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4 years ago

I need some help with perimeters of triangles

Mathematics

1 answer:

Gennadij [26K]4 years ago

5 0

36 inhes ..........................................

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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

What foreign language is this bro (requires answer for part a and b )

kotegsom [21]

Given

a) x+x+x+x+x+x

b) 30y-12

Find

Equivalent expressions

Explanation

a) x + x + x + x + x + x = 6x

b) 30y-12 = 6(5y-2)

$\begin{gathered} 30y-12 \\ 6\cdot5y-6\cdot2 \end{gathered}$

Final Answer

a) the equivalent expression is 6x .

b) the equivalent expression is

$\begin{gathered} 6\cdot5y-6\cdot2 \\ and \\ 6(5y-2) \end{gathered}$

5 0

2 years ago

The table represents a linear function

Anton [14]

Answer:

the answer is: False

8 0

3 years ago

A train leaves Ayr station everyday at 10:06 and arrives in Glasgow at 12:51. How long is the journey?

fenix001 [56]

Answer: 2hours 45 minutes

Hope I'm being helpful...!!!

4 0

3 years ago

1.Define phase shift. Could every sine function be expressed as a phase shifted cosine function? Explain.

Ann [662]

A phase shift is defined as the a<span>mount of x by which sinusoid is shifted to the left or right.

And yes, </span><span>every sine function be expressed as a phase shifted cosine function:
</span>
sin(t)=cos(90-t)

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

4 0

3 years ago