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3 years ago

Simplify 2 x × − 3 x × − x

Mathematics

1 answer:

Dahasolnce [82]3 years ago

7 0

Answer:

$\huge\boxed{2x^x-3x^x-x=-x^x-x}$

Step-by-step explanation:

$2x^x-3x^x-x=(2-3)x^x-x=-x^x-x$

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Simplify 1/4-7i to get a complex number in standard a + bi form.

Romashka [77]

Answer:

$\frac{1}{4-7i}=\frac{4}{65}+\frac{7}{65}i$

Step-by-step explanation:

we are given

$\frac{1}{4-7i}$

Firstly, we will get rid of imaginary term from denominator

so, we will multiply conjugate to both top and bottom term

$\frac{1}{4-7i}=\frac{1\times (4+7i)}{(4-7i)\times (4+7i)}$

$\frac{1}{4-7i}=\frac{4+7i}{4^2-(7i)^2}$

$\frac{1}{4-7i}=\frac{4+7i}{16+49}$

$\frac{1}{4-7i}=\frac{4+7i}{65}$

we can also write as

so, we get

$\frac{1}{4-7i}=\frac{4}{65}+\frac{7}{65}i$

7 0

3 years ago

An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers t

gregori [183]

Answer:

probability that all of the sprinklers will operate correctly in a fire: 0.0282

Step-by-step explanation:

In order to solve this question we will use Binomial probability distribution because:

In the question it is given that the sprinklers activate correctly or not independently.
The number of outcomes are two i.e. sprinklers activate correctly or not.

A binomial distribution is a probability of a success or failures outcomes in an repeated multiple or n times.

Number of outcomes of this distributions are two.

The formula is:

b(x; n, P) = $C_{n,x}*p^{x} * (1 - p)^{n-x}$

b = binomial probability also represented as P(X=x)

x =no of successes

P = probability of a success on a single trial

n = no of trials

$C_{n,x}$ is calculated as:

$C_{n,x}$ = n! / x!(n – x)!

= 10! / 10!(10-10)!

= 1

According to given question:

probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.

number of trials i.e. n = 10 as number of sprinklers are 10

To find: probability that all of the sprinklers will operate correctly in a fire

X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them

So putting these into the formula:

P(X=x) = $C_{n,x}*p^{x} * (1 - p)^{n-x}$

= C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰

= 1 * 0.0282 * (0.3) ⁰

= 1 * 0.0282 * 1

P(X=x) = 0.0282

5 0

3 years ago

How can you tell when a quadratic equation has no real solutions? . . A. when the radicand is negative. B. when b in the quadrat

Zepler [3.9K]

The nature of the roots of a quadratic equation may be readily determined through the use of its discriminant,
D = sqrt (b² - 4ac)
We can tell if the quadratic equation does not have a real root it the radicand is negative. Therefore, the answer is letter A.

3 0

4 years ago

How does finding the square root of a number compare to finding the cube root of a number?

Setler79 [48]

Answer:

See explanation below

Step-by-step explanation:

To find the principal square root of a number, we the number with an index of 2. The base then become the principal square root.

In the same way, we find the cube root of a number by writing the number with an index of 3 and the base becomes the cube root of the given number.

For instance:

$64=8^2\implies 8=\sqrt{64}$

$64=4^3\implies 4=\sqrt[3]{64}$

8 0

3 years ago

Find the range of the function. ƒ(x) = −5x^2 + 9

Gwar [14]

Answer:

D.) (−∞, −9]

Step-by-step explanation:

Range represents the set of values which the given function \[-5x^{2}+9\]

can assume. The function is quadratic and the square terms can only assume positive values. But the sign of the square term is negative so the overall square term with sign can only assume negative values. Maximum negative value possible is - infinity. Square term has the highest value of 0. On this case the value of the function becomes 9. So the range of the function is (−∞, −9].

8 0

4 years ago