Mathematics, 26.09.2019 18:40 juliomeadaptas

Suppose that the function f(x) = 2x + 12 represents the cost to rent x movies a month from an internet movie club. makayla now has $10. how many more dollars does makayla need to rent 7 movies next month?

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1) This equation is a polynomial to the second power, so lets use the quadratic formula.

[ -B +- squareroot(B^2 - 4AC) ] / 2A -A bit hard to read without the actual format.

= [ -20 +- squareroot( 20^2 - (4)(-5)(60) ) ] / (2)(-5) -A corresponds to -5, B to 20, and C to 60. Plug in.

= [ -20 +- squareroot(400 - (-1200) ) ] / (-10) - Simplifying

= [-20 +- 40] / (-10)

Because there is a plus/minus we now have two equations.

= [-20 - 40] / (-10) and = [-20 + 40] / (-10)

= 6 = -2

Now in case you aren't extremely familiar with the quadratic equation, by plugging in each piece and solving, we get the two x-intercepts that this parabola equation crosses and a graph. Lucky for us, this means that the two numbers we solved for is equal to the time at which this object touches the ground.

Common sense solves the rest. You cant have negative time so -2 is off our list.

That means it will take 6 seconds for this object to hit the ground.

2) We have f(x)=2x+12 and x is the amount of movies, and this function gives us the cost of the rental.

She requires 7 movies, so all we have to do is simply plug in 7 for x.

f(x) = 2x + 12

= 2(7) + 12

= 14 + 12

= $26 -So the cost for 7 movies will be $26.

We know she already has $10 so we just subtract $26 - $10 and we get $16.

In order for her to rent 7 movies, makayla needs $16 more dollars.

Answer from: Quest

The answer of this question is 672 .

Answer from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

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