Atruck's varying distance from the warehouse, d , measured in miles is modeled by the formula d=t2+50t where t is the varying number of hours since the truck left the warehouse. the truck's destination is 437.5 miles away.

a. how many hours will it take the truck to reach its destination? (hint: you may need to use your graphing calculator to answer this question).

b. a car left the warehouse at the same time as the truck and wants to get to the destination at the same time. what constant speed would the car have to travel in order to reach the destination at the same time as the truck?

Step-by-step explanation:

a) The distance is given as ...

  d = t^2 +50t

We want to find the value of t for which this distance is 437.5 miles. That means we want to solve the equation ...

  437.7 = t^2 +50t

We can complete the square by adding the square of half the t coefficient, (50/2)^2 = 625

  437.5 +625 = t^2 +50t +625

  1062.5 = (t +25)^2

  √1062.5 -25 = t ≈ 7.596 . . . . hours

It will take the truck about 7.596 hours to reach its destination.

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b) Average speed is total distance divided by total time. Here, we can find the average speed as ...

  d/t = (t^2 +50t)/t = t +50

That is, the average speed over the 437.5-mile trip is ...

  7.596 +50 = 57.596 . . . . miles per hour

The car must maintain a constant speed of 57.596 mph to reach the destination at the same time.

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When solving equations using a graphing calculator, I like to put them into a form such that the solution is the x-intercept. Here, that means the equation we're solving is ...

  x^2 +50x -437.5 = 0 . . . . x is hours to destination

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step-by-step explanation:

∠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.