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2 years ago

Determine the solution set of x^2-80=0.

2 answers:

6 0

X^2 - 80 = 0
x^2 = 80 ...take the square root of both sides, eliminating the ^2
x = (+-) sqrt 80
x = (+-) sqrt 16 * 5
x = (+-) 4 sqrt 5

so x = 4 sqrt 5 or x = -4 sqrt 5

eduard2 years ago

5 0

Answer: The required solution set of the given equation is $\{4\sqrt5,-4\sqrt5\}.$

Step-by-step explanation: We are given to determine the solution set of the following quadratic equation :

$x^2-80=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Since the given equation does not contain the term involving x, so we will use the method of square root to solve the given equation.

The solution of equation (i) is as follows :

$x^2-80=0\\\\\Rightarrow x^2=80\\\\\Rightarrow x=\pm\sqrt{80}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=\pm\sqrt{16\times5}\\\\\Rightarrow x=\pm4\sqrt5.$

Thus, the required solution set of the given equation is $\{4\sqrt5,-4\sqrt5\}.$

You might be interested in

Rewrite the given expression in the form 3^u where u is a constant or an algebraic expression.

lawyer [7]

Simplifying the given expressions we proceed as follows:
(5sqrt3)^x
=5^x*(3^1/2)^x
=5^x*3^x/2
=5^x3^u
where u=x/2

(1/2)^(x-3)
=1/2^(x-3)
=2^-(3-x)
=2^u
where u=-(3-x)

9/3sqrt(3)
=3/(3)^(1/2)
=3(3)^(-1/2)

16/(3sqrt (2^x))
=1/3*(2^4*2^(-x/2))
=1/3*2^(4-x/2)
=1/3*2^u
where:
u=4-x/2

8 0

2 years ago

Read 2 more answers

En una cancha se va a pintar la circunferencia central que tiene un diámetro de 5 m .¿cual es la longitud de la circunferencia?

Alona [7]

Answer:

The length of the circumference is $5\pi\ m$ or $15.70\ m$

Step-by-step explanation:

The question in English is

On a court, the central circumference will be painted, which has a diameter of 5 m. What is the length of the circumference?

we know that

The circumference of a circle is given by the formula

$C=\pi D$

we have

$D=5\ m$

substitute

$C=\pi (5)\\C=5\pi\ m$

This is the exact value

assume

$\pi=3.24$

$C=5(3.14)=15.70\ m$

4 0

1 year ago

An Epson inkjet printer ad advertises that the black ink cartridge will provide enough ink for an average of 245 pages. Assume t

Neko [114]

Answer:

35.2% probability that the sample mean will be 246 pages or more

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 245 \sigma = 15, n = 33, s = \frac{15}{\sqrt{33}} = 2.61$

What the probability that the sample mean will be 246 pages or more?

This is 1 subtracted by the pvalue of Z when X = 246. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{246 - 245}{2.61}$

$Z = 0.38$

$Z = 0.38$ has a pvalue of 0.6480.

1 - 0.6480 = 0.3520

35.2% probability that the sample mean will be 246 pages or more

4 0

2 years ago

The cost of an item is 100% of its price. What number goes in place of ? in the addition problem?

Dmitry_Shevchenko [17]

I believe this is the complete problem.

Anton bought a picnic cooler. His total bill, with tax, was $7.95. He paid 6 percent sales tax. How much did he pay for the cooler alone without the tax? The cost of an item is 100% of its price. What number goes in place of ? in the addition problem?

The answer is the below:

He paid $7.473 without tax because $7.95 x 96% or (0.96) =$7.473

8 0

1 year ago

Read 2 more answers

At a certain company, the annual winter party is always held on the second of Friday of December. What is the latest possible da

vitfil [10]

Answer:

The latest possible date is December, 14th.

Step-by-step explanation:

Notice that the second Friday of December is n+7, where n is the date for the first Friday of December. So, the latest the first Friday, the latest the second. As the weeks have seven days, the first Friday will be between 1st and 7th of each month. So, the latest first Friday will be 7th. Therefore, the latest second Friday will be 14th.

7 0

2 years ago