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attashe74 [19]
3 years ago
14

Show that p(x) = 2x^3 − 5x^2 − 10x + 5 has a real root.

Mathematics
1 answer:
jolli1 [7]3 years ago
6 0
All odd degrees polynomials with real coefficients have (at least) a real root, and are continuous.  This is because the curve goes diagonally and must pass through the x-axis.

The above polynomial can be evaluated at x1=-10 and x1=+10 (or any other large enough number)
f(-10)=-2395
f(10)=1405
Since they have opposite signs, the function must intersect the x-axis between x1 and x2 by the intermediate value theorem, hence there is (at least) one root.
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Find three consecutive positive integers such that the product of the first and third interger is 17 more than 3 times the secon
Komok [63]

Answer:

5, 6, 7

Step-by-step explanation:

In order to solve for the three integers, we can assign a variable and set up an equation:

first integer: x

second integer: x + 1

third integer: x + 2

Given that 'the product of the first and third integer is 17 more than 3 times the second integer':

x(x + 2) = 3(x + 1) + 17

Distribute: x² + 2x = 3x + 3 + 17

Combine like terms: x² - x - 20 = 0

Factor: (x - 5)(x + 4) = 0

Set them equal to '0' and solve:

x - 5 = 0      x + 4 = 0

x = 5               x = -4

Since the problem asks for positive integers, x must equal 5:

first = 5

second = 5 + 1 = 6

third = 5 + 2 = 7

3 0
3 years ago
The membership fee for joining a local indoor trampoline park is $24 per year. The
Zigmanuir [339]

Answer:

calculator g

Step-by-step explanation:

5 0
3 years ago
At the beginning of the day, the sum of the stocks in the Dow Jones was
12345 [234]

Answer:

- 1.15585%

Step-by-step explanation:

Given that:

Sum of stock at beginning = $10,335.24

Sum of stock at the end of the day = $10,215.78

Rate of change of the Down Jones on that day :

The change in price on the day:

Ending - Beginning

10,215.78 - 10,335.24 = −119.46

The rate if change is thus ;

(Change in price / beginning stock price) * 100%

(-119.46 / 10,335.24) * 100%

-0.0115585 * 100%

- 1.15585%

8 0
3 years ago
Read 2 more answers
Nine pairs of data yield r=0.867 and the regression equation y=19.4+0.93x
Gwar [14]

Answer:

38

Step-by-step explanation:

Regression analysis is the relationship among one dependent variable and one or more independent variables. Method of regression is used in finance, investing, and other disciplines.

Given:

Nine pairs of data yield and the regression equation y=19.4+0.93x

To find:

the best predicted value of y for x=20

Solution:

y=19.4+0.93x

Put x=20

y=19.4+0.93(20)\\=19.4+18.6\\=38

6 0
3 years ago
1. What represents the independent or x variable?
mel-nik [20]

Answer:

The independent variable belongs on the x-axis (horizontal line) of the graph and the dependent variable belongs on the y-axis (vertical line). The x and y axes cross at a point referred to as the origin, where the coordinates are (0,0).

A linear relationship is a relationship with a constant rate of change represented by a graph that forms a straight line that passes through the origin (0, 0) and is represented by y = kx. The rate of change is either positive, negative, zero, or undefined.

8 people

A 98″ rectangular dining table can seat up to 8 people comfortably. A 108″ rectangular dining table can seat up to 10 people comfortably.

Base Size 16" Extensions Seating for

48" x 72" 1 16" Extensions 10 - 12

48" x 72" 2 16" Extensions 12 - 14

48" x 72" 4 16" Extensions 14 - 16

48" x 72" 6 16" Extensions 16 - 18

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3 years ago
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