Adam is now 9 years older than brianna and 13 years ago he was twice as old as she was then. how old are adam and brianna now?

Let current age of Adam = x years

Let current age of Brianna = y years

Question says that "Adam is now 9 years older than Brianna "

Which means x=y+9 ...(i)

To find the age 13 years ago, we just subtract 13 from age of each person.

Age of Adam before 13 years = (x-13) years

Age of Brianna before 13 years = (y-13) years

Question says that "13 years ago he was twice as old as she was then"

Which means (x-13)=2(y-13) ...(ii)

plug value of x from equation (i) into (ii)

(x-13)=2(y-13)

(y+9-13)=2(y-13)

y-4=2y-26

y-2y=-26+4

-y=-22

y=22

plug value of y=22 into equation (i)

x=y+9 = 22+9 = 31

Hence Adam is 31 years old and Brianna is 22 years old.

pH = f(x) = -log₁₀x

1. Graphs

I used Excel to calculate the pH values and draw the graphs (see the Figure).

f(x) and f(x) +1 are plotted against the left-hand axis, while f(x+ 1) is plotted against the expanded right-hand axis.

The points at which pH = 0 and pH = 1 are indicated by the large red dots.

2. x = 0.5

When x = 0.5, pH ≈0.30. The point is indicated by the red diamond.

3. Transformations

(a) ƒ(x) = -log(x) + 1

This function has no y-intercept, because log(0) is undefined.

(b) ƒ(x +1) = -log(x + 1)

f(0) = -log(0 + 1) = -log(1) = 0

This function has a y-intercept at (0,0).

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