1/12 + 1/6x = 3/4...multiply everything by common denominator of 12
1 + 2x = 9
2x = 9 - 1
2x = 8
x = 8/2
x = 4 <== he can play 4 rounds
Yes, 23 has an inverse mod 1000 because gcd(23, 1000) = 1 (i.e. they are coprime).
Let <em>x</em> be the inverse. Then <em>x</em> is such that
23<em>x</em> ≡ 1 (mod 1000)
Use the Euclidean algorithm to solve for <em>x</em> :
1000 = 43×23 + 11
23 = 2×11 + 1
→ 1 ≡ 23 - 2×11 (mod 1000)
→ 1 ≡ 23 - 2×(1000 - 43×23) (mod 1000)
→ 1 ≡ 23 - 2×1000 + 86×23 (mod 1000)
→ 1 ≡ 87×23 - 2×1000 ≡ 87×23 (mod 1000)
→ 23⁻¹ ≡ 87 (mod 1000)
Answer:
The ship S is at 10.05 km to coastguard P, and 12.70 km to coastguard Q.
Step-by-step explanation:
Let the distance of the ship to coastguard P be represented by x, and its distance to coastguard Q be represented by y.
But,
<P = 048°
<Q = 
- 
= 0
Sum of angles in a triangle = 
<P + <Q + <S =
048° + 0 + <S =
+ <S =
<S = -
= 
<S =
Applying the Sine rule,
= 
= 
=
= 
= 
⇒ y = 
= 12.703
y = 12.70 km
=
=
=
⇒ x = 
= 10.0475
x = 10.05 km
Thus,
the ship S is at a distance of 10.05 km to coastguard P, and 12.70 km to coastguard Q.
I think it’s 90 just add them up the subtract 180
Answer:
1 cubic ft can also be 1728in3, or 0.03704 yd3
Step-by-step explanation:
To find the cubic feet of a square or rectangular shape, measure the length, width and height of the object in feet or inches. Once you have these three numbers, multiply them together to get the volume. If you measured in inches, divide your answer by 1728 to convert the measurement to feet.
