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aksik [14]
3 years ago
9

The sum of the digits of a certain two-digit number is 7. Reversing its digits increase the number by 9. What is the number?

Mathematics
2 answers:
Elis [28]3 years ago
5 0
Let the two numbers be x and y.

According to your question;

x + y = 7
10y + x = 10x + y + 9

By equation 1 ; x = 7-y

Substituting the value of x ;

10y + ( 7 -y) = 10(7-y) + y + 9

9y + 7 = 70 -10y + y + 9

9y + 7 = 70 - 9y + 9

=> 18y = 70 -7 + 9
=> 18y = 72
=> y = 4

Substituting for x ;

x = 7 - y
=> x = 7 -4
=> x = 3

Thus, x = 3 and y = 4;
=> The number is 34.
AleksandrR [38]3 years ago
3 0
The original number is <u>34 </u>.
The sum of its digits is (3 + 4) = 7 .
Reversing its digits makes it 43 . . . 9 more than 34.

How I did it:  (There must be a much more elegant mathematical method)

There are only 6 possibilities for the original number.
They are . . .

16
25
34
43
52
61 .

Instead of trying to dream up a sophisticated equation,
I decided it was faster and easier to just go down the list
and look for one that worked. 
The third one I tried worked.
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3 years ago
A horse ran 800 meters in 40 seconds , 1200 meters in 60 seconds , and 480 meters in 24 seconds . Is this a proportional relatio
frosja888 [35]

Answer:

This is a proportional relationship, the constant of proportionality is 20m/s and it represents that the horse can run 20 meters every second.  

Equation:  d = 20s, where d=distance and s=number of seconds.

Step-by-step explanation:

In order to find out whether this relationship is proportional, you need to see if the rate at which the horse runs is constant (the same).  If you look at the three sets of data (24, 480), (40, 800) and (60, 1200) where the pair is (seconds, meters), you can see that for any two sets of data the change in meters divided by the change in seconds is consistently 20m/s.  For example:

\frac{1200-800}{60-40}=\frac{400}{20}=20

Since the constant is 20, we know that the horse can run 20 meters every second.  To find the horse's total distance, we need to multiply the rate by the number of seconds that it runs:

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8 0
3 years ago
HELP What is the area of this figure?
Mademuasel [1]
The correct answer is:  [B]:  "40 yd² " .
_____________________________________________________
First, find the area of the triangle:

The formula of the area of a triangle, "A":

A = (1/2) * b * h ; 

in which:  " A = area (in units 'squared') ;  in our case, " yd² " ; 

                 " b = base length" = 6 yd.  

                 " h = perpendicular height" = "(4 yd + 4 yd)" = 8 yd.
___________________________________________________
→  A = (1/2) * b * h = (1/2) * (6 yd) * (8 yd) = (1/2) * (6) * (8) * (yd²) ; 
                                                                 
                                                                   =  " 24 yd² " .
___________________________________________________
Now, find the area, "A", of the square:

The formula for the area, "A" of a square:

   A = s² ;

in which:  "A = area (in "units squared") ; in our case, " yd² " ;
                 
                 "s = side length (since a 'square' has all FOUR (4) equal side lengths);

 A = s²  = (4 yd)² = 4² * yd² =  "16 yd² "
_________________________________________________
Now, we add the areas of BOTH the triangle AND the square:
_________________________________________________
        →  " 24 yd²  +  16 yd² " ; 

to get:  " 40 yd² " ;  which is:  Answer choice:  [B]:  " 40 yd² " .
_________________________________________________
4 0
3 years ago
Can someone help me again please. I will pay extra fr please
fgiga [73]

Answer:

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Step-by-step explanation:

First, you check for the y-intercept, which is 3 for this equation.

In order to find the slope, pick two points and apply the slope formula.

I would just use rise/run. The slope should be 3/1.

3 0
3 years ago
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