)}=1$

$\implies 18(v+15)+18v=v(v+15)$

$\implies 18v+270+18v=v^2+15v$

$\implies v^2-21v-270=0$

$\implies (v-30)(v+9)=0$

$\implies v=30, v=-9$

As v is positive, v = 30 only

So the average speed driving to the airport was 30 mph

(and the average speed driving from the airport was 45 mph)

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Answer:

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Step-by-step explanation:

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