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2 years ago

5. Given (x + 1) and (x-3) are factors of P(x) = x4-5x³-7x² + cx + d. Determine the values

1 answer:

4 0

By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.

<h3>How to determine the missing coefficients of a quartic equation</h3>

A value x is a root of a polynomial if and only if p(x) = 0. We must replace the given equation with the given roots and solve the resulting system of <em>linear</em> equations:

(- 1)⁴ - 5 · (- 1)³ - 7 · (- 1)² + (- 1) · c + d = 0

- c + d = 1 (1)

3⁴ - 5 · 3³ - 7 · 3² + 3 · c + d = 0

3 · c + d = 117 (2)

The solution of this system is c = 29 and d = 30.

By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.

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A certain type of brass contains 65% copper. How many pounds of copper are contained in 120 pounds of brass?

enyata [817]

The number of pounds of copper in 120 pounds of brass is = 78 pounds of copper

<h3>Calculation of number of pounds of copper</h3>

The percentage of copper in the brass = 65%

Therefore the quantity of copper in the brass = 65/100= 0.65 pounds

This means that 1 pound brass contains = 0.65 pounds of copper

The quantity of copper in 120 pounds of brass = 120 * 0.65

= 78 pounds of copper.

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7 0

2 years ago

Any one can help me please please I need help please each one 3 step explanation

Art [367]

Answer:

a) Area of wall to be painted = 114 sq ft

b) Number of cans required = 2×5 = 10

c) Total cost of paint = $338.43

Step-by-step explanation:

We are asked to find the area of wall that needs to be painted.

we need to subtract the area of window from the area of wall.

We know that area of a rectangular shape is given by

Area = Width×Length

Area of whole wall = 8×15 = 120 sq ft

Area of window = 2×3 = 6 sq ft

Area of wall to be painted = 120 - 6 = 114 sq ft

1 can of paint will cover 25 sq ft of area.

So to cover the area of wall to be painted,

114/25 = 4.56

since number of cans cannot be in fraction so we would need 5 cans

Since two coats of paints are needed so

Number of cans required = 2×5 = 10

1 can of paint costs $29.95

We have total 10 cans

$29.95×10 = $299.5

There is also a 13% tax so the total cost is

$299.5×0.13 = $38.93

Total cost of paint = $299.5 + $38.93

Total cost of paint = $338.43

3 0

3 years ago

Do these equations have infinite solutions 2x + 5y= 31 and 6x -y = 13

katovenus [111]

$2x = 31 - 5y \\ x = \frac{31}{2} - \frac{5}{2}y$

$6x = 13 + y \\ x = \frac{13}{6} + \frac{1}{6} y$

8 0

3 years ago

Margaret makes bracelets and sells them to tourists. the function s(t) approximates how many bracelets margaret makes per hour.

Fantom [35]

The units for the composite function s(w(h)) is <u>bracelets over a week</u> when the function s(t) approximates how many bangles Margaret makes per hour and the function w(h) represents how many hours per week Margaret spends making the bracelets.

To define the unit of the composite function s(w(h)), we first need to find the units of the functions s(t) and w(h).

The function s(t) represents the number of bangles per hour, so its unit will be bangles over an hour.

The function w(h) represents the hours per week spent on making the bracelets, so its unit will be hours over a week.

Now, we can define the unit of the composite function s(w(h)).

To find the unit of the composite function we follow these steps:-

s(w(h)),

= s(hours over a week) {replacing the function w(h) by its units},

= (bangles over an hour(hours over a week)) {replacing the function s(t) with its units},

= bangles over a week {Simplifying}.

Thus, the units for the composite function s(w(h)) is <u>bracelets over a week</u> when the function s(t) approximates how many bangles Margaret makes per hour and the function w(h) represents how many hours per week Margaret spends making the bracelets.

Learn more about the units of a composite function at

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4 0

2 years ago

Slader the internal revenue service claims it takes an average of 3.7 hours to complete a 1040 tax form, assuming th4e time to c

Vitek1552 [10]

Answer:

0.9953, 3.3629<x<4.0371

Step-by-step explanation:

Given that slader the internal revenue service claims it takes an average of 3.7 hours to complete a 1040 tax form, assuming th4e time to complete the form is normally distributed witha standard devait of the 30 minutes:

If X represents the time to complete then

X is N(3.7, 0.5) (we convert into uniform units in hours)

a) percent of people would you expect to complete the form in less than 5 hours

= $100*P(x$

b) P(b<x<c) = 0.50

we find that here

c = 4.0371 and

b = 3.3629

Interval would be

$(3.3629, 4.0371)$

6 0

3 years ago