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3 years ago

If r = -\sqrt{2}, and a5 = \sqrt{2}, what is the first term of the sequence?

Mathematics

1 answer:

shepuryov [24]3 years ago

6 0

Answer: C

Step-by-step explanation:

Let x represent the first term (a₁)

a₁ = x

a₂ = x(-√2) = -x√2

a₃ = -x√2(-√2) = 2x

a₄ = 2x(-√2) = -2x√2

a₅ = -2x√2(-√2) = 4x

Since it is given the a₅ = √2, then we can solve: 4x =√2

Divide both sides by 4 to get: x = $\frac{\sqrt{2}}{4}$

this can also be written as: $\frac{1}{4}\sqrt{2}$

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3 years ago

Tomas bought 80 tickets for rides at an amusement park. Each ride costs 5 tickets, and Tomas has been on x rides so far. Which e

Alex Ar [27]

Answer:

Option A, C and D are correct choices.

Step-by-step explanation:

Let x be the number of rides that Tomas has been on so far. Each ride costs 5 tickets. This means that cost of x rides will be 5x.

We are told that Tomas bought 80 tickets for rides at an amusement park.

To find the number of of tickets that Tomas has left we will subtract cost of x rides from total number of tickets that Thomas bought.

We can represent this information in an expression as: $80-5x$

Now let us see which of our given choices in equivalent to our expression.

A. $80-5x$

Upon looking at option A we can see that it is same as our expression, therefore, option A is the correct choice.

B. $80+5x$

We can see that in this expression cost of x rides in being added instead of subtraction, therefore, option B is not a correct choice.

C. $5(16-x)$

Upon distributing 5 we will get,

$80-5x$

Now this expression is same same as our expression, therefore, option C is the correct choice.

D. $-5x+80$

This expression is also same as our expression as we can rearrange the terms in this expression as: $80-5x$ , therefore, option D is a correct choice as well.

E. $5(16+x)$

Upon distributing 5 we will get,

$80+5x$

We can see that in this expression cost of x rides in being added instead of subtraction, therefore, option E is not a correct choice.

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3 years ago