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viktelen [127]
3 years ago
13

Select the two values of x that are roots of this equation 2x-3=-5x^2

Mathematics
1 answer:
zvonat [6]3 years ago
3 0

\bold{Answer}

\boxed{\bold{X \ = \ -1, \ X \ = \ \frac{3}{5} }}

\bold{Explanation}

  • \bold{Find \ Two \ Values \ Of \ X: \ 2x-3=-5x^2}

\bold{-------------------}

  • \bold{Switch \ Sides}

\bold{-5x^2=2x-3}

  • \bold{Add \ 3 \ To \ Both \ Sides}

\bold{-5x^2+3=2x-3+3}

  • \bold{Simplify}

\bold{-5x^2+3=2x}

  • \bold{Subtract \ 2x \ From \ Both \ Sides}

\bold{-5x^2+3-2x=2x-2x}

  • \bold{Simplify}

\bold{-5x^2-2x+3=0}

  • \bold{Solve \ With \ The \ Quadratic \ Formula}
  • \bold{For \ The \ Quadratic \ Form \ For \ ax^2+bx+c=0 \ The \ Solutions \ Are \ x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}
  • \bold{For \ A \ =-5,\:b=-2,\:c=3:\quad x_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\left(-5\right)3}}{2\left(-5\right)}}

\bold{\frac{-\left(-2\right)+\sqrt{\left(-2\right)^2-4\left(-5\right)\cdot \:3}}{2\left(-5\right)}: \ -1}

\bold{\frac{-\left(-2\right)-\sqrt{\left(-2\right)^2-4\left(-5\right)\cdot \:3}}{2\left(-5\right)}: \ \frac{3}{5} }

  • \bold{Solutions}

\bold{x=-1,\:x=\frac{3}{5}}

\boxed{\bold{Eclipsed}}

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3 years ago
4-(2y-1)=2(5y+9)+y please help quick
stich3 [128]

Step-by-step explanation:Step 1: Simplify both sides of the equation.

4−(2y−1)=2(5y+9)+y

4+−1(2y−1)=2(5y+9)+y(Distribute the Negative Sign)

4+−1(2y)+(−1)(−1)=2(5y+9)+y

4+−2y+1=2(5y+9)+y

4+−2y+1=(2)(5y)+(2)(9)+y(Distribute)

4+−2y+1=10y+18+y

(−2y)+(4+1)=(10y+y)+(18)(Combine Like Terms)

−2y+5=11y+18

−2y+5=11y+18

Step 2: Subtract 11y from both sides.

−2y+5−11y=11y+18−11y

−13y+5=18

Step 3: Subtract 5 from both sides.

−13y+5−5=18−5

−13y=13

Step 4: Divide both sides by -13.

−13y

−13

=

13

−13

y=−1

 Answer: y =-1

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2 years ago
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What is Negative three-fourths + 2 and three-fourths
KATRIN_1 [288]
Answer: -0.25

Explanation:
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3. A new process has been developed for applying pho­ toresist to 125-mm silicon wafers used in manufac­ turing integrated circu
dlinn [17]

Answer:

a

The null hypothesis is  H_o : \mu  =  13.4000

The alternative hypothesis is  H_a :  \mu \ne  13.4000

The null hypothesis is rejected

b

The  99% confidence level is   13.3930  < \mu  < 13.3994

Step-by-step explanation:

From the question we are told that

  The sample size is  n =  10

   The  population mean is  \mu =  13.4 000 \  angstroms

   The level of significance is  \alpha =  0.05

   The  sample data is  

13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002

Generally the sample mean is mathematically represented as

        \= x =  \frac{13.3987+ 13.3957\cdots +13.4002 }{10}

=>     \= x = 13.3962

Generally the sample standard deviation  is mathematically represented as

    \sigma = \sqrt{\frac{\sum (x_i - \= x)^2}{n} }

=> \sigma = \sqrt{\frac{ (13.3987 - 13.3962)^2 +  (13.3987 - 13.3962)^2 + \cdots + (13.3987 -13.4002)^2  }{10} }

=>  \sigma =0.0039

The null hypothesis is  H_o : \mu  =  13.4000

The alternative hypothesis is  H_a :  \mu \ne  13.4000

Generally the test statistics is mathematically represented as

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

=>    z  =  \frac{13.3962 -  13.4000}{\frac{0.0039}{\sqrt{10} } }

=>   z =  3.08

Generally the p-value is mathematically represented as

       p-value  = 2P( z   >  3.08)

From the z-table  P(z >  3.08)= 0.001035

So

       p-value  = 2* 0.001035

      p-value  = 0.00207

So from the obtained value we see that

     p-value  < \alpha

Hence the null hypothesis is rejected

Consider the b question

Given that the confidence level is  99%  then the level of significance is

    \alpha =  (100 -99)\%

=> \alpha =  0.01

Generally from the normal distribution table critical value  of  \frac{\alpha }{2} is  

    Z_{\frac{\alpha }{2} } =  2.58

Generally the margin of error is mathematically represented as  

     E =  Z_{\frac{\alpha }{2} } *  \frac{\sigma}{\sqrt{n} }

=>   E = 2.58  *  \frac{0.0039}{\sqrt{10} }

=>    E = 0.00318

Generally the 99% confidence interval is mathematically represented as

     13.3962   - 0.00318  < \mu  < 13.3962   +  0.00318

=>   13.3930  < \mu  < 13.3994

 

7 0
3 years ago
An online furniture store sells chairs for $200 each and tables for $600 each. Every
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Answer:

Step-by-step explanation:

Answer:

If the minimum 13 chair were sold , then the minimum number of Table sold is 14

Step-by-step explanation:

Given as :

The cost of each chair = $ 200

The cost of each table = $ 600

The total number of furniture sold per day = 32

The minimum amount of selling per day = $ 12000

Let the total number of chair = C

The total number of table = T

So , according to question

C + T = 32         .......1

200 C + 600 T = 12000         .......2

Solving eq 1 and 2

200 C + 600 T = 12000

200 × ( C + T ) = 32 × 200

I.e 200 C + 200 T = 6400

or, ( 200 C + 600 T ) - ( 200 C + 200 T ) = 12,000 - 6400

Or, 400 T =  5600

∴  T =

I.e T = 14

Put The value of T in eq 2

So, 200 C + 600 × 14 = 12000

or , 200 C + 8400 = 12,000

Or, 200 C = 12000 - 8400

Or, 200 C = 3600

∴   C =

I.e C = 18

The number of chair sold is 18

If the number of chair sold is 13 ,

Then the min number of table sold = 200 × 18 + 600 T = 12000

i.e 600 T = 12000 - 3600

or, 600 T = 8400

∴   T =

I.e T = 14

Hence if the minimum 13 chair were sold , then the minimum number of Table sold is 14 . Answer

8 0
3 years ago
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