6 is twice as much as 3...so x will be twice as much as 4. So the answer is...
C. 8
It’s 20f-30g I just took that question on a test
Answer:
see explanation
Step-by-step explanation:
a
The tangent and the radius at the point of contact form a right angle
Using Pythagoras' identity on the right triangle formed.
Let x be the distance from the centre to P, then
x² = 4² + 10² = 16 + 100 = 116 ( take the square root of both sides )
x = 
≈ 10.77 cm (to 2 dec. places )
b
let the required angle be Θ, then
Using the sine or cosine ratio in the right triangle.
cosΘ = 
= 
Θ = 
( ) ≈ 21.8°
Answer:
20
Step-by-step explanation:
To solve this you have to make a system of equations.
Since the father and son's age sum up to 60, the first equation will be:
f + s = 60
Secondly, since the father's age is 5 times the age of the son 6 years ago the equation will be:
6 - (5s) = f
Now, you have to solve the first equation to let it equal to s
f + s = 60
f = 60 - s
Plug in
6 - 5s = 60 - s
+s +s
6 - 4s = 60
-6 -6
---------------------
-4s = 54
----- -----
-4 -4
s ≅ 14
14 + 6 = 20
Answer: Yes, the point (3,4) is a solution to the system.
===================================================
Proof of this:
Replace x with 3 and y with 4 in the first equation
x+y = 7
3+4 = 7
7 = 7
This confirms the first equation. Repeat for the second equation
x-2y = -5
3-2(4) = -5
3 - 8 = -5
-5 = -5
We get true equations for both when we plug in (x,y) = (3,4). This confirms it is a valid solution to the system of equations. It turns out it's the only solution to this system of equations. Visually, the two lines cross at the single location (3,4).
