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Answers

Answer 1

Answer: the cattle train
speed - 36.5 km/h
time - x h

the passenger train
speed - 29.2 km/h
time - (2.4+x) h

The cattle train caught up to the passenger train so the distance they travelled is the same.
Distance is speed times time.

$36.5 * x=29.2 * (2.4+x) \n36.5x=70.08+29.2x \n36.5x-29.2x=70.08 \n7.3x=70.08 \nx=(70.08)/(7.3) \nx=9.6 \n \n 2.4+x=2.4+9.6=12$

The passenger train travelled for 12 hours before the cattle train caught up.

Answer 2

Answer: Used brute force to figure this one out and got lucky at t=12.

What you need to know:

$d=\left| x-y \right|$

t = time travelled (in hours)

x = distance passenger train has travelled

y = distance cattle train has travelled

d = distance between both trains in km

------------------------------------

RESULTS AND TIME SNAPSHOTS:

When:

t=0, x=0, y=0, d=0

t=2.4, x=70.08, y=0, d=70.08

t=4.8, x=140.16, y=87.6, d=52.56

t=7.2, x=210.24, y=175.2, d=35.04

t=9.6, x=280.32, y=262.8, d=17.52

t=12, x=350.4, y=350.4, d=0 <-------

So your answer is 12 hours.

x = 2 and y = 7

Step-by-step explanation:

$\text{Two complex numbers are equal when they have equal real parts}\n\text{ and equal imaginary parts}\n\na+bi=c+di\iff a=c\ and\ b=d$

$3x+(2x-y)i=6-3i\iff3x=6\ \wedge\ 2x-y=-3\n\n3x=6\qquad\text{divide both sides by 3}\n\n\boxed{x=2}\n\n\text{Put the value of x to the second equation:}\n\n2(2)-y=-3\n\n4-y=-3\qquad\text{subtract 4 from both sides}\n\n-y=-7\qquad\text{change the signs}\n\n\boxed{y=7}$

Write the equation and solve: eight more than the sum of a number and 5 is 20

Answers

Greetings!

You can solve this with a simple equation:

Take the letter x to be the unknown number:

20 = 8+ (X + 5)

Then you can move the 8 + to the opposite side making it a negative 8:

20-8 = X + 5

12 = X + 5

Move the +5 over to the other side, making it a negative 5:

12 - 5 = x

7 = x

So the value of x is 7.

Hope this helps!

Paolo pays $244 for 5 identical calculators. About how much does Paolo pay for one calculator?

Answers

In the question, all details are given. using these details it would be easy to determine the required answer. It is already given that Paolo paid $244 for buying 5 identical calculators. It is required to find the amount necessary to buy a single calculator.
Then
Amount required for buying 5 calculators = 244 dollars
Amount required to buy 1 calculator having same specification = (244/5) dollars
= 48.80 dollars
So the amount required to buy 1 calculator having identical features is $48.80

$244 for all 5 calculators so 244/5= $48.80 is what he paid for each calculator

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -36 and 2304, respectively.

Answers

When we find a geometric sequence using the first and second terms, what we do is divide the second by the first to find a "common ratio," the number you multiply by to get to the next term.

In this case, we only have the second and fifth terms. From the second to the fifth term, we've multiplied by that common ratio three times.
What we can do is divide the fifth by the second and then take the cube root to find our common ratio.

$2304/-36=-64\n\sqrt[3]-64=\boxed{-4}$

Now we know we're multiplying by -4 each time, let's find the first term.

The opposite of multiplying by -4 would be dividing by -4. We work back from our second term -36 to find that the first term would be 9.

For each sucessive term, we then multiply by -4.

Our equation is $a_n=9*-4^((n-1))$

What is the greatest common factor of 65 and 91

Answers

So,

First, we find the prime factored form (P.F.F.) of 65 and 91.

P.F.F. of 65: 5 * 13

P.F.F. of 91: 7 * 13

Find the common numbers
13

13 = G.C.F.

Note: This method works for finding any G.C.F. (find common primes)

The greatest common factor (GCF) of 65 and 91 is 13 by using prime factorization method:

To find the GCF of two numbers, to determine the largest number that divides both of them evenly.

To find the GCF of 65 and 91, use the prime factorization method:

Step 1: Prime factorize both numbers:

65 = 5 × 13

91 = 7 × 13

Step 2: Identify the common prime factors:

Both 65 and 91 share the prime factor 13.

Step 3: Determine the highest common prime factor:

The highest common prime factor of 65 and 91 is 13.

Therefore, the GCF of 65 and 91 is 13.

Learn more about greatest common factor here: