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3 years ago

Which function is linear?

Mathematics

1 answer:

Mariulka [41]3 years ago

7 0

Answer:

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

3 years ago

4x − 5y = 25 Make a table of values. ASAP

Lerok [7]

Answer:

Given Below.

explanation:

$4x - 5y = 25$

$-5y = 25 - 4x$

$y = \frac{25-4x}{-5}$

$y = \frac{4x- 25}{5}$

put x values in the function in order to find y values.

___x___ ___y___

0 | -5

1 | -4.2

2 | -3.4

3 | -2.6

4 | -1.8

5 | -1

6 | -0.2

6 0

3 years ago

List all the multiples of 4 up to 20

emmainna [20.7K]

4 , 8 , 12 , 16 , 20

3 0

3 years ago

Help me please All postulates have been proven to be true ? True or False

sashaice [31]

fales that is never gonna be proofen right

4 0

3 years ago

Read 2 more answers

What is the value of the expression (−2 4/5)÷(−1.4)

AysviL [449]

Answer:

Step-by-step explanation:

3 0

3 years ago