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Kipish [7]
3 years ago
14

If the simple interest on $5,000 for 4 years is $1,600, then what is the interest rate?

Mathematics
1 answer:
matrenka [14]3 years ago
8 0

Answer:

0.08, or 8%

Step-by-step explanation:

The appropriate formula is i = p*r*t, where p is the principal, r is the interest rate as a decimal fraction, and t is the time in years.

We want to calculate r when i, p and t are known.

                                                           i

Solving i = p*r*t for r, we get r = ------------

                                                       p*t

The interest rate in this case is

        $1600

r = ---------------- = 0.08, or 8%

      $5000*4

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F(x)=x^4-5x^2-6x-10 is divided by x-3
LiRa [457]

Answer:

Step-by-step explanation:

STEP

1

:

           10

Simplify   ——

           x

Equation at the end of step

1

:

                       10

 ((((x4)-(5•(x2)))-6x)-——)-3

                       x

STEP

2

:

Equation at the end of step

2

:

                           10    

 ((((x4) -  5x2) -  6x) -  ——) -  3

                           x      

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  x  as the denominator :

                     x4 - 5x2 - 6x     (x4 - 5x2 - 6x) • x

    x4 - 5x2 - 6x =  —————————————  =  ———————————————————

                           1                    x        

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  x4 - 5x2 - 6x  =   x • (x3 - 5x - 6)

Polynomial Roots Calculator :

4.2    Find roots (zeroes) of :       F(x) = x3 - 5x - 6

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -6.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,3 ,6

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -2.00    

     -2       1        -2.00        -4.00    

     -3       1        -3.00        -18.00    

     -6       1        -6.00        -192.00    

     1       1        1.00        -10.00    

     2       1        2.00        -8.00    

     3       1        3.00        6.00    

     6       1        6.00        180.00    

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

4.3       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • (x3-5x-6) • x - (10)     x5 - 5x3 - 6x2 - 10

————————————————————————  =  ———————————————————

           x                          x        

Equation at the end of step

4

:

 (x5 - 5x3 - 6x2 - 10)    

 ————————————————————— -  3

           x              

STEP

5

:

Rewriting the whole as an Equivalent Fraction

5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  x  as the denominator :

        3     3 • x

   3 =  —  =  —————

        1       x  

Checking for a perfect cube :

5.2    x5 - 5x3 - 6x2 - 10  is not a perfect cube

Trying to factor by pulling out :

5.3      Factoring:  x5 - 5x3 - 6x2 - 10

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -6x2 - 10

Group 2:  x5 - 5x3

Pull out from each group separately :

Group 1:   (3x2 + 5) • (-2)

Group 2:   (x2 - 5) • (x3)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

5.4    Find roots (zeroes) of :       F(x) = x5 - 5x3 - 6x2 - 10

    See theory in step 4.2

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -10.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,5 ,10

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -12.00    

     -2       1        -2.00        -26.00    

     -5       1        -5.00       -2660.00    

     -10       1       -10.00       -95610.00    

     1       1        1.00        -20.00    

     2       1        2.00        -42.00    

     5       1        5.00        2340.00    

     10       1        10.00       94390.00    

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

5.5       Adding up the two equivalent fractions

(x5-5x3-6x2-10) - (3 • x)      x5 - 5x3 - 6x2 - 3x - 10

—————————————————————————  =  ————————————————————————

            x                            x            

Polynomial Roots Calculator :

5.6    Find roots (zeroes) of :       F(x) = x5 - 5x3 - 6x2 - 3x - 10

    See theory in step 4.2

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -10.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,5 ,10

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -9.00    

     -2       1        -2.00        -20.00    

     -5       1        -5.00       -2645.00    

     -10       1       -10.00       -95580.00    

     1       1        1.00        -23.00    

     2       1        2.00        -48.00    

     5       1        5.00        2325.00    

     10       1        10.00       94360.00    

Polynomial Roots Calculator found no rational roots

Final result :

 x5 - 5x3 - 6x2 - 3x - 10

 ————————————————————————

            x            

3 0
3 years ago
–3.4 + (–8 + 2) = [ ? + (–8)] + 2<br><br> whats the missing number
Ilia_Sergeevich [38]
I suppose what makes this question annoying is that there is the question mark so what i'll do first is substitute the question mark with x. also, there are annoying parenthesis so we'll first eliminate the ones we don't need. now we just have to solve for x. -3.4 + (-8 + 2) = (x + (-8)) + 2 adding a negative number is subtracting that number so x + (-8) = x - 8 -3.4 + 2 - 8 = x - 8 + 2 -3.4 -6 = x - 6 x = -3.4 make sure you are aware that the negative sign belongs to the number after it so -2 + 4 is not -(2+4) = -6 but rather 4 - 2 = 2. let me know if you have any questions!
7 0
3 years ago
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