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Makovka662 [10]
3 years ago
10

Which number forms a Pythagorean Triple with 8 and 10? A: 6 B: 15

Mathematics
2 answers:
daser333 [38]3 years ago
6 0
Are 6 and 15 the legs of the triangle?
laila [671]3 years ago
3 0
(8•8)+(6•6)=(10•10)
64+36=100
100=100
The answer is B
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For which pairs of function is (f x g ) (x) = 12x
Contact [7]
The answer is (f * g) (x) = 12x
4 0
3 years ago
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How many sets of three consecutive integers are there in which the sum of the three integers equals their product?
skad [1K]

Answer:

3

Step-by-step explanation:

since the 3 integers are consecutive, we are dealing with x, x+1, x+2.

and their sum is the same as their product :

x + (x + 1) + (x + 2) = x(x + 1)(x + 2)

3x + 3 = x(x² + 3x + 2) = x³ + 3x² + 2x

x³ + 3x² - x - 3 = 0

this is a polynomial of third degree.

and as such it has 3 solutions.

of course, it could be that some of them are the same or are even in the realm of complex numbers (i = sqrt(-1)), but usually these 3 solutions are different real numbers.

I tried x=1 just to see, and, hey, it is a solution for this equation.

x = 1 means that the other 2 consecutive integers are 2 and 3.

and indeed, 1+2+3 = 1×2×3 = 6.

now it is easier to find the other 2 solutions, as a zero solution can be expressed as a factor of the whole expression.

for x = 1 the factor term is (x - 1), as this term is then turning 0, when x = 1.

I can divide the main expression by this factor and then analyze the quotient about the other 2 solutions.

x³ + 3x² - x - 3 : x - 1 = x² + 4x + 3

- x³ - x²

----------------

0 4x² - x

- 4x² - 4x

-----------------------

0 + 3x - 3

- 3x - 3

---------------------------

0 0

so, the original expression can be written as

(x² + 4x + 3)(x - 1).

now we need to find the 2 zero solutions for x²+4x+3

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 4

c = 3

so,

x = (-4 ± sqrt(4² - 4×1×3))/(2×1) =

= (-4 ± sqrt(16 - 12))/2 = (-4 ± sqrt(4))/2 =

= (-4 ± 2)/2 = -2 ± 1

x1 = -2 + 1 = -1

x2 = -2 - 1 = -3

so, we have the additional solutions :

-1 0 1

-3 -2 -1

-1 + 0 + 1 = -1×0×1 = 0

-3 + -2 + -1 = -3×-2×-1 = -6

and there we have it fully proven :

there are 3 different sets of 3 consecutive integers with the same sum as product.

4 0
2 years ago
Belinda git 18 out of 20 correct on a science test what percent of the questions did Belinda get correct
sveta [45]
92% of the questions were correct.
4 0
3 years ago
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WILL MARK BRAINLEIST please give me a good summary of the Pythagorean Theorem
Rudik [331]

Answer:

The Pythagorean Theorem is a statement about triangles containing a right angle. The Pythagorean Theorem states that: "The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides."

Step-by-step explanation:

6 0
3 years ago
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Jim was thinking of a number. Jim adds 20 to it, then doubles it and gets an answer of 99.2. What was the original number?
azamat

Alright, lets get started.

Jim was thinking of a number.

Suppose the number Jim was thinking, is x.

Jim adds 20 to it means number will be = x+20

And Jim doubles it, means 2*(x+20)

Jim gets 99.2 and as per us, he gets 2*(x+20)

So, making them equal

2(x+20)=99.2

2x+40=99.2

Subtracting 40 in both sides

2x+40-40=99.2-40

2x=59.2

x=29.6

It means the original number is 29.6.   :   Answer

Hope it will help :)



6 0
3 years ago
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