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3 years ago

How many times greater is the volue of the digit 7 in 52,221 than the volue of the digit 7 in 904,728?

Mathematics

1 answer:

Jlenok [28]3 years ago

4 0

Answer:

20,000

Step-by-step explanation:

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Two sets of equatic expressions are shown below in various forms: Line 1: x2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)2 − 0.25 Line 2: x

kherson [118]

Answer: The correct line is

$\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.$

Step-by-step explanation: We are given the following two sets of quadratic expressions in various forms:

$\textup{Line 1: }x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25,\\\\\textup{Line 2 :}x^2+5x+6=(x+2)(x+3)=(x+2.5)^2+6.25.$

We are to select one of the lines from above that represent three equivalent expressions.

We can see that there are three different forms of a quadratic expression in each of the lines:

First one is the simplified form, second is the factorised form and third one is the vertex form.

So, to check which line is correct, we need to calculate the factorised form and the vertex form from the simplified form.

We have

$\textup{Line 1: }\\\\x^2+3x+2\\\\=x^2+2x+x+2\\\\=x(x+2)+1(x+2)\\\\=(x+1)(x+2),$

and

$x^2+3x+2\\\\=x^2+2\times x\times 1.5+(1.5)^2-(1.5)^2+2\\\\=(x+1.5)^2-2.25+2\\\\=(x+1.5)^2-0.25.$

So,

$\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.$

Thus, Line 1 contains three equivalent expressions.

Now,

$\textup{Line 2: }\\\\x^2+5x+6\\\\=x^2+3x+2x+6\\\\=x(x+3)+2(x+3)\\\\=(x+2)(x+3),$

and

$x^2+5x+6\\\\=x^2+2\times x\times 2.5+(2.5)^2-(2.5)^2+6\\\\=(x+2.5)^2-6.25+6\\\\=(x+2.5)^2-0.25\neq (x+2.5)^2+6.25.$

So,

$\textup{Line 2 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2+6.25.$

Thus, Line 2 does not contain three equivalent expressions.

Hence, Line 1 is correct.

7 0

4 years ago

Find the slope of the line. - 3x – 2y = 7

Troyanec [42]

Answer:

-1.5

Step-by-step explanation:

7 0

3 years ago

An airplane left Atlanta with 20 empty seats. If the airplane was 75% full, what was the total number of seats on the airplane?

jek_recluse [69]

Answer is C. 80

hope that helps

75% are full with 20 seats empty so 20 seats empty = 25%

75% * 20 / 25% = 60

8 0

3 years ago

Katie has these 2 boxes shaped likerectangular prísms. How do the volumes of the two bones compare?

r-ruslan [8.4K]

Answer:

Box 2 has 3 times the volume of Box 1....

3 0

2 years ago

3. Is the relation {(1,2), (3, 10), (2,8), (5, 10)} a function? a) yes b) no a

Sedaia [141]

Answer:

the answer is yes

Step-by-step explanation:

4 0

3 years ago