The square of the sum of two numbers is 144 and the sum of their square is 180, find the numbers

x = 13.35, y = - 1.35

or, x = 1.35, y = - 13.35

or, x = - 13.35, y = 1.35

Step-by-step explanation:

Let us assume that x and y are the two numbers.

So, given that (x + y)² = 144

⇒ x² + 2xy + y² = 144 ........ (1)

⇒ x + y = ± 12 ......... (2)

Again, x² + y² = 180 ........... (3)

Now, from equations (1) and (3) we can write 2xy + 180 = 144

⇒ 2xy = - 36

⇒ xy = - 18 ........ (4)

Now, for x + y = 12

⇒

⇒ x² - 18 = 12x

⇒ x² - 12x - 18 = 0

Using the quadratic formula

⇒

Now, for x = 13.35, from equation (4) we get, y = - 1.35

And for x = 1.35, from equation (4) we get, y = - 13.35

Now, for x + y = - 12

⇒ x² + 12x - 18 = 0

Using the quadratic formula,

⇒

Now, for x = - 13.35, from equation (4) we get, y = 1.35

And for x = 1.35, from equation (4) we get, y = - 13.35

Therefore, x = 13.35, y = - 1.35

or, x = 1.35, y = - 13.35

or, x = - 13.35, y = 1.35 (Answer)

there is no

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).