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goblinko [34]
3 years ago
5

Explain in your own words the difference between a solid boundary line and a dashed boundary line on a graph of systems of inequ

alites. Elaborate on what it would mean for a solution to fall on a dashed boundary line in a system.
Mathematics
1 answer:
Mandarinka [93]3 years ago
8 0
A solid line would represent points on the graph that actually are included in the solution, while points that lie on dash lines aren’t included in the solution
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What is the length of MO, given that figure LMNO is a square?
fgiga [73]

Answer:

8 (C)

Step-by-step explanation:

The diagonals of a square are congruent and bisect each other.

One half of a diagonal = 4

Therefore, the whole diagonal is 8.

5 0
3 years ago
Read 2 more answers
What is the difference? StartFraction 2 x + 5 Over x squared minus 3 x EndFraction minus StartFraction 3 x + 5 Over x cubed minu
Sunny_sXe [5.5K]

Answer:

<h2>\frac{(x + 5)(x + 2)}{ {x}^{3} - 9x }</h2>

First option is the correct option.

Step-by-step explanation:

\frac{2x + 5}{ {x}^{2} - 3x }  -  \frac{3x + 5}{ {x}^{3} - 9x }  -  \frac{x + 1}{ {x}^{2} - 9 }

Factor out X from the expression

\frac{2x + 5}{x(x - 3)}  -  \frac{3x + 5}{x( {x}^{2}  - 9)}  -  \frac{x + 1}{ {x}^{2}  - 9}

Using {a}^{2}  -  {b}^{2}  = (a - b)(a + b) , factor the expression

\frac{2x + 5}{x(x - 3)}  -  \frac{3x + 5}{x(x - 3)(x + 3) }  -  \frac{x + 1}{(x - 3)(x + 3)}

Write all numerators above the Least Common Denominators x ( x - 3 ) ( x + 3 )

\frac{(x + 3) \times (2x - 5) - (3x + 5) - x \times (x + 1)}{x(x - 3)(x + 3)}

Multiply the parentheses

\frac{2 {x}^{2}  + 5x + 6x + 15 - (3x + 5) - x(x + 1)}{x(x - 3)(x + 3)}

When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression

\frac{2 {x}^{2}  + 5x + 6x + 15 - 3x - 5 - x \times (x + 1)}{x(x - 3)(x + 3)}

Distribute -x through the parentheses

\frac{2 {x}^{2}  + 5x + 6x + 15 - 3x - 5 -  {x}^{2} - x }{x(x - 3)(x + 3)}

Using {a}^{2}  -  {b}^{2}  = (a + b)(a - b) , simplify the product

\frac{2 {x}^{2}  + 5x + 6x + 15 - 3x - 5 -  {x}^{2}  - x}{x( {x}^{2}  - 9)}

Collect like terms

\frac{ {x}^{2}  + 7x + 15 - 5}{x( {x}^{2}  - 9)}

Subtract the numbers

\frac{ {x}^{2}  + 7x + 10}{ x({x}^{2}   - 9)}

Distribute x through the parentheses

\frac{ {x}^{2}  + 7x + 10}{ {x}^{3}  - 9x}

Write 7x as a sum

\frac{ {x}^{2} + 5x +2x + 10 }{ {x}^{3} - 9x }

Factor out X from the expression

\frac{x(x + 5) + 2x + 10}{ {x}^{3}  - 9x}

Factor out 2 from the expression

\frac{x( x + 5) + 2(x + 5)}{ {x}^{3} - 9x }

Factor out x + 5 from the expression

\frac{(x + 5)(x + 2)}{ {x}^{3} - 9x }

Hope this helps...

Best regards!!

6 0
3 years ago
Read 2 more answers
#2
I am Lyosha [343]

You have the right idea that things need to get multiplied.

What should be done is that the entire fraction needs to get multipled by the lowest common denominator of both denominators.

Let's look at the complex numerator. Its denominators are 5 and x + 6. Nothing is common with these, so both pieces are needed.

The complex denominator has x - 3 as its denominator. With nothing in common between it and the complex numerator, that piece is needed.

So we multiply the entire complex fraction by (5)(x + 6)(x -3).

Numerator: (\frac{1}{5} -\frac{5}{x + 6})(5)(x +6)(x-3) =\frac{1}{5}(5)(x +6)(x-3) -   \frac{5}{x + 6}(5)(x +6)(x-3)

= (x+6)(x-3) - (5)(5)(x-3)

= (x+6)(x-3) - 25(x-3)

= (x-3)(x + 6 - 25) <--- by group factoring the common x - 3

= (x -3)(x - 19)

Denominator:

\frac{25}{x - 3} * (5)(x + 6)(x - 3) = (25)(5)(x + 6) = 125(x + 6)


Now we put the pieces together.


Our fraction simplies to (x - 3) (x - 19) / 125 (x + 6)

5 0
3 years ago
A contractor estimated that one of his two brick layers would take 9 hours to build a certain wall and the other 10 hours. Howev
Dmitry [639]

Answer:

900

Step-by-step explanation:

Assume x brick

X*(1/9+1/10)一 10=X/5

X(19/90-1/5)=10

X*(1/90)=10

X=900

6 0
3 years ago
PLEASE ANSWERRRRRRRRRR
Jet001 [13]

Step-by-step explanation:

D. Both charges must be different.

Because, like charges repel each other and different charges attract each other.

5 0
3 years ago
Read 2 more answers
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