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igor_vitrenko [27]
3 years ago
10

1. & 2. In the diagram below, points A, B, and C are collinear. Answer each of the following questions. The figure shown bel

ow is not drawn to scale, meaning you cannot determine your answers by using your ruler.​

Mathematics
1 answer:
KiRa [710]3 years ago
4 0

Answer:

a). AB = 8 in

b). AB = 9.75 in

c). AC = 6.5 in

d). BC = 1.5 in

Step-by-step explanation:

a). Since, AB = AC + CB

   Length of AC = 5 in. and CB = 3 in.

   Therefore, AB = 5 + 3 = 8 in.

b). Given : AC = 6.25 in and CB = 3.5 in

   Therefore, AB = AC + CB = 6.25 + 3.5

   AB = 9.75 in.

c). Given: AB = 10.2 in. and BC = 3.7 in.

    AB = AC + BC

    AC = AB - BC

    AC = 10.2 - 3.7

    AC = 6.5 in

d). Given: AB = 4.75 in and AC = 3.25 in.

   BC = AB - AC

   BC = 4.75 - 3.25 = 1.5 in.

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__

<h3>adding 2 to each term</h3>

The new fraction is ...

  \dfrac{x+2}{(x+3)+2}=\dfrac{x+2}{x+5}\\

<h3>new value</h3>

Apparently, the new value of this fraction is 2/3. We can use this to find the value of x.

  \dfrac{x+2}{x+5}=\dfrac{2}{3}\\\\3(x+2)=2(x+5)\qquad\text{multiply by $3(x+5)$}\\\\3x+6=2x+10\qquad\text{eliminate parentheses}\\\\x=4\qquad\text{subtract $2x+6$}

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_____

<em>Alternate solution</em>

In the ratio 2/3, the numerator is twice the difference between the denominator and numerator. 2 = 2(3 -2)

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  (6-2)/(9-2) = 4/7

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