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3 years ago

Show that p(x)=2x3−5x2−10x+5 has a real root.

1 answer:

6 0

Let's pick an arbitrary value of 5.

$P(5) = 2(5)^{3} - 5(5)^{2} - 10(5) + 5$
$= 2(125) - 125 - 50 + 5$
$= 250 - 125 - 50 + 5$
$= 80 > 0$

Let's pick another arbitrary value: 1

$P(1) = 2 - 5 - 10 + 5$
$= -8 < 0$

Between these two values, the polynomial is continuous. This means for the two polynomial points to be satisfied, there must be at least one root between these two points.

We can either use the Intermediate Value Theorem or Newton's method to make a better approximation from there.

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A number x is equal to 7. 24. 48. What is the smallest positive integer y such that the product xy is a perfect cube

Tcecarenko [31]

What’s the questionv

8 0

2 years ago

Match the words in the left-hand column to the appropriate blank in the sentences in the right-hand column. Use each word only o

pshichka [43]

The slowly increasing distance between South America and Africa is due to: a. <u>Seafloor Spreading</u>.
Old Faithful Geyser at Yellowstone National Park in the United States of America acquires its energy from a: b. Hot Spot.
Layered <u>sedimentary rock</u> exposed by erosion can be seen when looking at the Grand Canyon in the United States of America.
Australia is made up of relatively old and thick: d. Continental Crust.
The extremely deep ocean Marianas Trench is a result of: g. Subduction.
<u>Seafloor Crust</u>: found in the Atlantic Ocean between North America and Europe comprises dense and relatively young rock.
The earthquakes that occur in Southern California generally occur above a: f. Fault.

<h3>What is seafloor spreading?</h3>

<u>Seafloor spreading</u> can be defined as a process that involves the formation of new oceanic crust as a result of volcanic activities and an upwelling of molten magma at mid-ocean ridges, as well as a slowly increasing distance (outward movement) from the ridge.

The theory of <u>seafloor spreading</u> was established by Harry Hammond Hess and it can be used to explain in details the slowly increasing distance between South America and Africa which grows from the center.

A <u>hot spot</u> refers to an area deep within Earth's mantle or under the rocky outermost layer of Earth, from which heat rises through convection and acquired as heat energy by a landform.

In the United States of America, you will see a layered <u>sedimentary rock</u> that is exposed by erosion when you view the Grand Canyon.

Furthermore, Australia is made up of relatively old and thick <u>continental crust</u>. Also, <u>subduction</u> causes the formation of extremely deep ocean Marianas Trench.

Read more on seafloor spreading here: brainly.com/question/12037536

7 0

2 years ago

Write an equation of the line that passes through the given point and is parallel to the given line.

saveliy_v [14]

the equation of line passing through given point parallel to y = -2x+7 is: $y = -2x+9$

Step-by-step explanation:

Given equation of line is:

$y = -2x+7$

As the given line is in slope intercept form, the coefficient of x is the slope

Let m1 be the slope of given line

$m_1 = -2$

Let m2 be the slope of second line then

$m_2= -2$

The equation of line is given by:

$y= m_2x+b$

Putting the value of slope

$y = -2x+b$

Putting the point (4,1) in the equation

$y = -2x+b\\1 = -2(4)+b\\1= -8+b\\b = 1+8\\b = 9$

Putting the value of b in the equation

$y = -2x+9$

Hence,

the equation of line passing through given point parallel to y = -2x+7 is: $y = -2x+9$

Keywords: Slope, intercepts

Learn more about slope at:

#LearnwithBrainly

3 0

4 years ago

A special discount was offered to the employees of Ryan's, a lead ing men's store. Employees were given their employee discount

Helen [10]

Answer: a) $2155, b) $1763.03.

Step-by-step explanation:

Since we have given that

Number of cable knit sweaters = 15

Cost per sweaters = $65.00

Number of pairs of khaki twill pants = 22

Cost of each pair = $50.00

Number of casual jackets = 18

Cost of each jackets = $62.00

total sale volume would be

$15\times 65+22\times 50+18\times 62\\\\=\$3191$

Employee discount = 35%

Additional discount = 15%

So, Total markdown dollars taken is given by

$3191\times \dfrac{100-35}{100}\times \dfrac{100-15}{100}\\\\=3191\times \dfrac{65}{100}\times \dfrac{85}{100}\\\\=3191\times 0.65\times 0.85\\\\=\$1763.0275$

Hence, a) $2155, b) $1763.03.

4 0

4 years ago

What is a probability ?

docker41 [41]

Answer:

A number that measures the likelihood that the event will occur.

Step-by-step explanation:

Probability is a measure of the frequency of occurrence of a phenomenon, the value of which can be expressed qualitatively or quantitatively. Probability is quantified as a real number between 0 and 1, although sometimes probability is also expressed as a percentage. The probability is 0 when the event cannot or will never happen, and the probability is 1 when it happens for sure or it always happens. If the probability is between these values, the event is not common and its occurrence is uncertain. The higher the probability value, the more common the event is or the more certain it will occur.

3 0

3 years ago