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Talja [164]
2 years ago
14

The distance between two cities is 145 miles. A truck can cover this distance in 2. 5 hours. A car is 1. 5 times as fast as the

truck. How long does it take them to meet, if they start moving towards each other simultaneously?.
Mathematics
1 answer:
Sophie [7]2 years ago
8 0

The relative speed of the car to the truck while moving towards each other is the sum of the speed of both vehicles.

  • The time it takes them to meet is <u>1 hour</u>

Reasons:

The distance between the cities, d = 145 miles

The time it takes a truck to cover the distance = 2.5 hours

The speed of the car = 1.5 × Th speed of the truck

Required:

The time it takes them to meet if they are moving towards each other.

Solution:

  • \displaystyle Speed = \mathbf{ \frac{Distance}{Time}}

\displaystyle Speed \ of \ the \ truck, \ v_{truck} = \frac{145 \ miles}{2.5 \ hours} = \mathbf{58 \ mph}

Therefore;

The speed of the car, v_{car} = 1.5 × 58 mph = 87 mph

At the time<em>, t</em>, the truck and the car meet, we have;

\mathbf{v_{car} \times t + v_{truck} \times t = d}

Which gives;

87 × t + 58 × t = 145

\displaystyle t = \mathbf{\frac{145}{87 + 58}} = 1

  • The time it takes them to meet, <em>t</em> = <u>1 hour</u>

Learn more about distance, time and speed here:

brainly.com/question/17609639

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Vlada [557]

The probability that the number selected is the square of a natural number will be  \frac{1}{5}.

<h3 /><h3>What is probability?</h3>

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1.

Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

P is the probability

F(E) is the favorable event

T(E)is the total event

The probability is found as;

\rm P = \frac{F(E)}{T(E)} \\\\ \rm P = \frac{4}{20)} \\\\ \rm P = \frac{1}{5}

Hence the probability that the number selected is the square of a natural number will be  \frac{1}{5}.

To learn more about the probability link is given below.

brainly.com/question/795909

8 0
2 years ago
What is the end behavior in the function y=2x^3-x
sasho [114]

Answer:

Step-by-step explanation:

When a question asks for the "end behavior" of a function, they just want to know what happens if you trace the direction the function heads in for super low and super high values of x. In other words, they want to know what the graph is looking like as x heads for both positive and negative infinity. This might be sort of hard to visualize, so if you have a graphing utility, use it to double check yourself, but even without a graph, we can answer this question. For any function involving x^3, we know that the "parent graph" looks like the attached image. This is the "basic" look of any x^3 function; however, certain things can change the end behavior. You'll notice that in the attached graph, as x gets really really small, the function goes to negative infinity. As x gets very very big, the function goes to positive infinity.

Now, taking a look at your function, 2x^3 - x, things might change a little. Some things that change the end behavior of a graph include a negative coefficient for x^3, such as -x^3 or -5x^3. This would flip the graph over the y-axis, which would make the end behavior "swap", basically. Your function doesn't have a negative coefficient in front of x^3, so we're okay on that front, and it turns out your function has the same end behavior as the parent function, since no kind of reflection is occurring. I attached the graph of your function as well so you can see it, but what this means is that as x approaches infinity, or as x gets very big, your function also goes to infinity, and as x approaches negative infinity, or as x gets very small, your function goes to negative infinity.

6 0
3 years ago
Factor completely 12x4 + 6x3 + 18x2.
Semmy [17]

Answer:

B)3x^2 (4*x^2 + 2x + 6)

Step-by-step explanation:

Step 1: Find the Greatest common factor of the given expression.

12x^4 + 6x^3 + 18x^2

The above expression can be written as .

= 2*2*3*x^4 + 2*3*x^3 + 2*3*3*x^2

Here 3x^2 is prime factor


Step 2: Let's take out the 3x^{2} and write the remaining terms in the parenthesis.

= 3x^2 (2*2*x^2 + 2x + 2*3)

= 3x^2 (4x^2 + 2x + 6)

Therefore, the answer is B)3x^2 (4*x^2 + 2x + 6)

Thank you.

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Pachacha [2.7K]
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natta225 [31]

Answer:

The statement is false.

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In order to prove the statement, you have to show that it's true for all odd integers. But, to disprove it, you just have to find a counterexample where the statement is false.

Notice that it is easier to try to find a counterexample.

For example, a=3 and b=5

A= \frac{3+5}{2} = \frac{8}{2} = 4

The result of the average is even, therefore the statement is false.

The previous calculation is a counterexample.

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