A) draw the graph of the relation y = x² - 2x -1 using scale of 2cm to 1unit on both axis
b) use the graph to find the roots of the equation x² - 2x -1 = 0
c)using the same axis, draw the graph of y=2x - 3
d) use your graph to solve simultaneously
y=x² - 2x - 1
y=2x - 3

See explanation and attachment

Step-by-step explanation:

a) To graph , we need to plot some few points.

When x=-2,  so we plot (-2,7).

When x=-1, so we plot (-1,2)

When x=0, so we plot (0,-1)

When x=1, so we plot (1,-2)

When x=2, so we plot (2,-1)

We then draw a smooth curve through the points to obtain the curve in the attachment.

b) The graph intersected the x-axis (y=0) at x=-0.41 and x=2.41. These are the roots.

c)  For the line y=2x-3

When x=0, y=2(0)-3=-3 so we plot (0,-3)

When x=1, y=2(1)-3=-1 So we plot (1,-1)

We draw a straight line through these two points to intersect the parabola as shown on the graph.

d) To solve

and

simultaneously using the graph, we look for the point of intersection of the parabola and the straight line.

The solution is (0.59,-1.83) and (3.41,3.83)

4 candies

step-by-step explanation:

7 x 28 = 196

200 - 196 = 4 candies remaining.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: