Solve the inequality.

Use the ordinary division of polynomials to find the quotient and remainder when the first polynomial is divided by the second.

Vanyuwa [196]

The quotient and remainder when the first polynomial is divided by the second are -4w^2 - 7w - 21 and -71 respectively

<h3>How to determine the quotient and remainder when the first polynomial is divided by the second?</h3>

The polynomials are given as:

-4w^3 + 5w^2 - 8, w - 3

Set the divisor to 0.

So, we have

w - 3 = 0

Add 3 to both sides

w = 3

Substitute w = 3 in -4w^3 + 5w^2 - 8 to determine the remainder

-4(3)^3 + 5(3)^2 - 8

Evaluate the expression

-71

This means that the remainder when -4w^3 + 5w^2 - 8 is divided by w - 3 is -71

The quotient (Q) is calculated as follows:

Q = [-4w^3 + 5w^2 - 8]/[w - 3]

The numerator can be expressed as follows:

Numerator = -4w^3 + 5w^2 - 8

Subtract the remainder.

So, we have:

Numerator = -4w^3 + 5w^2 - 8 + 71

This gives

Numerator = -4w^3 + 5w^2 + 61

So, the quotient becomes

Q = [-4w^3 + 5w^2 + 61]/[w - 3]

Expand

Q = [(w - 3)(-4w^2 - 7w - 21)]/[w - 3]

Evaluate

Q = -4w^2 - 7w - 21

Hence, the quotient and remainder when the first polynomial is divided by the second are -4w^2 - 7w - 21 and -71 respectively

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6 0

2 years ago

Rachel's learning to play the violin Monday through Friday she practices 45 minutes on each day on Saturday and Sundays he broug

I am Lyosha [343]

Rachel spends 6 hours 45 minutes a week trying to learn to play the violin.

Step-by-step explanation:

Step 1; Rachel learns for 45 minutes a day from Monday through Friday and in the weekend she learns to play the violin for one and a half hours. So she learns for the following periods of time

Monday - 45 minutes

Tuesday - 45 minutes

Wednesday - 45 minutes

Thursday - 45 minutes

Friday - 45 minutes

Saturday - 90 minutes (60 × 1.5 hours)

Sunday - 90 minutes (60 × 1.5 hours)

Step 2; To determine how much time she practices in a week we just add the individual times she plays on each day.

Total time practices in a week = 45 + 45 + 45 + 45 + 45 + 90 + 90 = 405 minutes = 6 hours 45 minutes.

5 0

3 years ago

Haley can bake 6 cookies with each scoop of flour. Write an equation that shows the relationship between the scoops of flour x a

m_a_m_a [10]

Answer:

the answer is y=6x

(6 is a constant)

Explanation:

3 0

3 years ago

Write the equation of a line that is perpendicular to the given line and that passes through the given point.

HACTEHA [7]

First, let's re-arrange to slope-intercept form.

x + 8y = 27

Subtract 'x' to both sides:

8y = -x + 27

Divide 8 to both sides:

y = -1/8x + 3.375

So the slope of this line is -1/8, to find the slope that is perpendicular to this, we multiply it by -1 and flip it. -1/8 * -1 = 1/8, flipping it will give us 8/1 or 8.

So the slope of the perpendicular line will be 8.

Now we can plug this into point-slope form along with the point given.

y - y1 = m(x - x1)

y - 5 = 8(x + 5)

y - 5 = 8x + 40

y = 8x + 45

7 0

3 years ago

David found and factored out the GCF of the polynomial 80b4 – 32b2c3 + 48b4c. His work is below. GFC of 80, 32, and 48: 16 GCF o

BlackZzzverrR [31]

Answer: The correct statements are

The GCF of the coefficients is correct.

The variable c is not common to all terms, so a power of c should not have been factored out.

David applied the distributive property.

Step-by-step explanation:

GCF = Greatest common factor

1) GCF of coefficients : (80,32,48)

80 = 2 × 2 × 2 × 2 × 5

32 = 2 × 2 × 2 × 2 × 2

48 = 2 × 2 × 2 × 2 × 3

GCF of coefficients : (80,32,48) is 16.

2) GCF of variables :( $b^4,b^2,b^4$ )

$b^4$ = b × b × b × b

$b^2$ = b × b

$b^4$ =b × b × b × b

GCF of variables :( $b^4,b^2,b^4$ ) is $b^2$

3) GCF of $c^3$ and c: c is not the GCF of the polynomial. The variable c is not common to all terms, so a power of c should not have been factored out.

4) $80b^4-32b^2c^3+48b^4c$

$=16b^2(5b^2-2c^3+3b^2c)$

David applied the distributive property.

7 0

3 years ago

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