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anastassius [24]
3 years ago
11

401(k) accounts are those that are partially funded by employers using a portion of wages before tax: true or false?

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
7 0

Answer:

FALSE

Step-by-step explanation:

It is false because 401(k) accounts are not funded by employer's wages but  <em>employees' </em>wages ; the latter voluntarily make contributions to a retirement account that is taken out of their wages before taxes . Employers on the other hand may partially or fully match a portion of these contributions.

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Solve for x 0=3x^2+3x+7​
Aloiza [94]

Answer:

x =(3-√-75)/-6=1/-2+5i/6√ 3 = -0.5000-1.4434i

x =(3+√-75)/-6=1/-2-5i/6√ 3 = -0.5000+1.4434i

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    0-(3*x^2+3*x+7)=0

Step by step solution:

Step  1:

Equation at the end of step  1  :

 0 -  ((-3x^{2} +  3x) +  7)  = 0  

<u>Step  2:</u>

Pulling out like terms:

2.1     Pull out like factors:

  -3x^{2} - 3x - 7  =   -1 • (3x^{2} + 3x + 7)

Trying to factor by splitting the middle term

2.2     Factoring  3x^{2} + 3x + 7

The first term is,  3x^{2}  its coefficient is  3 .

The middle term is,  +3x  its coefficient is  3 .

The last term, "the constant", is  +7

Step-1 : Multiply the coefficient of the first term by the constant   3 • 7 = 21

Step-2 : Find two factors of  21  whose sum equals the coefficient of the middle term, which is   3 .

     -21    +    -1    =    -22

     -7    +    -3    =    -10

     -3    +    -7    =    -10

     -1    +    -21    =    -22

     1    +    21    =    22

     3    +    7    =    10

     7    +    3    =    10

     21    +    1    =    22

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  3  :

 -3x^{2} - 3x - 7  = 0

<u>Step  3:</u>

Parabola, Finding the Vertex:

3.1      Find the Vertex of   y = -3x^{2}-3x-7

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -0.5000  

Plugging into the parabola formula  -0.5000  for  x  we can calculate the  y -coordinate :

 y = -3.0 * -0.50 * -0.50 - 3.0 * -0.50 - 7.0

or   y = -6.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = -3x^{2}-3x-7

Axis of Symmetry (dashed)  {x}={-0.50}

Vertex at  {x,y} = {-0.50,-6.25}

Function has no real roots

Solve Quadratic Equation by Completing The Square

3.2     Solving   -3x^{2}-3x-7 = 0 by Completing The Square .

Multiply both sides of the equation by  (-1)  to obtain positive coefficient for the first term:

3x^{2}+3x+7 = 0  Divide both sides of the equation by  3  to have 1 as the coefficient of the first term :

  x^{2}+x+(7/3) = 0

Subtract  7/3  from both side of the equation :

  x^{2}+x = -7/3

Now the clever bit: Take the coefficient of  x , which is  1 , divide by two, giving  1/2 , and finally square it giving  1/4

Add  1/4  to both sides of the equation :

 On the right hand side we have :

  -7/3  +  1/4   The common denominator of the two fractions is  12   Adding  (-28/12)+(3/12)  gives  -25/12

 So adding to both sides we finally get :

  x^{2}+x+(1/4) = -25/12

Adding  1/4  has completed the left hand side into a perfect square :

  x^{2}+x+(1/4)  =

  (x+(1/2)) • (x+(1/2))  =

 (x+(1/2))2

Things which are equal to the same thing are also equal to one another. Since

  x^{2}+x+(1/4) = -25/12 and

  x^{2}+x+(1/4) = (x+(1/2))2

then, according to the law of transitivity,

  (x+(1/2))2 = -25/12

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x+(1/2))2   is

  (x+(1/2))2/2 =

 (x+(1/2))1 =

  x+(1/2)

Now, applying the Square Root Principle to  Eq. #4.2.1  we get:

  x+(1/2) = √ -25/12

Subtract  1/2  from both sides to obtain:

  x = -1/2 + √ -25/12

 √ 3   , rounded to 4 decimal digits, is   1.7321

So now we are looking at:

          x  =  ( 3 ± 5 •  1.732 i ) / -6

Two imaginary solutions :

x =(3+√-75)/-6=1/-2-5i/6√ 3 = -0.5000+1.4434i

 or:

x =(3-√-75)/-6=1/-2+5i/6√ 3 = -0.5000-1.4434i

6 0
3 years ago
simplify 3/18 ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????
Anna [14]
The simplified version of 3/18 is 1/6
7 0
3 years ago
Please answer the picture
dimaraw [331]
The area is equal to 230 CM.
area for rectangle :
area = width times length
area = 7 x 20 = 140CM
area for triangle:
area = 1/2 times base times height
area = 1/2 x 20 x 9 = 90CM

ADD:
140+90 = 230 CM
3 0
3 years ago
Read 2 more answers
The table below represents the atmospheric temperature at a location as a function of the altitude:
RSB [31]

from x15 to x 25 is 4 - -16 = -20 degree change

25 -15 = 10000 feet

-20/10 = -2 degrees every 1000 feet


7 0
3 years ago
What is the value of x?<br> x = [ ? ]
Mnenie [13.5K]

Answer:

Step-by-step explanation:

The tangent to the angle makes an angle of 90° with the radius.

The interior angle of the equilateral triangle is 60, so that leaves 90-60 = 30° for the remaining angle with the tangent.

By the exterior angle theorem, 30°+x° = 60° (interior angle of the equilateral triangle), therefore

x = 60-30 = 30°.

4 0
3 years ago
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