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3 years ago

Find the value of two numbers if their sum is 12 and their difference is 4. Show work please.

Mathematics

2 answers:

Elza [17]3 years ago

6 0

Answer:

8,4

Step-by-step explanation:

x+y=12

x-y=4

(x+y)(x-y)=12*4

x^2-y^2=48

x=8 y=4

Irina18 [472]3 years ago

5 0

Answer:

4 & 8

Step-by-step explanation:

x-y = 4 -> x = 4+y

x+y = 12 = 4+y+y -> 4+2*y = 12

-> 2*y = 8 -> y = 4

-> x = 4+y = 8

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The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer l

Licemer1 [7]

Answer:

longer leg: 20 in

shorter leg: 15 in

hypotenuse: 25 in

Formulas:

<u>Pythagorean Theorem</u>

$c^2 = a^2 + b^2$

c ... hypotenuse

a ... one leg

b ... another leg

Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).

Step-by-step explanation:

longer leg: x

shorter leg: x - 5

hypotenuse: x + 5

To find x (longer leg), let's use Pythagorean theorem.

$c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x$

Now let's factorize to get solutions for x.

$0 = x(x-20)$

First solution:

$x = 0$

Second solution:

$x - 20 = 0\\x = 20$

Since a side of a triangle has to be a positive number, x is equal to 20.

Now let's just substitute x back to get side lengths. From the question the lengths are in inches.

longer leg: x = 20 in

shorter leg: x - 5 = 20 - 5 = 15 in

hypotenuse: x + 5 = 20 + 5 = 25 in

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2 years ago