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IrinaVladis [17]
3 years ago
11

The graph of the function f(x) = x3 – 2x2 – 19x + 20 intersects the x-axis at the points (–4, 0), (1, 0), and (5, 0) as shown.

Mathematics
2 answers:
Alona [7]3 years ago
7 0
-4, 5, and 1


......................
Oksana_A [137]3 years ago
3 0

Answer: A) x = –4, x = 1, and x = 5

the verified answer actually didn't answer the question so

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Simplify u^2+3u/u^2-9<br> A.u/u-3, =/ -3, and u=/3<br> B. u/u-3, u=/-3
VashaNatasha [74]
  The correct answer is:  Answer choice:  [A]:
__________________________________________________________
→  "\frac{u}{u-3} " ;  " { u \neq ± 3 } " ; 

          →  or, write as:  " u / (u − 3) " ;  {" u ≠ 3 "}  AND:  {" u ≠ -3 "} ; 
__________________________________________________________
Explanation:
__________________________________________________________
 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)" ;
___________________________________________________________
Let us rewrite as:
___________________________________________________________

→    \frac{u(u+3)}{(u-3)(u+3)}  ;

___________________________________________________________

→  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:
_________________________________________________________

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

→ which is:  "Answer choice:  [A] " .
_________________________________________________________

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\neq3" ; 

→ 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:
_______________________________________________________ 

→  " 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 } " .

_________________________________________________________
6 0
3 years ago
What is the 38th term of 459,450,441,..
galina1969 [7]

Answer:

The 38th term of 459,450,441,.. will be:

a_{13}=351

Step-by-step explanation:

Given the sequence

459,450,441,..

An arithmetic sequence has a constant difference 'd' and is defined by

a_n=a_1+\left(n-1\right)d

computing the differences of all the adjacent terms

450-459=-9,\:\quad \:441-450=-9

so

d=-9

The first element of the sequence is

a_1=459

so the nth term will be

a_n=-9\left(n-1\right)+459

a_n=-9n+468

Putting n=38 to find the 38th term

a_n=-9n+468

a_{13}=-9\left(13\right)+468

a_{13}=-117+468

a_{13}=351

Therefore, the 38th term of 459,450,441,.. will be:

a_{13}=351

3 0
2 years ago
Tom bought a soft drink for $4.00 and 7 candy bars. He spent a total of $18.00. How
olga2289 [7]

Answer:

$2

Step-by-step explanation:

$18-$4=$14

$14/7=$2

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Madison Middle School has a math and science club that holds meetings after school. The club has decided to enter a two-day comp
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Answer:

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