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3 years ago

How many seven-digit numbers are there when 0 and 8 cannot be the leading number?

Mathematics

1 answer:

qwelly [4]3 years ago

3 0

It is given that leading number cannot be 0 and 8 . So, choices are :

[ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 9 ] i.e 8 choices.

Now, choices of other six digits are [ 0, 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8, 9 ] i.e 10 choices.

So, number of seven digits with given constraint is :

N = 8×10×10×10×10×10×10

N = 8000000

Therefore, seven-digit numbers with given constrain are 8000000.

Hence, this is the required solution.

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3 years ago

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Agata [3.3K]

Answer:

Option (d).

Step-by-step explanation:

Note: The base of log is missing in h(x).

Consider the given functions are

$h(x)=\log_2x$

$m(x)=\log_2(x+3)$

The function m(x) can be written as

$m(x)=h(x+3)$ ...(1)

The translation is defined as

$m(x)=h(x+a)+b$ .... (2)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2), we get

$a=3,b=0$

Therefore, we have to translate each point of the graph of h(x) 3 units left to get the graph of m(x).

Hence, option (d) is correct.

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3 years ago

a container built in the shape of a cylinder has a circular base with a radius of 1.5 meters. the altitude of the container is 3

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Answer:

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4 years ago

Read 2 more answers

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Answer:

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Step-by-step explanation:

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castortr0y [4]

Answer: second option y = 2(x + 7/2)^2 + 1/2

Explanation:

1) given:

y = (x + 3)^2 + (x + 4)^2

2) expand the binomials:

y = x^2 + 6x + 9 + x^2 + 8x + 16

3) add like terms:

y = 2x^2 + 14x + 25

4) take common factor 2 of the first two terms:

y = 2 (x^2 + 7x) + 25

5) complete squares for x^2 + 7x

x^2 + 7x = [x +(7/2)x ]^2 - 49/4

6) substitue x^2 + 7x = (x + 7/2)^2 - 49/4 in the equation for y:

y = 2 [ (x + 7/2)^2 - 49/4] + 25

7) take -49/4 out of the square brackets.

y = 2 (x + 7/2)^2 - 49/2 + 25

8) add like terms:

y = 2(x + 7/2)^2 + 1/2

And that is the vertex for of the given expression.

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3 years ago