Financial
Rebecca has $30,000 in a savings account that earns 9% annually. The interest is not compounded. How much interest will she earn in 2 year?
$5400
A right-angled triangle has a shorter side of 8cm and its hypotenuse is 17cm. What is the length of the its other shorter side?
15cm
Find the value of y, when x = 4.
y = (3/4)x + 5
y = 8
Expand the following expression (2x+4)(x-5)
2x2-x-20
Simplify (p3)0 × (p1/2)4
p2
Find the total amount of interest earned when $3200 is invested at 6% compounded annually for 5 years
$1082.32
The length of the hypotenuse of a right-angled triangle is 8cm and adjacent side is 3cm. Find the angle between the hypotenuse and opposite side, rounded to 2dp.
22.02∘
A linear graph passes through the points (3, -2) and (-1, 4). Find the equation of the line and write it in standard form.
3x + 2y = 5
Factorise 2x2 − 24x + 72
2(x−6)2
If 5m = 3125, find the value of 4(m – 2).
64
After 5 years, the loan grows to $45,200. If the interest was compounded annually at a rate of 6% p.a., find the size of the initial loan to the nearest dollar.
$33,776
Find the exact area of a square (of side length x cm) that has a diagonal length of 10 cm. Answer in cm2.
50cm2
A hot air balloon and a drone are both rising from different heights. The hot air balloon starts from ground level and rises at a rate of 8 meters every 3 seconds. The drone starts from a platform 20 meters above the ground and rises at a rate of 5 meters every 2 seconds. If both start ascending at the same time, after how many seconds will they be at the same height? What will that height be?
They will be at the same height after 120 seconds, and that height will be 320 meters
Factorise 6w2 - 11w - 10
(3w+2)(2w-5)
Simplify the following expression:
(3a+1 x 9-a) / 27(2a/3)
31-3a
How much more interest is earned on $50,000 if interest at 8% p.a. is compounded quarterly over 5 years rather than simple interest 8% over the same time? Answer to the nearest cent.
$163,047.86
The triangular faces of a right square-based pyramid are at an angle of 60° to the base. The height of the pyramid is 30m. Find the perimeter of the base of the pyramid, correct to one decimal place.
138.6m
Sophia and Noah are planning a jogging route in Sydney. Sophia starts her run from Bondi Beach, located 6 kilometers east of the city center, while Noah starts his run from his home at (-3, -2).
They decide to meet exactly halfway between their starting points. How far away from their starting points will they be meeting? Round to 2dp.
4.61km
Simplify: (x2 - 5x + 6)/18 ÷ (x2 - 4)/(6x + 12)
(x-3)/3
Solve: 9-(1/2) = 27(1/4) ÷ 3x+1
x = 3/4
An investment of $12,000 grew to approximately $21,673.33 in 5 years after 3% p.a. compounded a certain number of times for 5 years. Find how frequently interest was compounded each year.
Quarterly.
Right-angle triangle ABC has ∠ ABC = 90°, ∠ BAC = 48.1897°, and Length AB = 9cm. There is a quarter of a circle attached to the triangle, with its centre is at Point C and its radius is Length CB. Work out the area of the full shape, correct to 3 significant figures.
55.5cm2
A linear graph line goes through the points A(-2,9) and B(-4,4). Find the y-intercept of the perpendicular line that goes through the same Point A.
(0, 41/5) or (0,8.2)
A length of a pool is (3x+4)m and its width is (2x+3)m. The house owners want to install a footpath that is (2x-1)m wide around the pool. Find an expression for the area for the footpath.
36x2 + 9x - 2
Simplify:
1 – {1 + (x2 – 1)-1}-1
1/x2