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2 years ago

How many real number solutions does the equation x3 + 5x2 + 3x – 9 = 0 have?

2 answers:

8 0

F(x) = x³ + 5x² + 3x - 9 = 0
There is 1 sign change in f(x), so there is 1 positive real root.

f(-x) = -x³ + 5x² - 3x - 9
There are 2 sign changes in f(-x), so there are either
(a) 2 negative real roots, or
(b) a pair of complex roots.

Use the Remainder Theorem to test for the positive real root.
f(1) = 1 + 5 + 3 - 9 = 0
Therefore (x-1) is a factor of f(x).

Perform synthetic division.
1 | 1 5 3 -9
1 6 9
---------------
1 6 9 0

f(x) = (x-1)(x² + 6x + 9) = (x-1)(x+3)²
The zeros or roots are 1, -3, -3.
Therefore there are 3 real solutions for f(x) = 0.

Answer: 3 real solutions

likoan [24]2 years ago

6 0

Answer:

Step-by-step explanation:

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Help pls!

photoshop1234 [79]

Answer: 1526.8 cubic inches

Step-by-step explanation: Volume = base times height.

The base of the cylinder is πr²

We can use a scientific calculator with π, or we can use 3.14 for π. the radius is 9, 9² = 81.

The Area of the base of this cylinder is about 254.46 square feet

Multiply by the height, 6 feet

We get the volume of the cylinder 1526.82 cubic inches.

Round to 1526.8 cubic feet

5 0

3 years ago

A marketing research company needs to estimate the average total compensation of CEOs in the service industry. Data were randoml

mezya [45]

SOLUTION:

Step 1 :

In this question, we are told that a marketing research company needs to estimate the average total compensation of CEOs in the service industry.

We also have that: Data were randomly collected from 38 CEOs and the 98% confidence interval was calculated to be ($2,181,260, $5,836,180).

Then, we are asked to find the margin error for the confidence interval.

Step 2:

We need to recall that:

$\text{Higher Confidence Interval, CI}_{H\text{ = }}X\text{ + }\frac{Z\sigma}{\sqrt[]{n}}$ $\text{Lower Confidence Interval , CI}_{L\text{ }}=\text{ X - }\frac{Z\sigma}{\sqrt[]{n}}$

It means that:

$\vec{}X\text{ = }\frac{CI_{H\text{ }}+CI_L}{2}$ $\text{Margin of error, }\frac{Z\sigma}{\sqrt[]{n}\text{ }}\text{ = }\frac{CI_{H\text{ - }}CI_L}{2}$

where,

$CI_H\text{ = }$$5,836,180$\text{ }$$$$ $CI_{L\text{ }}=\text{ }2,181,260$

putting the values into the equation for the margin of error, we have that:

$\text{Margin of error,}\frac{Z\sigma}{\sqrt[]{n}\text{ }}\text{ = }\frac{5,836,180\text{ - }2,181,260\text{ }}{2}$ $\begin{gathered} =\text{ }\frac{3654920}{2} \\ =1,\text{ 827, 460} \end{gathered}$

CONCLUSION:

The margin error for the confidence interval is 1, 827, 460

5 0

10 months ago

PLS ANSWER ASAP THIS QUESTION IS VERY HARD FOR ME

Tpy6a [65]

Answer:

its D if not im so sorry i found the answer on a website

Step-by-step explanation:

6 0

2 years ago

Is -(-3) = 3 . i know its simple but I need it