One lap. Usually, it would take 4 laps to walk a mile, but since its 1/4 it equals One lap.
we can see that
the above curve is parabola
so, firstly , we can find vertex
vertex is (4,0)
now, we can use vertex formula of parabola
we can plug h and k
and we get
so, we can factor it as
............Answer
Represent 'a number' by x
7 times x equals 9 more than 4 times x
7 times x=9+4 times x
7x=9+4x
subtract 4x from both sides
3x=9
divide 3
x=3
the number is 3
49=16+x^2
x^2= 33
x= square root of 33
A) I would make the positive integer x and then form an equation.
x + 30 = x^2 - 12
x + 42 = x^2
0 = x^2 - x - 42 this can be factorised
(x - 7) ( x + 6) Therefore x = 7 or x = -6
Since the question asks for a positive integer the answer is 7.
B) two positive numbers x and y.
X - y = 3
x^2 + y^2 = 117
Use these simultaneous equations to figure out each number.
Rearrange the first equation
x = y + 3
Then substitute it into the second equation.
(y+3)^2 + y^2 = 117
y^2 + 6y + 9 + y^2 = 117
2y^2 + 6y - 108 = 0
then factorise this.
(2y - 12) (y + 9)
This means that y = 6 or y = -9 but it’s 6 because that’s the only positive number.
Use y to find x
x = y + 3
x = 6 + 3
x = 9
So the answers are x = 9 and y = 6.
