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3 years ago

10. The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46

Mathematics

1 answer:

Zarrin [17]3 years ago

7 0

Answer:

hope this helps

Step-by-step explanation:

The sum of the digits of a three-digit number is 11.

If the digits are reversed, the new number is 46 more than five times the old number.

If the hundreds digit plus twice the tens digit is equal to the units digit, then what is the number?

Write an equation for each statement:

"The sum of the digits of a three-digit number is 11."

x + y + z = 11

The three digit number = 100x + 10y + z

The reversed number = 100z + 10y + x

" If the digits are reversed, the new number is 46 more than five times the old number."

100z + 10y + x = 5(100x + 10y + z) + 46

100z + 10y + x = 500x + 50y + 5z + 46

combine on the right

0 = 500x - x + 50y - 10y + 5z - 100z + 46

499x + 40y - 95z = -46

"the hundreds digit plus twice the tens digit is equal to the units digit,"

x + 2y = z

x + 2y - z = 0

Three equations, 3 unknowns

x + y + z = 11

x +2y - z = 0

-----------------Addition eliminates z

2x + 3y = 11

From the 2nd equation statement, we know that the 1st original digit has to be 1

2(1) + 3y = 11

3y = 11 - 2

3y = 9

y = 3 is the 2nd digit

then

1 + 3 + z = 11

z = 11 - 4

z = 7

137 is the original number

Check solution in the 2nd statement

If the digits are reversed, the new number is 46 more than five times the old number."

731 = 5(137) + 46

731 = 685 + 46

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Mashutka [201]

Answer:

a. Convex solutions ,GO Methods

b. market efficiency

Explanation :

Step-by-step explanation:

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In convex optimization problems, a locally optimal solution is also globally optimal. These include LP problems; QP problems where the objective is positive definite (if minimizing; negative definite if maximizing); and NLP problems where the objective is a convex function (if minimizing; concave if maximizing) and the constraints form a convex set. But many nonlinear problems are non-convex and are likely to have multiple locally optimal solutions, as in the chart below. (Click the chart to see a full-size image.) These problems are intrinsically very difficult to solve; and the time required to solve these problems to increases rapidly with the number of variables and constraints.

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pishuonlain [190]

Answer:

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