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Sav [38]
3 years ago
7

on the set of axes below, the vertices of triangle PQR have coordinates P (-6,7) Q (2,1) and R (-1,-3) what is the area of trian

gle PQR?
Mathematics
1 answer:
VashaNatasha [74]3 years ago
3 0

Answer:

Area of ΔPQR = 25 units

Step-by-step explanation:

We will use the following formula to calculate the area of triangle ΔPQR:

A = 1/2 | x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂) | = 1/2 |(-6(1+3) +2(-3-7) +(-1)((7-1)| =

A = 1/2 |-6 · 4 + 2 · (-10) + (-1) · 6| = 1/2 | -24-20-6| = 1/2 | -50| = 1/2 · 50 = 25

A = 25 units

God with you!!!

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Ralph is 3 times as old as Sara. In 6 years , Ralph will be only twice as old as Sara will be then. Find Ralph’s age now .
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Answer:

Ralph's current age is 18.

Step-by-step explanation:

Let r and s represent the current ages of Ralph and Sara respectively.  Our task here is to determine r, Ralph's age now.

If Ralph is 3 times as old as Sara now, then r = 3s.

Six years from now, Ralph's age will be r + 6 and Sara's will be s + 6.  Ralph will be only twice as old as Sara will be then.  This can be represented algebraically as

r + 6 = 2(s + 6).

We now have the following system of linear equations to solve:

r + 6 = 2s + 12, or r - 2s = 6, and r = 3s (found earlier, see above).

r - 2s = 6

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Substituting 3s for r in r - 2s = 6, we get 3s = 2s + 6, or s = 6.  Sara is 6 years old now, meaning that Ralph is 3(6 years), or 18 years old.

Ralph's current age is 18.


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