apply the pythagorean theorem to find the distance between points a and c.

a)

29

units

eliminate

b)

40

units

c)

58

units

d)

116

units

So the correct option is C )  58 units.

Also If we require Distance then l(AC) = √58 = 7.615 units

Step-by-step explanation:

Let the Points be

point A( x₁ , y₁) ≡ ( -2 , 1)  

point C( x₂ , y₂) ≡ (5 , -2)  

To Find:

d(AC) = ?

Solution:

By Applying the Pythagorean Theorem to find the distance between points A and C we get

Substituting A( x₁ , y₁) ≡ ( -2 , 1) and C( x₂ , y₂) ≡ (5 , -2) we get

So the correct option is C )  58 units.

If we require Distance then l(AC) = √58 = 7.615 units

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).