From the question given, we were told that the nth tower is formed by stacking n blocks on top of an n times n square of blocks. This implies that the number of blocks in n tower will be:

n + n²

Now let us use the diagram to validate the idea.

Tower 1:

n = 1

Number of blocks = 1 + 1² = 2

Tower 2:

Number of blocks = 2 + 2² = 6

Tower 3:

Number of blocks = 3 + 3² = 12

Using same idea, we can obtain the number of blocks in the 99th tower as follow:

Tower 99:

n = 99

Number of blocks = 99 + 99² = 9900

Therefore, the 99th tower contains 9900 blocks.

7 0

3 years ago

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

3 years ago

Read 2 more answers

The university is trying to compile a visual display of the different majors of honor roll students which type of display will g

nordsb [41]

I believe that the answer to the question provided above is that the type of display will give them the best picture of her students data is a bar graph.
Hope my answer would be a great help for you. If you have more questions feel free to ask here at Brainly.

4 0

3 years ago

Read 2 more answers

(4, -2), y = –2x + 3 PLS HELP HOW DO I DO THIS?

Alex787 [66]

It looks like your instructor wants you to write in point-slope form.

the equation for point slope form is quite simple

y-y1=m(x-x1)

your variables:

y and x: just state these as they are

m: slope

y1 and x1: the numbers in the point given

keep in mind a double negative equals a positive, so when you come across a negative coordinate you would put + instead of - in your equation.

your final answer would be

y+2=-2(x-4)

I hope this helped :)

please don't hesitate to ask if you have any more questions

3 0

2 years ago