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3 years ago

Find the product and sum of the roots of the equation: 2x^2-9x-10=0

Mathematics

1 answer:

BabaBlast [244]3 years ago

3 0

Answer:

<h3> sum of the roots: $x_1+x_2=4\frac12$ </h3><h3> product of the roots: $x_1x_2=-5$ </h3><h3> Step-by-step explanation:</h3>

$2x^2-9x-10=0\quad\implies\quad a=2\,,\ b=-9\,,\ c=-10$

$b^2-4ac=(-9)^2-4(2)(-10)=81+80=161>0$

From Vieta's formulas applied to quadratic polynomial we have:

if $b^2-4ac\geqslant0$ then

sum of roots: $x_1+x_2=-\dfrac ba=-\dfrac{-9}2=4\frac12$

product of the roots: $x_1x_2=\dfrac ca=\dfrac{-10}2=-5$

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Answer:

Infinitely many

Step-by-step explanation:

Because the equation is equal to 0+0

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3 years ago

which number is a prime factor of 210 A.2 to the 6th power B.6 to the 2nd power or 6 squared C.12 to the 6th power.Exponents and

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210=2*3*5*7
none of them

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3 years ago

BRAINLIEST TO THE PERSON THAT ANSWERS FIRST

Oksana_A [137]

Answer:

A repeating decimal can be written as a fraction using algebraic methods, so any repeating decimal is a rational number.

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2 years ago

A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimat

Vedmedyk [2.9K]

Using the z-distribution, we have that:

a) A sample of 601 is needed.

b) A sample of 93 is needed.

c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which z is the z-score that has a p-value of $\frac{1+\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so $z = 1.96$ .

For this problem, we consider that we want it to be within 4%.

Item a:

The sample size is <u>n for which M = 0.04.</u>

There is no estimate, hence $\pi = 0.5$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}$

$\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2$

$n = 600.25$

Rounding up:

A sample of 601 is needed.

Item b:

The estimate is $\pi = 0.96$ , hence:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.96(0.04)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.96(0.04)}$

$\sqrt{n} = \frac{1.96\sqrt{0.96(0.04)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.96(0.04)}}{0.04}\right)^2$

$n = 92.2$

Rounding up:

A sample of 93 is needed.

Item c:

The closer the estimate is to $\pi = 0.5$ , the larger the sample size needed, hence, the correct option is A.

For more on the z-distribution, you can check brainly.com/question/25404151

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2 years ago

Sherry brings two containers of cookies to a party. Each container contains 6 cookies. Sally shows up with a dozen cookies. Sand

kotykmax [81]

Answer:

22 cookies

Step-by-step explanation:

A dozen items means 12 number of items.

Number of cookies brought by Sherry = No. of containers multiplied by number of cookies in one container

= 2 $\times$ 6 = 12

Number of cookies brought by Sally = A dozen cookies = 12

Number of cookies brought by Sandy = 2

Number of cookies brought by Sherry, Sally and Sandy together = 12 + 12+2 = 26

Total number of cookies to be brought = 4 dozen = 48 cookies

Number of cookies to be brought by Harry = Total number of cookies to be brought - Number of cookies brought by Sherry, Sally and Sandy together

48 - 26 = <em>22 cookies</em>

8 0

3 years ago