A digit is a number in one of the places, so for example the number 54 has two digits; a tens place digit (5) and a ones place digit (4).
Say the mystery number is a two digit number = xy
* that's not x times y but two side by side digits.
Info given:
<span>the sum of the digits of a two-digit number is 6
x + y = 6 </span>
<span>if the digits are reversed, yx the difference between the new number and the original number is 18.
**To obtain the number from digits you must multiply by the place and add the digits up. (Example: 54 = 10(5) + 1(4))
Original number = 10x + y
Reversed/New number = 10y + x
Difference:
10y + x - (10x + y) = 18
9y - 9x = 18
9(y - x) = 18
y - x = 18/9
y - x = 2
Now we have two equations in two variables
</span>y - x = 2
<span>x + y = 6
Re-write one in terms of one variable for substitution.
y = 2 + x
sub in to the other equation to combine them.
x + (2 + x) = 6
2x + 2 = 6
2x = 6 - 2
2x = 4
x = 2
That's the tens digit for the original number. Plug this value into either of the equations to obtain y, the ones digit.
2 + y = 6
y = 4
number "xy" = 24
</span>
Answer:
8, 10
Step-by-step explanation:
Multiplying the equation by the product of the denominators, we have ...
40(x+2) +40x = 9x(x+2)
80x +80 = 9x^2 +18x . . . . eliminate parentheses
9x^2 -62x -80 = 0 . . . . . . put in standard form
9x^2 -72x +10x -80 = 0 . . . prepare to factor by grouping
9x(x -8) +10(x -8) = 0 . . . . . factor pairs of terms
(9x +10)(x -8) = 0
Solutions are ...
x = -10/9 and x = 8
The integers are 8 and 10.
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<em>Comment on the attachment</em>
I find a graphing calculator to be a nice tool for solving these. It finds zeros easily, so writing the equation so it equals zero is a useful first step.
Try 21 if its wrong sorry im not very smart
Answer:
5^20 • 7^40
Step-by-step explanation:
each exponent needs to multiply each 10.
