Question

1. y = (x - 5)(x + 1), Find y if x = - 3.

2. v= u + at
(a)
YEAR 7 HOME WORK
Work out v when u = 23, a = 4, and t = 3
(b)
Work out u when v= 30, a = 2 and t = 8
(c) Work out t when v = 40, u = 12 and a = 4
3. The circumference of a circle can be found using the formula C = 2nr or C = nd
Find the circumference of a circle with radius 8 cm.
Leave your answer to one decimal place.

4. Speed is calculated using the formula S=
Find the speed at which a car travelled if it took 2 hours to travel a distance of 100 km
D
T
where D is distance and T is time.

Answer 1

1) y=-2, y=-8

2a) v=35

b) u=12

c) t=7

3) c=50.3

4) s=50

Answer 2

1 ]

Given:-

• 
  `\tt{y = ( x - 5 ) ( x + 1 ) }`

`\:`

• 
  `\tt{x = - 3}`

`\:`

To find:-

• 
  `\tt \: y = ?`

`\:`

Solution:-

• 
  `\tt{y = ( x - 5 ) ( x + 1 )}`

`\:`

now , put the value of x = -3 in equation

• 
  `\tt \: y = ( -3 - 5 ) ( -3 + 1 )`

`\:`

• 
  `\tt \: y = ( - 8 ) ( - 2 )`

`\:`

or

• 
  `\tt \: y = 16`

`\:`

`\texttt{The value of \boxed{ \tt \red{ y = ( -8 ) ( -2 )} } \: or \boxed{ \tt \red{ 16}} !}`

`\:`

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2 ]

`\texttt{v = u + at} \: - - - \texttt{given \: formula \: or \: eqn}`

a ) ----»

Given:-

• 
  `\tt \: u = 23`

`\:`

• 
  `\tt \: a = 4`

`\:`

• 
  `\tt \: t = 3`

`\:`

To find:-

• 
  `\tt \: v = ?`

`\:`

Solution:-

• 
  `\tt \: v = u + at`

`\:`

now , put the given value in equation

• 
  `\tt \: v = 23 + 4×3`

`\:`

• 
  `\tt \: v = 23 + 12`

`\:`

• 
  `\boxed{\tt \purple{ v = 35}}`

`\:`

____________________________________

b )

Given:-

• 
  `\tt \: v = 30`

`\:`

• 
  `\tt \: a = 2`

`\:`

• 
  `\tt \: t = 8`

`\:`

To find:-

• 
  `\tt \: u = ?`

`\:`

Solution:-

• 
  `\tt \: v = u + at`

`\:`

put the given value in equation

• 
  `\tt \: 30 = u + 2×8`

`\:`

• 
  `\tt \: 30 = u + 16`

`\:`

• 
  `\tt \: 30 - 16 = u`

`\:`

• 
  `\tt \: 14 = u`

`\:`

• 
  `\boxed{ \tt \pink{ u = 14}}`

`\:`

____________________________________

c )

Given:-

• 
  `\tt \: v = 40`

`\:`

• 
  `\tt \: u = 12`

`\:`

• 
  `\tt \: a = 4`

`\:`

To find:-

• 
  `\tt \: t = ?`

`\:`

Solution:-

• 
  `\tt \: v = u + at`

`\:`

now , put the given value in equation

• 
  `\tt \: 40 = 12 + 4t`

`\:`

• 
  `\tt \: 40 - 12 = 4t`

`\:`

• 
  `\tt \: 28 = 4t`

`\:`

• 
  `\tt \cancel (28)/(4) = t`

`\:`

• 
  `\tt \: 7 = t`

`\:`

• 
  `\boxed{\texttt{ \green{t = 7}}}`

`\:`

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3 ]

Given:-

• 
  `\tt \: radius = 8`

`\:`

To find:-

• 
  `\texttt{circumference of circle = ?}`

`\:`

By using given formula:-

• 
  `\underline{ \tt \: \: C = 2πr \: \: }`

`\:`

Solution:-

• 
  `\tt \: C = 2πr`

`\:`

• 
  `\texttt{C = 2× 3.14× 8 [ as we know that the value of π = 3.14 constant ]}`

`\:`

• 
  `\tt{C = 16 × 3.14}`

`\:`

• 
  `\tt{C = 50.24}`

`\:`

`\texttt{The Circumference of the circle is { \blue{50.24}} !}`

`\:`

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4 ]

Given:-

• 
  `\texttt{Time ( T ) = 2h}`

`\:`

• 
  `\texttt{Distance ( D ) = 100km}`

`\:`

To find:-

• 
  `\texttt{Speed ( S ) = ?}`

`\:`

By using formula:-

• 
  `\underline{\tt{ \: \: Speed= (Distance)/(Time) \: \: }}`

`\:`

Solution:-

• 
  `\tt \: S = (D)/(T)`

`\:`

• 
  `\tt \: S = \cancel(100)/(2)`

`\:`

• 
  `\tt \: S = 50`

`\:`

`\texttt{The Speed of the car is \color{green}50.}`

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hope it helps⸙