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artcher [175]
3 years ago
5

11.1.30 How many three-digit even numbers are possible if the leftmost digit cannot be zero?

Mathematics
1 answer:
Ann [662]3 years ago
4 0

The total number of 3 digit even numbers is 450

Step-by-step explanation:

Step 1 :

We need to determine the  number of 3 digit numbers which is even and the leftmost digit is not zero .

The  3 digits with left most digit not equal to zero starts from 100 and goes up to 998

If we consider only the even 3 digit numbers in this interval, this would form an arithmetic progression with the first number a = 100 and the common difference d = 2.

Step 2:

The last number l  in this series is 998 .

So we have

a = 100

l = 998

d = 2

The nth term in the arithmetic progression is given by a + (n-1) d

so substituting the above values we get

100 + (n-1) 2 = 998

2n = 900  => n = 450

Step 3 :

Answer :

The total number of 3 digit even numbers is 450

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Answer:

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Step-by-step explanation:

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Solve the following System of Three Equations:<br> x−3y+z=−15<br> 2x+y−z=−2<br> x+y+2z=1
SashulF [63]

Answer:

x = -3 , y = 4 , z = 0

Step-by-step explanation:

Solve the following system:

{x - 3 y + z = -15

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Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for z:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Solve for z.

Subtract x - 3 y from both sides:

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x + y + 2 z = 1

Hint: | Perform a substitution.

Substitute z = -15 - x + 3 y into the second and third equations:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

x + y + 2 (-15 - x + 3 y) = 1

Hint: | Expand the left hand side of the equation x + y + 2 (-15 - x + 3 y) = 1.

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15 + 3 x - 2 y = -2

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Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for x:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Isolate terms with x to the left hand side.

Subtract 15 - 2 y from both sides:

{z = -15 - x + 3 y

3 x = 2 y - 17

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Hint: | Solve for x.

Divide both sides by 3:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

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Hint: | Perform a substitution.

Substitute x = (2 y)/3 - 17/3 into the third equation:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

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Hint: | Choose an equation and a variable to solve for.

In the third equation, look to solve for y:

{z = -15 - x + 3 y

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Hint: | Isolate terms with y to the left hand side.

Add 73/3 to both sides:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 = 76/3

Hint: | Solve for y.

Multiply both sides by 3/19:

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Hint: | Perform a back substitution.

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Hint: | Perform a back substitution.

Substitute x = -3 into the first equation:

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Hint: | Sort results.

Collect results in alphabetical order:

Answer:  {x = -3 , y = 4 , z = 0

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