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denis23 [38]
2 years ago
8

Can someone please help me workout this problem? If the quotient obtained by dividing 8x^4 - 2x^2 + 6x - 7 by 2x+1 is equal to 4

x^3 + px^2 - qx +3, then find the remainder and also the values of p and q.
Mathematics
1 answer:
Angelina_Jolie [31]2 years ago
5 0

Answer:

The answer to your question is p = -2 q = -6  remainder = -10

Step-by-step explanation:

Data

Dividend = 8x⁴ - 2x² + 6x - 7

Divisor    = 2x + 1

Quotient = 4x³ + px² - qx + 3

Process

1.- Divide using long division

                                4x³ - 2x² + 3                          

                   2x + 1   8x⁴ + 0x³ - 2x² + 6x - 7

                             - 8x⁴ - 4x³

                                 0   - 4x³ - 2x²

                                      + 4x³ +2x²

                                          0       0   + 6x - 7

                                                          -6x - 3

                                                             0 - 10    Remainder

         px² = -2x²  then  p = -2

         -qx = 6x     then q = -6

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Step-by-step explanation:

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A bike shop rents bikes for $4.50 per hour, plus a $7.50 insurance charge. For how many hours can Peter rent a bike if he has $3
Mandarinka [93]

Answer:

With $30, Peter can afford 5 hours

Step-by-step explanation:

Given

Insurance Charge = $7.5

Charges = $4.5 per hour

Required

Determine the number of hours $30 can afford

First, we need to determine the equation.

<em>Total Charges = Charges per hour + Insurance Charge</em>

Substitute values for Charges per hour and Insurance Charge

Total Charges = 4.5 per hour + 7.5

Let the number of hours be n;

So,

Total Charges = 4.5n + 7.5

To calculate Peter's; substitute 30 for total charges

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Subtract 7.5 from both sides

4.5n = 30 - 7.5

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Divide both sides by 4.5

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Step-by-step explanation:

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1 child took 1 piece that actually means that x+y=18 and 3*x+5*y=84.

( Because total number of all kids is 19. We just deduct one kid (Let his name is John) who took only 1 candy.  So we have 19-1 =18 kids without John. The similar is with the candies. Total number is 85. We deduct 1 piece which John has taken. )

So we have 2 equations or the system of 2 equations:

1).  x+y=18

2). 3*x +5*y=84

Multuply both sides of equation 1) by 3

We have   3*x+3*y=18*3

Deduct 3*y from both sides of this equation

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Substitute 3*x in equation  2).  by 54-3*y

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y=15  ( kids take 5 pieces of candy each)

Using equation 1) find x

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