Sure, let's go through each part step by step.
g) Convert 120,000 from standard notation to scientific notation.
To convert a number into scientific notation, we express it in the form [tex]\( a \times 10^n \)[/tex] where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( n \)[/tex] is an integer.
120,000 can be written as [tex]\( 1.2 \times 10^5 \)[/tex].
So, the scientific notation for 120,000 is [tex]\( 1.2 \times 10^5 \)[/tex].
h) Given the equation [tex]\( 3x + 15 = 8b + c \)[/tex]
i) Make [tex]\( c \)[/tex] the subject of the formula.
To isolate [tex]\( c \)[/tex], subtract [tex]\( 8b \)[/tex] from both sides of the equation:
[tex]\[ 3x + 15 - 8b = c \][/tex]
So, the equation with [tex]\( c \)[/tex] as the subject is:
[tex]\[ c = 3x + 15 - 8b \][/tex]
ii) Calculate the value of [tex]\( c \)[/tex] if [tex]\( x = 5 \)[/tex] and [tex]\( b = 16 \)[/tex]
Now, substitute [tex]\( x = 5 \)[/tex] and [tex]\( b = 16 \)[/tex] into the derived equation [tex]\( c = 3x + 15 - 8b \)[/tex]:
[tex]\[ c = 3(5) + 15 - 8(16) \][/tex]
Let's break it down step by step:
- Calculate [tex]\( 3(5) \)[/tex], which is [tex]\( 15 \)[/tex].
- Add [tex]\( 15 \)[/tex] to the result, so [tex]\( 15 + 15 = 30 \)[/tex].
- Calculate [tex]\( 8(16) \)[/tex], which is [tex]\( 128 \)[/tex].
- Subtract [tex]\( 128 \)[/tex] from [tex]\( 30 \)[/tex], thus [tex]\( 30 - 128 = -98 \)[/tex].
Hence, the value of [tex]\( c \)[/tex] is [tex]\( -98 \)[/tex].
So, the final answers are:
- g) [tex]\( 120,000 \)[/tex] in scientific notation is [tex]\( 1.2 \times 10^5 \)[/tex].
- h) ii) The value of [tex]\( c \)[/tex] when [tex]\( x = 5 \)[/tex] and [tex]\( b = 16 \)[/tex] is [tex]\( -98 \)[/tex].
