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3 years ago

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Mathematics

1 answer:

s344n2d4d5 [400]3 years ago

4 0

This problem is quite simple, but it may seem tricky at first.
y is a function of x, so replace y with f(x)
You get f(x) = 2x - 4
D is your answer.
Have an awesome day! :)

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The third through the fifth terms of a geometric sequence are given by a3 = 18, a4 = 27 , and a5 = 81/2

Kaylis [27]

Let a be the first term in the sequence. If r is the ratio between consecutive terms, then the second term is ar, the third term is ar ^2, the fourth is ar ^3, and so on, up to the n-th term ar ^(n - 1).

So the third, fourth, and fifth terms are such that

ar ^2 = 18

ar ^3 = 27

ar ^4 = 81/2

Solve for a and r :

(ar ^3) / (ar ^2) = 27/18 => r = 3/2

ar ^2 = a (3/2)^2 = 9/4 a = 18 => a = 8

Then the n-th term in the sequence is

ar ^(n - 1) = 9 (3/2)^(n - 1)

You can rewrite this by first rewriting 9 = 3^2, then

9 (3/2)^(n - 1) = 3^2 * 3^(n - 1) / 2^(n - 1) = 3^(n + 1)/2^(n - 1)

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3 years ago

Translate the triangle by (-2 -4)

Gnom [1K]

Translating the triangle using the vector $(^{-2}_{-4})$ means translating 2 units left and 4 units down.

<h3>What is transformation?</h3>

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Translating the triangle using the vector $(^{-2}_{-4})$ means translating 2 units left and 4 units down.

Find out more on transformation at: brainly.com/question/4289712

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6 0

2 years ago

the third term and the fifth term of a geometric progression are 2 and 1/8 respectively. If all terms are positive, find the sum

loris [4]

Answer:

42 + 2/3

Step-by-step explanation:

First, to calculate the sum of an infinite geometric series, our formula is

a₁/(1-r), with a₁ being the first term of the series and r being the common ratio. Therefore, we want to find both a₁ and r.

To find r, we can first determine that 2 * r = a₄ and a₄ * r = a₅, as the ratio separates one number from the next in a geometric series. Therefore, we have

2 * r * r = a₅

2 * r² = 1/8

divide both sides by 2 to isolate the r²

r² = 1/16

square root both sides to isolate r

r =± 1/4. Note the ± because r²=1/16 regardless of whether r = 1/4 or -1/4. However, because all terms are positive, r must be positive as well, or a₄, for example, would be 2 * (-1/4) = -0.5

Therefore, r = 1/4 .

To find the first term, we know that a₁ * r = a₂, and a₂ * r = a₃. Therefore, a₁ * r² = a₃ = 2

a₁ * 1/16 = 2

divide both sides by 1/16 to isolate a₁

a₁ = 2 * 1/ (1/16)

= 2 * 16

= 32

Plugging a₁ and r into our infinite geometric series formula, we have

a₁/(1-r)

= 32 / (1-1/4)

= 32/ (3/4)

= 32/ 0.75

= 42 + 2/3

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3 years ago

What are the formulas for right triangles

Elan Coil [88]

Answer:

The Pythagorean theorem is

a^2 + b^2 = c^2

where a and b are the lengths of the legs (the sides that form the right angle), and c is the length of the hypotenuse (the side opposite the right angle.)

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3 years ago

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Which expression are equivalent to 2.5-4(1.5-10)+3 their are multiply answers

Yuri [45]

2.5−4(1.5−10)+3=39.5

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4 years ago