+ 1 = 3
First, multiply both sides by 3. / Your problem should look like: x + 3 = 9.
Second, subtract 3 from both sides. / Your problem should look like: x = 9 - 3.
Third, simplify 9 - 3 to 6. / Your problem should look like:
x = 6, which is your answer.
Answer: £535
Step-by-step explanation:
Herr is the complete question:
Tim and three friends go on holiday together for a week.
The 4 friends will share the costs of the holiday equally,
Here are the costs of the holiday.
£1280 for 4 return plane tickets
£640 for the villa
£220 for hire of a car for the week
Work out how much Tim has to pay for his share of the costs.
Firstly, we have to calculate the total cost of the holiday. This will be:
= £1280 + £640 + £220
= £2140
We are also told that they will share the costs equally. Since there are 4 people, Tim will have to pay:
= £2140 ÷ 4
= £535
Tim will pay £535
Combine like terms in the first set and get
41.6x +52/2.6x + 13
I got 16x + 4
The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².
The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines
b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°) ⇒ b = 96√3 cm
Call b the base of this triangle.
The vertex angle is 120°, so the other two angles have measure θ such that
120° + 2θ = 180°
since the interior angles of any triangle sum to 180°. Solve for θ :
2θ = 60°
θ = 30°
Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find
tan(30°) = h / (b/2) ⇒ h = 48 cm
Then the area of the triangle is
1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²
and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:
3072π cm² - 2304√3 cm² ≈ 5660.3 cm²
