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3 years ago

Can a negative sign be used to describe a dilation?

Mathematics

1 answer:

hichkok12 [17]3 years ago

4 0

Answer:

Not on a coordinate plane

Step-by-step explanation:

We must use absolute value because lengths should always be positive you cannot have a negative length or distance.

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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.

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3 years ago

Convert to cups.<br><br> 9 quarts

arsen [322]

36 cups ........................................

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3 years ago

0.001 in Standard form

horrorfan [7]

1*10<span>- 3 is the standard form of 0.001</span>

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3 years ago

-2, -1, -1, 0, -1, 1, 2, ...

Andrei [34K]

2,3,3,4
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3 years ago

Read 2 more answers

A couple wants to install hardwood into their bedroom. The wood is bought in 0.5×5 square foot pieces. They have 422 square feet

Lesechka [4]

Answer:

169 sections

Step-by-step explanation:

A couple wants to install hardwood into their bedroom. The wood is bought in 0.5×5 square foot pieces

The area of the 0.5×5 square foot pieces

Area= 0.5*5.

Area= 2.5 square feet

They have 422 square feet of floor on which to install the hardwood.

Number of sections to be purchased

= 422/2.5

= 168.8 sections

Approximately= 169 sections

6 0

3 years ago