What is the gfc of 18,54 and 72

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

3 years ago

plz help im stuck on it. caterers are planning to use 5 pounds of salad greens with 1/3 pound of greens in each salad how many s

sweet [91]

I believe the most logical answer would be is to divide so us the kcf method keep change flip so 5 stays the same then change division into multiplication then flip the fraction 1/3 into 3/1 so now we have 5 times 3 is 15

7 0

2 years ago

The graph below shows two polynomial functions, f(x) and g(x): Graph of f of x equals x squared minus 2 x plus 1. Graph of g of

IceJOKER [234]

9514 1404 393

Answer:

(c) f(x) is an even degree polynomial with a positive leading coefficient.

Step-by-step explanation:

The leading terms of the two functions are ...

f(x): x² (even degree, positive coefficient: 1)

g(x): x³ (odd degree, positive coefficient: 1)

Then it is true that ...

f(x) is an even degree polynomial with a positive leading coefficient

8 0

2 years ago

HELPPPPPPP MEEEEEEEEE

boyakko [2]

Answer:

The first table

Step-by-step explanation:

the third and fourth table are incorrect because it says Jo bought 25 apples in total but in the third and fourth table there are 35 apples in total.

the second table is incorrect because it said three of the 12 large apples were red. In the second table its says 12 large apples when its supposed to say three and the total in 15 instead of 12.

3 0

2 years ago

Read 2 more answers

What is the perimeter of the figure?

Allisa [31]

Answer:

Answer is D, all you do is add the numbers

7 0

2 years ago