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Studentka2010 [4]
3 years ago
13

Katherine wants to construct a small box with a volume of 20 cubic inches with the following specifications. The length of a box

is five more than its width. Its depth is one less than its width. What are the dimensions of the box in simplest radical form and rounded to the nearest hundredth? Only and algebraic solution will receive full credit.
Mathematics
1 answer:
kondor19780726 [428]3 years ago
4 0
In this question, you have to form the equation given the formula of the volume : L x W x D
L = W+5
W = W
D = W-1

(W+5)(W)(W-1) = 20
(W^2+5W)(W-1) = 20
W^3+4W^2-5W-20 = 0

Get the roots by factoring it out.
<span>(w +4) *(w +2.236) *(w -2.236)
</span>
So the roots are: -4, -2.236, 2.236.
Since we're talking about dimensions, let's use the positive root..

L = 7.24
W = 2.24
D = 1.24
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7 0
3 years ago
Tom has 5 comic books in his collections and receives 5 new comic books each month. Joe has 145 comic books, but sends 5 to each
Sindrei [870]

Answer:

In 7 Months both will have same number of comic books.

The both will have 40 comic books in 7 months.

Step-by-step explanation:

Let Number of months be x.

Given:

Tom Has number comic books = 5

Each month he receives number of books = 5

Total Number of books he has after x month can be calculated by sum of number of comic books he has + number of comic books he receives multiplied by number of months

Hence Total Number of books he has after x month = 5+5x

Also Given:

Joe Has number comic books = 145

Each month he send number of books to 1 friend = 5

Number of friends = 3

Hence books send to friend each month = 5\times3 =15

Total Number of books he has after x month can be calculated by Difference of number of comic books he has and number of comic books he send to friends multiplied by number of months

Hence Total Number of books he has after x month = 145-15x

We need to find the number of months in which both will have same number of of comic book.

Hence we can find by making both equation equal we get;

5+5x=145-15x

Combining same terms we get;

5x+15x=145-5\\20x =140\\x=\frac{140}{20}=7 \ months

Hence the will have same number of comic books after 7 months.

Now we need to find the number of books the both had after 7 months:

Tom has = 5+5x=5+5\times7= 5+35=40\ books

Joe has = 145 - 15x = 145 - 15\times7 = 145-105 = 40 \ books

Hence they both will have 40 comic books after 7 months.

4 0
3 years ago
Joe’s annual income has been increasing each year by the same dollar amount the first year his income was 19,500. 8 years later
Anna007 [38]

Answer:

The question is either poorly constructed or it is a trick question. We do not know "In what year was his income 30,300" because the years correlating to his income are not disclosed.  Even assuming the question was meant to be posed as "how many years later was his income 30,300" it is still flawed.

Step-by-step explanation:

To arrive at Joe's annual income increase, first subtract 19,500 from 27,900 to get 8400, which is his overall increase over the 8 years. Now divide 8400 by 8. You will get 1050.  Beginning with his income of 27,900, add 1,050 to each successive income amount and you will get the following progression:

27,900, 28,950, 30,000, 31,050, 32,100, 33,150, 34,200, 35,250, 36,300.

Therefore, two years after his income was 27,900 it would be 30,000 and 6 years after that it would be 36,300.  It would  never be 30,300.

6 0
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Evaluate 3f(2) what is it
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Answer:

12

Step-by-step explanation:

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