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3 years ago

A triangle with sides of lengths 9,22 and 24 is a right triangle True or false

Mathematics

2 answers:

olya-2409 [2.1K]3 years ago

8 0

Answer:

False

Step-by-step explanation:

Test this theory by using the pythagorean theorem.

for a right triangle with sides a, b and c

if c is they hypotenuse (i.e longest side) then the following must be true:

a² + b² = c² or c = √(a² + b²)

in this case, we assume the longest side to be c=24

also assume a=9 and b = 22

√ (a² + b² )

= √ (9² + 22² )

= √(81 + 484)

= √565

= 23.77 (close but NOT quite 24)

Hence this is NOT a right triangle.

Dmitry [639]3 years ago

5 0

Answer:

False

Step-by-step explanation:

If the triangle is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

9^2 + 22^2 = 24^2

81+484=576

565 = 576

This is false, so the triangle is not a right triangle

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What is the decimal of 64/100

DENIUS [597]

Answer:

0.64

Step-by-step explanation:

Divide the numerator by the denominator. hope this helps! :))

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3 years ago

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F(x)=x^2+6x+3 complete The square and put the equation into vertex form

Svet_ta [14]

Answer:

y=(x+3)^2−6

Step-by-step explanation:

im not 100% but i think its right

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3 years ago

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Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.

-BARSIC- [3]

Answer:

Step-by-step explanation:

Hello, please consider the following.

$3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)$

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

$4^n+17$ is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so $4^k+17$ is divisible by 3

and we check what happens for k+1

$4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17$

$3\cdot 4^k$ is divisible by 3 and

$4^k+17$ is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that $4^n+17$ is divisible by 3 for all positive integers n.

Thanks

4 0

3 years ago

When two computers are working together, they can finish updating software in 9 minutes. How long would they take individually t

tensa zangetsu [6.8K]

First computer takes x min. For 1 min it does 1/x part of work.

Second computer takes (x+24) min. For one min it does 1/(x+24) part of work.

Both computers for one min do (1/x+1/(x+24)) part of work.

At the same time, both computers for one min do 1/9 part of work.

$\frac{1}{x} + \frac{1}{x+24} = \frac{1}{9} 
\\ \\ \frac{x+24+x}{x(x+24)} = \frac{1}{9} 
\\ \\9(2x+24)=x^{2} +24x
\\ \\ 18x+216=x^{2} +24x
\\ \\ x^{2}+6x-216=0
\\ \\ D=b^{2}-4ac=36+4*216 = 900
\\ \\ x= \frac{-b+/- \sqrt{D} }{2a} = \frac{-6+/-30}{2} 
\\ \\ x_{1}=-18, x_{2}=12

We can use only positive number here. So, 

for the first computer x=12 min,

 for second computer x+24=12+24= 36 min

Answer 12 min and 36 min.$

7 0

3 years ago

Find an ordered pair (x, y) that is a solution to the equation 4x + y = 1

Mila [183]

Answer:

(0,1)

Step-by-step explanation:

There are infinite number of (x,y) pairs in a line, so it should be easy to use any value for one of the coordinates (x or y) and find what the other coordinate should be. We can use a simple value that would make our solving easy, for example x = 0. We use this value to replace x in the equation of the line, and solve for y:

$4x+y=1\\4(0)+y=1\\0+y=1\\y=1$

Therefore the pair (0,1) is a solution for the given equation.

5 0

3 years ago