Answer:
10 ball caps
Step-by-step explanation:
In this question, we are trying to know the number of caps the manger would buy that would equate the cost at both companies.
How do we get this?
Since we do not know the number of caps, let’s assign a variable. Let the number of caps that is required be x. Let’s now make some costings in terms of x. We proceed;
Company X charges $50 fee plus $7 per cap. Total amount company X will charge on x caps will be; $50 + $7(x) = $50 + $7x
Company Y will charge $30 plus $9 per cap. Total amount company Y will charge on x caps will be $30 + $9(x) = $30 + $9x
We are trying to look at the value of x that will make both costs equal. What we do is to equate both costs.
30 + 9x = 50 + 7x
We simply by taking like terms to the same sides
9x-7x = 50-30
2x = 20
x = 20/2 = 10
X = 10
So what this means is that manger has to buy 10 caps to have the same cost in both companies
Rudy answered 2 more questions correctly
...........
46x2=92
44x2=88
...........
92-88=4
Answer:
The factorization of
is 
Step-by-step explanation:
This is a case of factorization by <em>sum and difference of cubes</em>, this type of factorization applies only in binomials of the form
or
. It is easy to recognize because the coefficients of the terms are <u><em>perfect cube numbers</em></u> (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).
Let's solve the factorization of
by using the <em>sum and difference of cubes </em>factorization.
1.) We calculate the cubic root of each term in the equation
, and the exponent of the letter x is divided by 3.
![\sqrt[3]{729x^{15}} =9x^{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B729x%5E%7B15%7D%7D%20%3D9x%5E%7B5%7D)
then ![\sqrt[3]{10^{3}} =10](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B10%5E%7B3%7D%7D%20%3D10)
So, we got that
which has the form of
which means is a <em>sum of cubes.</em>
<em>Sum of cubes</em>

with
y 
2.) Solving the sum of cubes.


.
Answer:
Step-by-step explanation:
Given
- 3 rectangular cards
- each card is 8 inches by 9 inches
The way that she can arrange the cards, without overlapping, to make one larger polygon with the smallest possible perimeter is that:
Put 3 cards together according to the length
So the smallest possible perimeter is:
8 + 8 + 8 + 8 + 8 + 8 + 9 + 9 = 66 inches as you can see in the attached photo.
The area of the polygon is equal to the combined area of the 3 cards without overlapping or extending.
Hope it can find you well.
Answer: dependent
Step-by-step explanation: