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Radda [10]
3 years ago
6

Find the x if the sequence 3, x, 4x/3 is (a)arithmetic and (b)geometric

Mathematics
1 answer:
jolli1 [7]3 years ago
6 0

(a) When the sequence is arithmetic, sequential terms have a common difference.

... x - 3 = (4x/3) - x . . . . differences of sequential terms are equal

... (2/3)x = 3 . . . . . . . add 3-(1/3)x

... x = 9/2 . . . . . . . . . multiply by 3/2

(The arithmetic sequence is 3, 4.5, 6. The common difference is 3/2.)

(b) When the sequence is geometric, sequential terms have a common ratio.

... x/3 = (4x/3)/x . . . . . ratios of sequential terms are equal

... x^2 = 4x . . . . . multiply by 3x

... x = 4 . . . . . . . . divide by x. (the "solution" x=0 is extraneous)

(The geometric sequence is 3, 4, 16/3. The common ratio is 4/3.)


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Answer:

m∠2 = 78°

Step-by-step explanation:

From the given picture,

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3 years ago
Triangles triangle ABC and triangle DEF are similar. Find the angles of these triangles if Mesurements of angle A=100 degrees, a
beks73 [17]

Answer:

<D = 100

<E =30

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Step-by-step explanation

Given that triangles triangle ABC and triangle DEF are similar, this means that their angles are congruent i.e

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<C = <F

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To get <F, we will use the expression

<D+<E+<F = 180 (sum of angles in a triangle is 180°)

100+30+<F = 180

130+<F = 180

<F = 180-130

<F = 50°

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