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3 years ago

Find the value of the variable and GH if H is between G and I. GI = 5b + 2, HI = 4b – 5, HI = 3

Mathematics

1 answer:

Katen [24]3 years ago

6 0

Answer:

b = 2, GH = 9

Step-by-step explanation:

The last two equations tell you ...

HI = 3 = 4b -5

8 = 4b . . . . . . . . . add 5

2 = b . . . . . . . . . . divide by 4

Then ...

GI = 5·2 +2 = 12

So ...

GI/HI = 12/3 = 4 = G/H . . . . use the found value for GI and the given HI

G = 4H . . . . . . . multiply by H

GH = 4H² . . . . . multiply by H again

At this point, it can be useful to try the offered solutions to see what works.

GH = 4H² = 9

H = ±√(9/4) = ±3/2

G = 4H = ±6

Then ...

I = 3/H = 3/(±3/2) = ±2 . . . . matching the sign of H

We want values of G and H such that H is between G and I.

positive H: (G, H, I) = (6, 3/2, 2/3) . . . . yes, H is between G and I

negative H: (G, H, I) = (-6, -3/2, -2/3) . . yes, H is between G and I

The solution b=2, GH=9 satisfies problem requirements.

GH = 4H² = 12

H = ±√(12/4) = ±√3

G = 4H = ±4√3

I = 3/H = 3/±√3 = ±√3 . . . . sign matches H

Then (G, H, I) = (4√3, √3, √3) . . . . . H = I; is not "between" G and I

or (G, H, I) = (-4√3, -√3, -√3) . . . . . . H = I; is not "between" G and I

The solution b=2, GH=12 will only satisfy the problem requirements if you interpret "between G and I" to allow that H = I.

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You are being asked to observe the graphs of the various equations and identify something they have in common. To answer the question, it usually works well to do exactly what the question asks you to do.

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