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3 years ago

Is 7.2 a rational number

Mathematics

1 answer:

padilas [110]3 years ago

6 0

Step-by-step explanation:

A decimal is a number that represents a fractional part of a whole. For example, the decimal 0.25 represents 25/100. Numbers with decimals are not integers because an integer is defined as a whole number with no fractional part.

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Hot dogs come in packages of 10 and hot dog buns come in packages of 8 . What is the least amount of product that you need to Bu

lubasha [3.4K]

This exercise is solved by finding the least common multiple between 10 and 8.

In fact, you have to buy a certain number $h$ of hot dog package, and you will have $10h$ hot dogs, since there are 10 hot dogs in each package. The key concept here is that the number of hot dogs you have in the end is a multiple of the number of hot dogs in each box.

Similarly, you have to buy a certain number $b$ of hot dog buns package, and you will have $8b$ hot dogs, since there are 8 hot dog buns in each package. Again, the key concept here is that the number of hot dog buns you have in the end is a multiple of the number of hot dog buns in each box.

Then, you want to have the same number of hot dogs and hot dog buns, i.e. you want

$10h = 8b$

but you also want $h$ and $b$ to be the first values to satisfy this equation.

This means that you want a multiple of 10 to equal a multiple of 8, and you want the smallest possible number which does the trick. Again, this is exactly the definition of the least common multiple.

To find the least common multiple of two numbers, find their prime factorization, and collect all the primes from both factorizations, with the highest exponent possible. Since $10 = 2\cdot 5$ and $8 = 2^3$ , the primes appearing are 2 and 5. The higher exponent for 2 is 3, and the only exponent for 5 is 1. So, the answer is $2^3\cdot 5 = 40$ .

So, if you buy 4 packages of hot dogs and 5 packages of hot dog buns, you will have 40 hot dogs and 40 hot dog buns, as requested.

4 0

4 years ago

Read 2 more answers

Do you know what is 1/5 of 35

deff fn [24]

Answer:

Step-by-step explanation:

Because 35/5=7 so 1/5 of 35 would = 7

7 0

4 years ago

Read 2 more answers

F(x) = x^2+3x-4 and g(x)=x-1

padilas [110]

Answer:y ÷ 2 + x; use x = 1, and y = 2y ÷ 2 + x; use x = 1, and y = 2y ÷ 2 + x; use x = 1, and y = 2y ÷ 2 + x; use x = 1, and y = 2y ÷ 2 + x; use x = 1, and y = 2y ÷ 2 + x; use x = 1, and y = 2y ÷ 2 + x; use x = 1, and y = 2y ÷ 2 + x; use x = 1, and y = 2y ÷ 2 + x; use x = 1, and y = 2y ÷ 2 + x; use x = 1, and y = 2y ÷ 2 + x; use x = 1, and y = 2y ÷ 2 + x; use x = 1, and y = 2

Step-by-step explanation:

7 0

3 years ago

Need help with homework

motikmotik

We have two points describing the diameter of a circumference, these are:

$\begin{gathered} A=(-12,-4) \\ B=(-4,-10) \end{gathered}$

Recall that the equation for the standard form of a circle is:

$(x-h)^2+(y-k)^2=r^2$

Where (h,k) is the coordinate of the center of the circle, to find this coordinate, we find the midpoint of the diameter, that is, the midpoint between points A and B.

For this we use the following equation:

$M=(\frac{x_1+x_2_{}_{}}{2},\frac{y_1+y_2}{2})$

Now, we replace and solve:

$\begin{gathered} M=(\frac{-12+(-4)}{2},\frac{-4+(-10)}{2} \\ M=(\frac{-12-4}{2},\frac{-4-10}{2}) \\ M=(\frac{-16}{2},\frac{-14}{2}) \\ M=(-8,-7) \end{gathered}$

The center of the circle is (-8,-7), so:

$\begin{gathered} h=-8 \\ k=-7 \end{gathered}$

On the other hand, we must find the radius of the circle, remember that the radius of a circle goes from the center of the circumference to a point on its arc, for this we use the following equation: