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3 years ago

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An airplane left Miami, FL. At the same time another plane left Santiago, Chile. The two planes flew toward each other at rates

of 625 mph and 575 mph. If Miami and Santiago are 4200 miles apart, how long will it take until the planes pass each other?

1 answer:

Evgesh-ka [11]3 years ago

7 0

To solve the above question we use the concept of relative speed.
The rates of the two planes are 625 mph and 575 mph.
Relative speed will be:
[speed of plane A]+[speed of plane B]
=625+575
=1,200 mph
Distance=4200 miles
Thus the time taken for them to meet will be:
Time=distance/speed
=4200/1200
=3.5 hours
We therefore conclude that the planes met after 3.5 hours

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Leon spins both spinners. How many outcomes are in the sample space?

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Answer:

20 Outcomes.

Step-by-step explanation:

A-1 A-2 A-3 A-4

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3 years ago

What are the first 3 terms in. t(n)=-2n+7

seropon [69]

Answer:

The first 3 terms of the sequence $t(n)=-2n+7$ are:

$5, 3, 1$

Step-by-step explanation:

Given the sequence

$t(n)=-2n+7$

Here $n$ represents any term number in the sequence

Determining the first term

substitute n = 1 in the sequence to determine the first term

$t(n)=-2n+7$

$t(1)=-2(1)+7$

$t(1)=-2+7$

$t(1) = 5$

Determining the 2nd term

substitute n = 2 in the sequence to determine the 2nd term

$t(n)=-2n+7$

$t(2) = -2(2) + 7$

$t(2) = -4 + 7$

$t(2) = 3$

Determining the 3rd term

substitute n = 3 in the sequence to determine the 3rd term

$t(n)=-2n+7$

$t(3) = -2(3) + 7$

$t(3) = -6 + 7$

$t(3) = 1$

Therefore, the first 3 terms of the sequence $t(n)=-2n+7$ are:

$5, 3, 1$

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3 years ago

Find the slope of the line that passes through A(0,−5) and B(3,−4) .

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2 years ago

The first three terms of an arithmetic series are 6p+2, 4p²-10 and 4p+3 respectively. Find the possible values of p. Calculate t

Doss [256]

Answer:

First Case:

$\displaystyle p=\frac{5}{2}\text{ and } d=-2$

Second Case:

$\displaystyle p=-\frac{5}{4}\text{ and } d=\frac{7}{4}$

Step-by-step explanation:

We know that the first three terms of an arithmetic series are:

$6p+2, 4p^2-10, \text{ and } 4p+3$

Since this is an arithmetic sequence, each subsequent term is <em>d</em> more than the previous term, where <em>d</em> is our common difference.

Therefore, we can write the second term as;

$4p^2-10=(6p+2)+d$

And, likewise, for the third term:

$4p+3=(6p+2)+2d$

Let's solve for <em>d</em> for each of the equations.

Subtracting in the first equation yields:

$d=4p^2-6p-12$

And for the second equation:

$2d=-2p+1$

To avoid fractions, let's multiply the first equation by 2. Hence:

$2d=8p^2-12p-24$

Therefore:

$8p^2-12p-24=-2p+1$

Simplifying yields:

$8p^2-10p-25=0$

Solve for <em>p</em>. We can factor:

$8p^2+10p-20p-25=0$

Factor:

$2p(4p+5)-5(4p+5)=0$

Grouping:

$(2p-5)(4p+5)=0$

Zero Product Property:

$\displaystyle p_1=\frac{5}{2} \text{ or } p_2=-\frac{5}{4}$

Then, we can use the second equation to solve for <em>d</em>. So:

$2d_1=-2p_1+1$

Substituting:

$\begin{aligned} 2d_1&=-2(\frac{5}{2})+1 \\ 2d_1&=-5+1 \\ 2d_1&=-4 \\ d_1&=-2\end{aligned}$

So, for the first case, <em>p</em> is 5/2 and <em>d</em> is -2.

Likewise, for the second case:

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So, for the second case, <em>p </em>is -5/4, and <em>d</em> is 7/4.

By using the values, we can determine our series.

For Case 1, we will have:

17, 15, 13.

For Case 2, we will have:

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Okay! Who Needs Points? Give Your Explanation!

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4x+<span><span>7x</span><span>(12)</span></span>+12=<span><span>1008−<span>4x</span></span>+<span>12

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