Answer:
x = 13
y = 9
Step-by-step explanation:
Answer:
The value of x is 9 ⇒ C
Step-by-step explanation:
In a circle, if two chords intersected at a point inside it there are four segments created, two in each cord, the products of the lengths of the line segments on each chord are equal.
<em>Let us use this rule to solve the question</em>
In circle H
∵ Jk and LM are chords intersected at point N inside the circle
∴ The created segments are JN, Nk, and LN, NM
→ By using the rule above
∴ JN × NK = LN × NM
∵ JN = x and NK = 2
∵ LN = 3 and NM = 6
→ Substitute these values in the equation above
∴ x × 2 = 3 × 6
∴ 2x = 18
→ Divide both sides by 2 to find x
∴ 
∴ x = 9
∴ The value of x is 9
Remainder: 6 when divided by 12
So 12x6= 72
Original number: 72
72/9= 8
The remainder: 8
Answer:
4 sqrt(5)
-----------------
5
83 +12 sqrt(35)
Step-by-step explanation:
1. 4 sqrt(6)
--------------------
sqrt(30)
Multiply the top and bottom by sqrt(30) to rationalize the denominator
4 sqrt(6) *sqrt(30)
--------------------
sqrt(30)*sqrt(30)
4 sqrt(180)
--------------------
30
Simplify
2 sqrt(36 *5)
--------------------
15
We know that sqrt(ab) = sqrt(a) sqrt(b)
2 sqrt(36)sqrt(5)
--------------------------
15
2 *6*sqrt(5)
-------------------
15
Simplify
2 * 2 sqrt(5)
---------------------
5
4 sqrt(5)
-----------------
5
2. (2 sqrt(5) + 3 sqrt(7))^2
(2 sqrt(5) + 3 sqrt(7)) (2 sqrt(5) + 3 sqrt(7))
FOIL
first 2sqrt(5)*2sqrt(5)=4*5=20
outer 2 sqrt(5) * 3 sqrt(7) = 6 sqrt(35)
inner 3 sqrt(7) *2 sqrt(5) = 6 sqrt(35)
last 3sqrt(7) 3sqrt(7) = 9*7 = 63
Add them together = 20 + 6 sqrt(35)+ 6 sqrt(35) +63 = 83 +12 sqrt(35)
