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gregori [183]
3 years ago
12

The sum of the digits of a 2-digit number is 10. If 18 is added to the number, the digits of the new number are those of the ori

ginal number but in reverse order. Find the original number.
Mathematics
1 answer:
Aliun [14]3 years ago
7 0

Answer:

46

Step-by-step explanation:

Let (ab) represent a number with a in the ten's position and b is the one's position.

This means (ab) actually has value of 10a+b.

We are given the sum of those digits of (ab) is 10; this means a+b=10.

It says if 18 is added to the number (ab), then the result is (ba).

So (ab) has value 10a+b and

(ba) has value 10b+a.

We are given then:

(ab)+18=(ba)

10a+b+18=10b+a

Subtract 10a on both sides:

b+18=10b+a-10a

Simplify:

b+18=10b-9a

Subtract b on both sides:

18=10b-b-9a

18=9b-9a

Divide both sides by 9:

2=b-a

Rearrange by commutative property:

2=-a+b

So the system of equations we want to solve is:

a+b=10

-a+b=2

-------------------------Add equations together (this will eliminate the variable a and allow you to go ahead and solve for b:

0+2b=12

2b=12

Divide both sides by 2:

b=\frac{12}{2}

Simplify:

b=6

If b=6 and a+b=10, then a=4.  a=4 since 4+6=10.

So the original number is (46).

18 more than 46 is 18+46=(64) which is what we wanted.

We also have the sum of 4 and 6 is 10 as well.

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Solve for these letters<br> X<br> Y<br> Z
tester [92]
Z = 140
X = 40
Y = 40
Explanation:
Z and the angle given (140 degrees) are vertical angles, and are therefore congruent
We know that x and y are vertical angles, so they are also congruent to each other
You know that together, the angles have to add up to 360
140 + 140 + x + y = 360
Another way of putting it:
360-280 = 80
Now, we have to divide by two since we need to find x AND y
80/2 = 40
Therefore, your answers for x and y are 40
To double check, you can add up the angles and see if they equal 360
140 + 140 + 40 + 40
280 + 80 = 360
7 0
3 years ago
Which is equal to (2x − 3y + 5z) − (−4x − y + 8z)?
Fittoniya [83]
(2x - 3y + 5z) - (-4x - y + 8z)
= 2x - 3y + 5z + 4x + y - 8z
= 6x - 2y - 3z

In short, Your Answer would be Option D

Hope this helps!
8 0
3 years ago
Please help me thank you so much
HACTEHA [7]
I think the answer is 15
5 0
2 years ago
In the kite, if PN=10 inched, MN=5 inches and NQ=8 inches find the length of MP
irga5000 [103]

It is C

Step-by-step explanation:

Because if you take into consideration that pn is equal to 10 and mn is equal to 5 and nq is equal to 8 then you add all them up which gives you 23 then subtract 14, and you get 9

Hope this helped you

7 0
3 years ago
How many three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters
Vadim26 [7]
So basically you just want to say:

5 choices, with five choices stemming from that, with five more choices stemming from that.

(Drawing a tree would show that well)

Or, 

5 * 5 * 5

Which is,

25 * 5

Or 125.

So 125 three letter words can be made from the letter FGHIJ 
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