What two fractions multiply to equal -1 and add to equal 1/4

The two such fractions are: 113/100 and -22/25.

Step-by-step explanation:

Let us assume two such fractions are P and Q.

⇒ P x Q  = -1

and P + Q = 1/4

Now, to solve for the values of P and Q:

P + Q = 1/4 ⇔ Q = 1/4 - P

Substitute this value of Q in P x Q  = -1, we get:

P x Q  = -1  

Now, solving this with the help of QUADRATIC Formula:

We get: P = 1.13 or P  = -0.8825

Now, if P = 1.13, Q  = -1/1.13 = -0.88  = -88/100  = -22/25

If P = -0.88, then Q = 1/0.88 = 1.13  = 113/100

Hence, The two such fractions are: 113/100 and -22/25.

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).