Math Homework Solution: Number Systems, Algebra, and Equations

This document presents a comprehensive solution to a mathematics homework assignment. The solution covers a range of topics including rounding numbers to two decimal places, converting fractions to decimals and percentages, calculating assessment task weightings and scores, and solving algebraic expressions. The assignment also includes problems involving forming and solving equations for consecutive odd numbers and calculating the perimeter of a hexagonal. Finally, the solution provides steps to make a variable the subject of a given equation. The document provides detailed explanations and step-by-step solutions for each problem, making it a useful resource for students studying mathematics.

mathematics
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Grizli777

Question 1
Numbers to two decimal places
(a) 5.435 = 5.44
(b) 142.9247 =142.92
(c) 0.00968 = 0.01
Question 2
S. No. Fraction
(simplified forms)
Decimal
(two decimal places)
Percentage
(nearest whole percent)
(a) 18
25
0.72 72%
(b) 12
25
0.48 48%
(c) 13
20
0.65 65%
(d) 13
40
0.325 33%
Question 5
Weightage of the tasks is highlighted below.
Assessment Task Weighting Mark
Written Assignments 30% 40
50
Participation 30% 12
20
Exam 40% ?
100
The combined assessment marks that needs to be obtained by Kermit in order to get the
Credit (60% - 69%) score is calculated as shown below.
Let the exam mark obtained by Kermit is x.

Written assignments score = 30% of 40 = 40*30% = 12
Participation score = 30% of 12 = 12*30% = 3.6
Exam score = 40% of x = x*40% = 0.40x
The minimum percentage for Credit score = 60%
Total marks = 60% of {(30%* 50) + (30%*20) + (40%*100)} = 60% * 61 = 36.6
Hence,
Minimum marks for Credit score = 12 +3.6 +0.40x = 36.6
15.6+0.40 x=36.6
x=52.5
And
The maximum percentage for Credit score = 69%
Total marks = 69% of {(30%* 50) + (30%*20) + (40%*100)} = 69% * 61 = 42.09
Maximum marks for Credit score = 12 +3.6 +0.40x = 42.09
15.6+0.40 x=42.09
x=66.23
Therefore, it can be concluded that assessment marks that needs to be obtained by Kermit in
order to get the Credit (60% - 69%) score would fall between 53 and 67.
Question 8
(i) Three less than the product of eight and a number x
Here,
The first number = 8
The second number = x
Product of eight and a number x = 8x
The product is less than 3 = 8x – 3

Hence, the expression = 8x-3
(ii) The difference of twice a number x and 3, increased by negative four
The given number is x
Twice of number x = 2x
The difference twice a number x and 3 = 2x-3
The difference is increased by negative four = (2x-3) + (-4)
Hence, the expression= (2x-3) + (-4)
In simplified for = 2x-7
(iii) Algebraic expression as a sentence
( 4 + x ) −(5 ÷ y )
Here,
(4+ x ) would be written as “four increased by a number x”
(5 ÷ y)would be written as “five divided by y”
Hence,
( 4 + x )−(5 ÷ y )would be written as “four increased by a number x is decreased by a
number five divided by y”
Question 9
(a) Sum of three consecutive odd numbers = 249
Middle number = Prime number
Smallest of the three number =?
Variable: Let the first odd number is x.
The second odd number would be x+2

The third odd number would be (x+2) +2 =x+4
Now,
Equation:
The equation can be formed as
x + ( x+2 ) + ( x +4 ) =249
3 x+ 6=249
3 x=249−6
3 x=243
x= 243
3 =81
Hence, the three consecutive oddnumbers would be
x=81 , x+2=83 , x+4=85
The smallest of the three consecutive odd numberswould be 81.
(b) Perimeter of the hexagonal = 74 meters
Variable:
Length of shortest side is x meter.
Four shortest sides (each of same length) = x meters
Fifth side five meter longer than x = x+5
Sixth side = 2x-1
Now,
Equation:
Sum of all six sides would be the perimeter of the hexagonal. Hence,

x + x+ x +x + ( x+ 5 ) + ( 2 x −1 ) =74
4 x+ x +5+2 x−1=74
7 x +4=74
7 x=70
x=10
Length of each four shortest sides = x= 10 meters
Fifth side five meter longer than x = x+5 = 15 meters
Sixth side = 2x-1= 20-1 = 19 meters
Therefore,
Length of shortest side would be10 meters.
Question 10
Equation to make k as the subject
(a) k −3 j= j
k = j +3 j
k =4 j

(b) 4 k +8=6−2 j
4 k=6−2 j−8
4 k=−2−2 j