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Simplify u^2+3u/u^2-9 A.u/u-3, =/ -3, and u=/3 B. u/u-3, u=/-3

VashaNatasha [74]

  The correct answer is: Answer choice: [A]:
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→  " $\frac{u}{u-3}$ " ; " { u $\neq$ ± 3 } " ;

  →  or, write as: " u / (u − 3) " ;  {" u ≠ 3 "}  AND: {" u ≠ -3 "} ;
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Explanation:
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We are asked to simplify:

   $\frac{(u^2+3u)}{(u^2-9)}$ ;

Note that the "numerator" —which is: "(u² + 3u)" — can be factored into:
  → " u(u + 3) " ;

And that the "denominator" —which is: "(u² − 9)" — can be factored into:
  → "(u − 3) (u + 3)" ;
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Let us rewrite as:
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→ $\frac{u(u+3)}{(u-3)(u+3)}$ ;

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→ We can simplify by "canceling out" BOTH the "(u + 3)" values; in BOTH the "numerator" AND the "denominator" ;  since:

" $\frac{(u+3)}{(u+3)} = 1$ " ;

→ And we have:
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→  " $\frac{u}{u-3}$ " ; that is: " u / (u − 3) " ; { u $\neq 3$ } .
and: { u $\neq-3$ } .

→ which is:  "Answer choice: [A] " .
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NOTE:  The "denominator" cannot equal "0" ; since one cannot "divide by "0" ;

and if the denominator is "(u − 3)" ; the denominator equals "0" when "u = -3" ; as such:

"u $\neq$ 3" ;

→ Note: To solve: "u + 3 = 0" ;

Subtract "3" from each side of the equation;

→ " u + 3 − 3 = 0 − 3 " ;

→ u = -3 (when the "denominator" equals "0") ;

→ As such: " u $\neq$ -3 " ;

Furthermore, consider the initial (unsimplified) given expression:

→   $\frac{(u^2+3u)}{(u^2-9)}$ ;

Note:  The denominator is: "(u²  − 9)" .

The "denominator" cannot be "0" ; because one cannot "divide" by "0" ;

As such, solve for values of "u" when the "denominator" equals "0" ; that is:
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→ " u² − 9 = 0 " ;

→ Add "9" to each side of the equation ;

→ u² − 9 + 9 = 0 + 9 ;

→ u² = 9 ;

Take the square root of each side of the equation;
to isolate "u" on one side of the equation; & to solve for ALL VALUES of "u" ;

→ √(u²) = √9 ;

→ | u | = 3 ;

→ " u = 3" ; AND; "u = -3 " ;

We already have: "u = -3" (a value at which the "denominator equals "0") ;

We now have "u = 3" ; as a value at which the "denominator equals "0");

→ As such: " u $\neq 3$ " ; "u $\neq$ -3 " ;

or, write as: " { u $\neq$ ± 3 } " .

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6 0

3 years ago

Help me ill give branilyest

Luda [366]

Answer:

The unit price is the cost per unit of an item or the cost/price for each item.

1) 4$ per pound. By simplifying the proportion (constant ratio) between the cost, and the pounds of apples. 3 pounds of apples cost 12$ → 3/3 pounds of apples cost 12/3$ → 4 dollars for every pound.

2) 2$ per pound. By evaluating the rate of change (change in the y over x or dependent variable over independent) in the equation: y = 2x. y is the cost in dollars, and x is the pounds of apples. So there are 2 pounds (weight) of apples for every dollar.

3) 3$ per pound. Given a graph with a y scaled by 3, and an x scaled by 1 with a graph y = x or 1 unit up for every unit right. This must be equivalent to y = 3x. Where y is labeled as the cost in dollars, and x as the weight in pounds. So there are 3 dollars for every pound of apples.

4) Store B. Because 2 is less than 3 which is less than 4.

7 0

3 years ago

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Consider a uniform distribution from aequals4 to bequals29. (a) Find the probability that x lies between 7 and 27. (b) Find th

weeeeeb [17]

Answer:

a) 80% probability that x lies between 7 and 27.

b) 28% probability that x lies between 6 and 13.

c) 44% probability that x lies between 9 and 20.

d) 28% probability that x lies between 11 and 18.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value x between c and d, in which d is larger than c, is given by the following formula.

$P(c \leq x \leq d) = \frac{d - c}{b - a}$

Uniform distribution from a = 4 to b = 29

(a) Find the probability that x lies between 7 and 27.

So $c = 7, d = 27$

$P(7 \leq x \leq 27) = \frac{27 - 7}{29 - 4} = 0.8$

80% probability that x lies between 7 and 27.

(b) Find the probability that x lies between 6 and 13. 

So $c = 6, d = 13$

$P(6 \leq x \leq 13) = \frac{13 - 6}{29 - 4} = 0.28$

28% probability that x lies between 6 and 13.

(c) Find the probability that x lies between 9 and 20.

So $c = 9, d = 20$

$P(9 \leq x \leq 20) = \frac{20 - 9}{29 - 4} = 0.44$

44% probability that x lies between 9 and 20.

(d) Find the probability that x lies between 11 and 18.

So $c = 11, d = 18$

$P(11 \leq x \leq 18) = \frac{18 - 11}{29 - 4} = 0.28$

28% probability that x lies between 11 and 18.

3 0

3 years ago

Which algebraic expression is equivalent to the expression below?

prohojiy [21]

You can again ignore the parenthesis because you are not distributing anything.
Your equation will look like this

3x + 11 + 6x

You can move each of these numbers around any way you like. You can combine the 3x and the 6x if you want, but they did not do that. You cannot take the x away and put it in front of the 11 though.

B. is your answer. All they did was move the 6x inside the parenthesis and the 11 out of the parenthesis.

Always remember, when you are adding things together, the parenthesis don't matter!

3 0

3 years ago

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When ordering a student desk priced at $69.00, the shipping charges are 6%. What is the total cost of the desk?

Wittaler [7]

Since the desk is $69.00 and the shipping charges are 6%

69*.06= 4.14

Your tax would be $4.14 so,

$4.14+$69.00= A total of $73.14

7 0

3 years ago

Read 2 more answers