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Irina-Kira [14]
3 years ago
12

Prove that the inequality x(x+ 1)(x+ 2)(x+ 3) ≥ −1 holds for all real numbers x.

Mathematics
1 answer:
vredina [299]3 years ago
6 0
(x²+x)(x²+5x+6) = x^4 + 6x³ + 11x² + 6x  + 1 ≥0
f(x) = x^4 + 6x³ + 11x² + 6x  + 1
f'(x) = 4x³ + 18x² +22x +6 
racines x1 = -0,301 x2 = -1,5 x3 = -2,618
variations 

x                                  -2,62                    -1,5                   -0,3
f'(x)                      -          0             +          0           -            0          +
f(x)    -inf            \            0             /                        \             0           /

on voit que cette fonction st toujours positive
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Can't get my head around this at all any help would be greatly appreciated.​
chubhunter [2.5K]

Answer:

The input is -6, hope this helps :D

Step-by-step explanation:

Represent the machines as expressions:

outputA= 7x-6

outputB= 3x+2

Find the input when the outputA is 3*outputB:

outputA=3outputB

(7x-6)=3(3x+2)

7x-6=9x+6

2x=-12

x=-6

3 0
2 years ago
Read 2 more answers
PLS HELP DUE IN 10 MINUTES I WILL GIVE BRAINLIEST FIVE STARS AND A THANKS NO JOKE IM RLLY DESPERATE SO PLS HELPPPPPP :c IF U DID
frutty [35]

Answer:

-1/2

Step-by-step explanation:

counting down by 2 over one

6 0
2 years ago
Lexie, a bowler, claims that her bowling score is more than 140 points, on average. Several of her teammates do not believe her,
Crazy boy [7]

Answer:

The  test statistic is  t  = 3.744

Step-by-step explanation:

From the question we are told that

  The population mean is  \mu  =  140

  The  The  level of significance is  \alpha  =  0.05

  The  sample size is  n =  18

   The  null hypothesis is  H_o :  \mu =  140

    The  alternative hypothesis is  H_a  :  \mu > 140

    The sample mean is  \= x  =  155

     The  standard deviation is  \sigma  =  17

Generally the test statistics is mathematically represented as

       t  =  \frac{\= x  - \mu }{ \frac{ \sigma}{ \sqrt{n} } }

substituting values

      t  =  \frac{ 155  - 140 }{ \frac{ 17 }{ \sqrt{18} } }

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7 0
3 years ago
The value of 8-[12-(-4)]
pochemuha

Answer:

-8

Step-by-step explanation:

Following Order of Operations rules, we evaluate anything within parentheses first:

8-[12-(-4)] = 8 - 16 = -8

8 0
2 years ago
From this given statement, select the definition , property, postulate, or theorem that justifies the prove statement.
USPshnik [31]
Additive property of equality states that:

if a=b, then a+c = b+c, 

that is, if 2 quantities of the same value are added the same quantity, they are again equal.


In our problem a=AD, b=DB,    and c= CD=DE

thus a+c=b+c means <span>AD + CD = DE + DE, 

by the </span><span>Addition Property


Answer: </span><span>Addition Property

</span>
5 0
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