Answer:
You can use Desmos, or any online graph-er to graph the line.
Answer:
y=2/3x + 5
Step-by-step explanation:
If you would like
to write the following in the math expression, you can do this using these
steps:<span>
<span>a number ... </span>n
eight less than four times a number ... 4 * n - 8</span>
<span>
is less than 56 ... < 56
4 * n - 8 < 56
4 * n < 56 + 8</span>
<span>4 * n < 64 /4</span>
<span>n < 64 / 4</span>
<span>n < 16</span>
The possible values of that number are less than 16.
We have two unknowns from the equation therefore, two equations are needed. These equations are:
<span>
3x + y = 9
y = –4x +10
To solve for y, we first substitute the second equation to the first one.
</span>3x + –4x +10<span>= 9
</span><span>x = 1
We substitute the value of x to either of the equations and solve for y.
</span>y = –4(1) +<span>10
</span><span>y = 6
</span>
Answer:
Yes!
Step-by-step explanation:
Let x be the tens place and y be the units place. x and y need to be odd because in other case a or b will not be odd. For example, if x=1 and y=2 a will be 21 but b will be 12 that is not odd.
Now, a+b = xy+yx. Note that xy is not x*y, is just the digits concatenated.Then, there are two cases:
If x+y<10 then xy+yx = (x+y)(x+y) (again, that is not a multiplication is x+y concatenated with x+y) and that is 11*(x+y) a multiple of 11.
If x+y≥10 then xy+yx = (x+y+1)(x+y-10) because x+y<20.
Now we are going to see that last result without the concatenation, as a sum, that is
(x+y+1)*10 + x+y-10 = 10x+10y+10+x+y-10 = 11x+11y = 11(x+y). This result is clearly a multiple of 11.
In conclusion, in all cases the result of a+b is a multiple of 11.
