6.08 times 3.15 is 19.152.
9514 1404 393
Answer:
D. Henry's started farther, went faster
Step-by-step explanation:
Henry's balloon traveled 18 additional miles (from 30 to 48) in 2 hours, so had a speed of 18mi/(2h) = 9 mi/h. The equation for his position could be ...
y = 9x +30 . . . . . 9 is the rate of change; 30 is the initial value
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Comparing this to Tasha's position function, we see her balloon started 20 miles from town and traveled 8 miles per hour.
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Henry started farther from town and traveled faster.
<span>the sum of three consecutive odd integers is 69. Find the integers.
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1st: 2x-1
2nd: 2x+1
3rd: 2x+3
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Equation:</span>2x-1 + 2x+1 + 2x+3 = 69<span>
</span><span>6x + 3 = 69
2x + 1 = 23
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So 2x-1 = 21
And 2x+3 = 25
</span><span>let:
x be the first odd integer
x + 2 be the 2nd odd integer
x + 4 be the 3rd odd integer
solution:
1st odd integer + 2nd odd integer + 3rd odd integer = 69
x + (x+2) + (x+4)= 69
</span>
<span>3x + 6 = 69
3x = 69 - 6
3x = 63 (dividing both sides by three)
x = 21
_______________________________________
x=21
x+2=23
x+4=25
therefore, the 1st integer is 21, the 2nd is 23 and the 3rd is 25..</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.
