A train traveling south leaves the station at a constant rate of 62 kilometers per hour. A second train traveling north leaves the station at the same time traveling at a constant rate of 68 kilometers per hour. How many hours after the trains leave will they be 455 kilometers apart?
A 3.5


B.
4.5


C.
5.5


D.
6.5

Answer:

0.4

Step-by-step explanation:

Let x be 1/10 of 0.04.

1/10 of x would be [tex]\frac{1}{10}x[/tex].

We can represent our given information in an equation as:

[tex]\frac{1}{10}x=0.04[/tex]

Let us solve for x.

[tex]10*\frac{1}{10}x=10*0.04[/tex]

[tex]x=0.4[/tex]

Therefore, 0.04 is 1/10 of 0.4.

The equation of the line having The x-intercept of the line is 2, The y-intercept of the line is 12, is y = -6x + 12.

Lines are defined as objects with an infinite length and no width, depth, or curvature. Lines are one-dimensional objects even though they can occur in contexts that are two, three, or higher dimensional.

A simple line in Euclidean geometry. A line, according to Euclid, is the distance between two points and can stretch forever in either direction.

Given:

The x-intercept of the line is 2,

The y-intercept of the line is 12,

Write the equation of the line as shown below,

y = m x + 12

Here, m is the slope,

At y = 0 we get the x-intercept, so

0 = m × 2 + 12

m = -12 / 2

m = -6

Thus, the equation of the line is y = -6x + 12.

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Answer:

20.6%

Step-by-step explanation:

To calculate the percentage of how much increase, we must first know how much is the difference in the price of May with that of September.

That difference will represent how many $ increase the gallon

[tex]3.05-2.53=0.52[/tex]

We know that a $ 0.52 increase now we must calculate to what percentage of the initial price this value is equivalent to know in what percentage the price of May increased.

[tex]2.53 \longrightarrow 100\%\\0.52 \longrightarrow x\\x=\frac{(0.52)(100)}{2.53} \\x=20.6\%[/tex]

Albrecht Dürer used the term 'net' to describe a pattern because of its geometric nature and the way it mirrors a literal fishing net, which can be both flat and three-dimensional. His background in printmaking and geometry likely influenced this descriptor, showing his dedication to precision and instruction in visual arts.

The term net used by Albrecht Dürer in 1525 refers to a pattern that when folded, creates a three-dimensional shape. Dürer, a prominent figure in the Northern Renaissance, was a master in various forms of visual art. He possessed expertise in painting, printmaking, and had an understanding of geometrical principles as well as the new technology of print. The use of the word 'net' to describe a flattenable 3D pattern aligns with Dürer's keen attention to detail, precision, and geometry in his artworks. His choice of the term could have been inspired by the resemblance of the interconnected lines in a pattern to a fishing net, which can be spread out flat but typically exists in a more complex, three-dimensional form.

Through his prints and craft manuals, Dürer contributed to the dissemination of knowledge on artistic techniques and the use of geometry in art. His detailed illustrations often acted as visual instructions, which would align with the concept of a 'net' aiding in the construction of a three-dimensional understanding of shapes and forms. The term might have been quite intuitive for someone with Dürer's graphical sensibility, as it connects the craft of design with a term that people could visualize and comprehend easily.

1 mile = 1760 yards

13.1 * 1760 = 23056 yards / 58.38 = 394.93 yards per minute

394.93/60 = 6.58 yards per second

30/4.8 = 6.25 yards per second

13.1miles in 58 minutes 23 seconds is faster

Answer:

75.4296 meters

Step-by-step explanation:

Use the circle area equation: pi(r)^2 to do 4.9^2 multiplied by pi

To find the amount of white sugar if it were increased by a factor of 2 1/2, multiply the original amount by 2 1/2. The answer is A. 2 1/2 cups.

To find the amount of white sugar if it were increased by a factor of 2 1/2, we need to multiply the original amount by 2 1/2. Let's assume the original amount is x. Multiplying x by 2 1/2 gives us:

x × 2 1/2 = x × 2 + x × 1/2 = 2x + (1/2)x = (4/2)x + (1/2)x = (5/2)x

So, the amount of white sugar after it is increased by a factor of 2 1/2 is (5/2)x cups. This is equivalent to 2 1/2 times the original amount of white sugar. Therefore, the answer is A. 2 1/2 cups.

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To start off, identify your equation. You know P= 46, and L= 11, so you need to find W=. To do that, first you need to double your length, and width. So, L now equals 22, and W now equals 2W. Now, add W, and L, and it will need to be the original number. Simply subtract 22, from your product,  and divide by two, and you'll have W. Here's what the equation should look like.

(2 * 11) + 2W= 46

22 + 2W= 46

46 - 22= 24

2W= 24

W= 12 ft. Or, the width is 12 feet.

t = time to hike up the hill

3-t is the time to hike down the hill

 so 4t = 6(3-t)

4t = 18-6t

10t = 18

t = 18/10 = 1.8 hours to hike up the hill

1.8 hours = 1 hour 48 minutes

Answer:

The time it took him to climb up the hill is 1.8 hours.

Step-by-step explanation:

Here, t represents the the time it took him to climb up the hill,

Total time taken by it = 3 hours,

Thus, the time taken by it to climb down the hill = ( 3 - t ) hours.

Since, Trent hikes up a hill at 4 km/h,

⇒ Total distance covered by it to climb up = 4 t    (Distance = Speed × Time)

Since, Trent go down a hill at 6 km/h,

⇒ Total distance covered by it to go down = 6(3-t)  

We know that,

Total distance covered by it to climb up = Total distance covered by it to go down

⇒ 4t = 6(3-t)

Which is the required equation.

⇒ 4t = 18 - 6t

⇒ 10 t = 18

⇒ t = 1.8

Hence, the time it took him to climb up the hill is 1.8 hours.

The value of 6 cube or 6×6×6 or 6³ is 216.

A perfect square number when taken the square root of it results in an integer.

Numbers that are not perfect squares when taken the square root of it are irrational numbers.

One method of obtaining square roots for perfect squares is prime factorization.

Now, A perfect cube number is which when taken cube root results to an integer.

A number multiplied by itself by twice results in a cube of that number.

Therefore, The value of 6 cube would be 6 multiplied twice to itself, which is, = 6×6×6 = 36×6 = 216.

It can also be written as exponent form which is, 6³.

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The correct answer is

8,6 & 6, 9

Answer:

The correct options are 1 and 3.

Step-by-step explanation:

It is given that x represents the number of small boxes and y represents the number of large boxes.

The post office has 10 small boxes and 9 large boxes in stock.

He needs at least 4 small boxes.

[tex]4\leq x\leq 10[/tex]

He will buy no more than 15 boxes.

[tex]6+9=15\leq 15[/tex]

[tex]8+6=14\leq 15[/tex]

Therefore options 1 and 3 are correct.

[tex]x+y\leq 15[/tex]

[tex]7+10=17>15[/tex]

[tex]9+8>15[/tex]

Therefore options 2 and 4 are incorrect.

L'area del rettangolo in questione è 6449.5 cm quadrati, calcolata risolvendo l'equazione che unisce le due lunghezze date.

In questo problema matematico, siamo interessati a trovare l'area di un rettangolo. Sappiamo che la somma delle lunghezze dei due lati del rettangolo è 154 cm e che un lato è 5/6 della lunghezza dell'altro .

Possiamo iniziare ponendo x come la lunghezza più corta e 5x/6 come la lunghezza più lunga, in quanto è 5/6 della lunghezza di x. Sommando questi due valori, otteniamo l'equazione: x + 5x/6 = 154. Risolvendo questa equazione, otteniamo x = 88 cm.

Il lato più lungo del rettangolo sarà quindi 5/6 * 88, che è uguale a 73.33 cm. Per calcolare l'area del rettangolo, moltiplichiamo la lunghezza con la larghezza: 88 cm * 73.33 cm = 6449.5.

Quindi, l'area del rettangolo è 6449.5 cmquadrati.

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