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topjm [15]
3 years ago
15

"the sum of the digits of a two-digit number is 13. reversing the digits produces a number that is 9 less than the original numb

er. what is the original number?"
Mathematics
1 answer:
Ksenya-84 [330]3 years ago
6 0
Suppose the one's digit is x, the ten's digit is y. the original number is 10y+x, the reversed number is 10x+y

x+y=13
(10x+y)=(10y+x)-9 =>9y-9x=9 =>y-x=1
Add the two equation to solve: 2y=14 =>y=7
x=13-7=6
the original number is 76. 


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3 similar shirts and 4 similar jackets cost $360. 1 such shirt and 3 such jackets cost $220. Find the costof each shirt.
Lyrx [107]
3s + 4j = 360
1s + 3j = 220

This one we can solve using substitution, in that
s + 3j = 220 implies s = 220 - 3j (subtract 3j from each side).

Now substitute into the first equation:

3(220 - 3j) + 4j = 360.  Solve for jackets.
660 - 9j + 4j = 360  [Distributive property]
660 - 5j = 360 [Add -9j + 4j]
Subtract 360 from each side, and add 5j to each side.
660 - 360 - 5j + 5j = 360 - 360 + 5j
300 = 5j
Divide each side by 5.
$60 = price of a jacket.

Three of these plus a shirt runs $220.
3(60) = 180
180 + s = 220
180 - 180 + s = 220 - 180 [Subtract 180 from each side]
s =   40

Now we double check.
3(40) + 4 (60) = 120 + 240 = 360.  This satisfies the first equation.
We could check the second one too, but I'm satisfied.
4 0
3 years ago
Which of the following sets are closed under multiplication? Select all that apply.
ivolga24 [154]

Answer:

Integers, whole numbers and polynomials are sets of closed under multiplication.

Only Irrational numbers are not the sets of closed under multiplication.                  

Step-by-step explanation:

To find : Which of the following sets are closed under multiplication?

1. Integers  

Yes, integers is a sets of closed under multiplication as if you multiply an integer by an integer, you will always get another  integer.

Example - 3\times 3=9 is an integer

2. Irrational numbers


No, irrationals are not closed under multiplication.

Example - \sqrt{3} \times \sqrt{3} =3 is a rational number

3. Whole numbers


Yes, whole numbers is a sets of closed under multiplication as if you multiply a whole number by a whole number, you will always get another  whole number.

Example - 5\times 5=25 is a whole number

4. Polynomials

Yes, polynomial is sets of closed under multiplication as if you multiply the variables' exponents are added, and the exponents in polynomials are whole numbers so the new exponents will be whole numbers.

Example - (x + 1)(x^2 + 4x + 3) = x^3 + 5x^2 + 7x + 3 is a polynomial.


4 0
3 years ago
Read 2 more answers
A tablet data provider offers different plans for data usage. The plan Raul chose has a monthly fee of $29.99 per month for 5 GB
jeka57 [31]

Answer:

The minimum number is 9 GB to make the unlimited cheaper

Step-by-step explanation:

* <em>Lets explain how to solve the problem</em>

- A tablet data provider offers different plans for data usage

- The plan Raul chose has a monthly fee of $29.99 per month for

 5 GB of data with an additional cost of $10 for each gigabyte

 over 5

* <u><em>Assume that he will use </em></u><u><em>n gigabyte per month</em></u>

∵ The monthly fee is $29.99 for 5 GB

∵ The cost per GB after the first 5 GB is $10

∵ The number of GB whose cost is $10 is (n - 5)

∴ His monthly fees = 29.99 + 10 (n - 5) ⇒ current plan

- Raul learns that his data provider is offering an unlimited data

 plan for $59.99 per month

∵ The fees of the unlimited is $59.99 per month

∵ We need the unlimited cheaper than current plane

- Let the current plan greater than the unlimited plan

∴ 29.99 + 10 (n - 5) > 59.99

- Subtract both sides by 29.99

∴ 10 (n - 5) > 30

- Divide both sides by 30

∴ n - 5 > 3

- Add both sides by 5

∴ n > 8

∴ The minimum number is 9 GB to make the unlimited cheaper

6 0
3 years ago
Which expression is equivalent to -<br> -9x-1,-9<br> -1575/-3 ? Assume X+0.
DedPeter [7]

Answer:

-9x-1534

Step-by-step explanation:

Simplifying the equation given will result in this answer. They are equal in value.

Hope this helps!

6 0
2 years ago
What is 6 times 6 times 2 equal?
Sedaia [141]
6×6×2=72 because 6×6=36 then do 36×2=72 so 6×6×2=72
8 0
3 years ago
Read 2 more answers
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