Can someone help me please

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

How much does an ice cream cost with 11 ounces of toppings?

oksano4ka [1.4K]

$3.00 for ice cream

+ $2.00 for the 4 ounces of toppings

$5.00

hope it helps!!

SMILE!!

4 0

3 years ago

What is factored form of the expression 16st+15t

svet-max [94.6K]

Answer:

t(16s+15)

Step-by-step explanation:

The highest common factor of 16st+15t is t.

t(16s) + t(15)

Factor.

t(16s+15)

8 0

3 years ago

Read 2 more answers

Joan draws a bar chart to show the temperatures at midday on March 1st in five cities. Joan has made four mistakes in her diagra

Aleksandr [31]

Answer:

Step-by-step explanation:

Properties of a bar graph:

1). There should be equal space between the bars or the columns.

2). Width of each bar or columns should be same.

3). All bars should have same base.

4). Height of each bar will show the value of the data.

By these properties,

- Space between London-Paris, Rome-Oslo are not equal.

- Width of Munich bar is different from other bars.

8 0

3 years ago

Read 2 more answers

Shanta got 215 marks in an examination. if she had got 10 marks more, she would have scored 60% of the total marks. What are the

ololo11 [35]

She got 215....but if she would have gotten 10 more, she would have scored 60% of the total marks......so if she got (215 + 10) = 225 she would have scored 60% of the total marks...

so 60% of the total marks = 225
0.60x = 225
x = 225/0.60
x = 375 <===

8 0

3 years ago