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3 years ago

3 Sean has 8-inch pieces of toy train track and Ruth has 18-inch pieces of train track. How

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

7 0

Answer:

Step-by-step explanation:

The smallest number that is divisible by two given numbers is called the Least Common Multiple (LCM) of those numbers.

What's the smallest number that is a multiple of 8 and also a multiple of 18?

One way to find out is to start making lists of multiples:

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, and so on,

Multiples of 18: 18, 36, 54, 72, 90, 108, and so on.

This method can be a bit tedious, but in this case, it's clear that 72 is the LCM of 8 and 18.

Another method is to use the prime factorization of the two numbers.

Write 8 and 18 as the product of prime numbers; each number has a unique prime factorization.

8 = 2 x 2 x 2 = 2^3

18 = 2 x 3 x 3 = 2^1 x 3^2

To form the LCM, build a product of primes using the highest exponent in either of the two numbers.

LCM = 2^3 x 3^2 = 8 x 9 = 72.

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Having trouble with add or subtracting the given polynomials

Bumek [7]

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Hope this helps!

3 0

3 years ago

Read 2 more answers

An inequality is shown below. x + 2.5 < 20 What is the greatest value of x from the set {10.5, 12.5, 17.5, 19.5} that makes t

34kurt

C is the final answer :)

4 0

3 years ago

Which equation does not represent a direct variation?

tatuchka [14]

Okay I think there has been a transcription issue here because it appears to me there are two answers. However I can spot where some brackets might be missing, bear with me on that.

A direct variation, a phrase I haven't heard before, sounds a lot like a direct proportion, something I am familiar with. A direct proportion satisfies two criteria:

The gradient of the function is constant s the independent variable (x) varies

The graph passes through the origin. That is to say when x = 0, y = 0.

Looking at these graphs, two can immediately be ruled out. Clearly A and D pass through the origin, and the gradient is constant because they are linear functions, so they are direct variations.

This leaves B and C. The graph of 1/x does not have a constant gradient, so any stretch of this graph (to y = k/x for some constant k) will similarly not be direct variation. Indeed there is a special name for this function, inverse proportion/variation. It appears both B and C are inverse proportion, however if I interpret B as y = (2/5)x instead, it is actually linear.

This leaves C as the odd one out.

I hope this helps you :)

4 0

3 years ago

the radius of a gold atom is 1.35 angstroms. how many gold atoms would it take to line up a span of 8.5 mm?

serg [7]

The angstrom, also known as the angstrom unit, is a measure of displacement equal to 0.0000000001 meter (10 -10 m). It would be helpful to convert the units of angstrom to mm. We do as follows:

diameter = 2 x 1.35 x10^ -10 m ( 1000 mm / 1 m ) = 2.7 x 10^-10 mm / atom

Number of gold atoms = 8.5 mm / 2.7 x 10^-10 mm / atom = 31481481481.481 atoms

6 0

3 years ago

Read 2 more answers

Which of the following polynomial functions is graphed below? OA. f(x) = (x - 2) ^ 2 * (x + 3) * (x - 1) O B. f(x) = (x + 2) ^ 2

laila [671]

The function of the polynomial is (b) $f(x) = (x + 2) ^ 2 * (x - 3) * (x + 1)$