Algebra
Evaluate the expression
2x-3y
when x = -2 and y = 9
-27
Jennifer needs to build a fence around her house. The block is a rectangle with dimensions
50m \times 42m.
Fencing costs $13 per metre. What will be the total cost of fencing?
$2,392
Express 60c as a percentage of $5
12%
Is 16, 36, 52 a Pythagorean triad?
yes
What is the gradient and y intercept of the line with equation
y=3x-1
?
m = 3 b = (0,-1)
A plumber charges a $70 call-out fee and then $90 per hour. Write an expression for the total cost (C) of calling a plumber out for (x) hours.
C=70+90x
Find the area of a square if its perimeter is 20cm.
25cm2
Decrease $63 by 15%
$53.55
A ladder that is 2 m in length is placed against a wall 1.2 m from its base. How far up the wall does the ladder reach?
height = 1.6 m
Complete the following conversion:
5m^2 = ? cm^2
50 000cm^2
Write an expression for the following statement and then expand it to solve:
A number w is tripled, and then 5 is subtracted. The result is doubled.
6w - 10
Calculate the perimeter of a quadrant with a radius of 3cm. Answer correct to the nearest whole number.
11cm
Calculate the pre-GST price if the final cost to the consumer was $352
$320
A rectangle has a length of 24cm and a perimeter of 62 cm.
Find the length of the rectangle's diagonal.
diagonal = 25
Angle T is complementary to angle Q and co-interior to angle R.
If Q = 67°, what is the size of R?
R= 157o
A box has a height of x cm. It is 3 times as wide as it is high, and 2 times as long as it is wide. Find an expression for the volume of the box, given that volume = length × breadth × height.
18x3
What is the height of a triangle that has a base of 13 cm and an area of 45.5 cm2?
7cm
Gemma purchased a $400 foal, which she later sold for $750. Calculate the percentage profit Gemma made.
87.5%
Two plants are placed 9cm apart. One is 21cm in height and the other is 34cm in height. What is the distance between the top of the two plants? Give your answer to 2 decimal places.
15.81 cm
The two base angles of an isosceles triangle are equal to
3x-15
and
-5x+1.
What is the value of x?
x = 2
Factorise and simplify the following expression:
(7p+14pq)/(9p+18pq)
7/9
Water is being poured into a fish tank at a rate of 2 L every 10 seconds. The tank is 1.2 m long by 1 m wide by 0.8 m high. How long will it take to fill the tank? Give the answer in minutes.
8 minutes
Three different brands of washing powder are on sale. Their prices are shown below.
Work out which brand provides the best value for money.
A) 400g for $2.56
B) 750 g for $5.10
C) 1.2 kg for $7.38
C) 1.2kg for $7.38
What is the base of an isosceles triangle with equal sides of 15 mm and a height of 12 mm. Answer to 2 decimal places.
base = 18 mm
Sarah has achieved 72%, 76% and 84% in her last three assessment tasks. After she received her fourth assessment task result, her new average is 80%
What percentage did Marlene achieve on her fourth assessment task?
88%