We can write this out as an equation. Let's say that the teacher's age is x. Triple the teachers age plus the students age is 163, which can be written out as:

$3x + 7 = 163$

We want to isolate the variable, so subtract 7 from both sides. This gives us:

$3x = 156$

Finally, we divide both sides by 3, giving:

$x=52$

So the teacher is 52 years old.

Hope this helps!

4 0

3 years ago

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A segment with endpoints A (3, 4) and C (5, 11) is partitioned by a point B such that AB and BC form a 2:3 ratio. Find B.

Dima020 [189]

Answer:

(3.8, 6.8)

Step-by-step explanation:

Point B:

Has coordinates (x,y)

AB and BC form a 2:3 ratio.

This means that:

$B - A = \frac{2}{2+3}(C - A)$

$B - A = \frac{2}{5}(C - A)$

We apply this both for the x-coordinate and for the y-coordinate.

x-coordinate:

x-coordinate of A: 3

x-coordinate of C: 5

x-coordinate of B: x

$B - A = \frac{2}{5}(C - A)$

$x - 3 = \frac{2}{5}(5 - 3)$

$x - 3 = \frac{4}{5}$

$x = 0.8 + 3 = 3.8$

y-coordinate:

y-coordinate of A: 4

y-coordinate of C: 11

y-coordinate of B: y

$B - A = \frac{2}{5}(C - A)$

$y - 4 = \frac{2}{5}(11 - 4)$

$y - 4 = \frac{14}{5}$

$y = 2.8 + 4 = 6.8$

Thus the correct answer is:

(3.8, 6.8)

7 0

3 years ago

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