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3 years ago

Is 6.584 a rational number?

Mathematics

1 answer:

Dmitry_Shevchenko [17]3 years ago

8 0

Answer:

Step-by-step explanation:

To get rid of the decimal point in the numerator, we count the numbers after the decimal in 6.584, and multiply the numerator and denominator by 10 if it is 1 number, 100 if it is 2 numbers, 1000 if it is 3 numbers, and so on.

Therefore, in this case we multiply the numerator and denominator by 1000 to get the following fraction: 6584 / 1000

Then, we need to divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction.

The GCD of 6584 and 1000 is 8. When we divide the numerator and denominator by 8, we get the following: 823 / 125

Therefore, 6.584 as a fraction is as follows: 823 / 125

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Whats the GFC of 18 , 60 ?

kirill [66]

Answer:

If you are reffering to GCF then the GCF would be explained like this

Find the prime factorization of 18

18 = 2 × 3 × 3

Find the prime factorization of 60

60 = 2 × 2 × 3 × 5

To find the gcf, multiply all the prime factors common to both numbers:

Therefore, GCF = 2 × 3

GCF = 6

6 0

3 years ago

Read 2 more answers

Solve quadratic equation (x-3)^2+5=14

loris [4]

(X-3)^2+5=14
Step 1: simplify both sides of the equation
X^2-6x+14=14

Step 2: subtract 14 from both sides
X^2-6x+14-14=14-14
X^2-6x=0

For this equation: a=1, b=-6,c=0
1x^2+-6x+0=0

Step 3: Use quadratic formula with a=1, b=-6, c=0

The answer is x=6 or x=0

5 0

3 years ago

What is the standard form of (2-4i)(3+51)/(3+i)

garri49 [273]

(1⋅3+1(5i)−2i(3+5i))(3−i)51⋅3+15i-2i3+5i3-i5

6 0

3 years ago

Find the vertical and horizontal asymptotes, domain, range, and roots of f (x) = -1 / x-3 +2.

gladu [14]

Answer:

Vertical asymptote: $x=3$

Horizontal asymptote: $f(x) =2$

Domain of f(x) is all real numbers except 3.

Range of f(x) is all real numbers except 2.

Step-by-step explanation:

Given:

Function:

$f (x) = -\dfrac{1 }{ x-3} +2$

One root, $x = 3.5$

To find:

Vertical and horizontal asymptote, domain, range and roots of f(x).

Solution:

First of all, let us find the roots of f(x).

Roots of f(x) means the value of x where f(x) = 0

$0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5$

One root, $x = 3.5$

Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.

For x = 3, the value of f(x) $\rightarrow \infty$

For all, other values of $x$ , $f(x)$ is defined.

Hence, Domain of f(x) is all real numbers except 3.

Range of f(x) i.e. the values that are possible output of the function.

f(x) = 2 is not possible in this case because something is subtracted from 2. That something is $\frac{1}{x-3}$ .

Hence, Range of f(x) is all real numbers except 2.

Vertical Asymptote is the value of x, where value of f(x) $\rightarrow \infty$ .

$-\dfrac{1 }{ x-3} +2 \rightarrow \infty$

It is possible only when

$x-3=0\\\Rightarrow x=3$

$\therefore$ vertical asymptote: $x=3$

Horizontal Asymptote is the value of f(x) , where value of x $\rightarrow \infty$ .

$x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2$

$\therefore$ Horizontal asymptote: $f(x) =2$

Please refer to the graph of given function as shown in the attached image.

5 0

3 years ago

Find the exact value of cos(7\pi /12)

Naya [18.7K]

7π/12 lies in the second quadrant, so we expect cos(7π/12) to be negative.

Recall that

$\cos^2x=\dfrac{1+\cos(2x)}2$

which tells us

$\cos\left(\dfrac{7\pi}{12}\right)=-\sqrt{\dfrac{1+\cos\left(\frac{7\pi}6\right)}2}$

Now,

$\cos\left(\dfrac{7\pi}6\right)=-\cos\left(\dfrac\pi6\right)=-\dfrac{\sqrt3}2$

and so

$\cos\left(\dfrac{7\pi}{12}\right)=-\sqrt{\dfrac{1-\frac{\sqrt3}2}2}=\boxed{-\dfrac{\sqrt{2-\sqrt3}}2}$

7 0

3 years ago