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3 years ago

How are radicals and rational exponents related?

Mathematics

1 answer:

icang [17]3 years ago

8 0

Answer:

Any radical in the form can be written using a fractional exponent in the form . The relationship between and works for rational exponents that have a numerator of 1 as well. For example, the radical can also be written as , since any number remains the same value if it is raised to the first power.

Step-by-step explanation:

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israel started to solve a radical equation in this way: square root of x plus 6 − 4 = x square root of x plus 6 − 4 4 = x 4 squa

agasfer [191]

Lets solve our radical equation $\sqrt{x+6}-4=x$ step by step.

Step 1 add 4 to both sides of the equation:

$\sqrt{x+6} -4+4=x +4$

$\sqrt{x} +6=x+4$

Step 2 square both sides of the equation:

$\sqrt{x+6} =x+4$

$\sqrt{x+6}^2 =(x+4)^2$

$x+6=(x+4)^2$

Step 3 expand the binomial in the right hand side:

$x+6=x^2+8x+16$

Step 4 simplify the expression:

$0=x^2+8x-x+16-6$

$x^2+7x+10=0$

Step 5 factor the expression:

$(x+2)(x+5)=0$

Step 6 solve for each factor:

$x+2=0$ or $x+5=0$

$x=-2$ or $x=-5$

Now we are going to check both solutions in the original equation to prove if they are valid:

For $x=-2$

$\sqrt{x+6}-4=x$

$\sqrt{-2+6}-4=-2$

$\sqrt{4}-4=-2$

$2-4=-2$

$-2=-2$

The solution $x=2$ is a valid solution of the rational equation $\sqrt{x+6}-4=x$ .

For $x=-5$

$\sqrt{x+6}-4=x$

$\sqrt{-5+6}-4=-5$

$\sqrt{1}-4=-5$

$1-4=-5$

$-3\neq -5$

Since -3 is not equal to -5, the solution $x=-5$ is not a valid solution of the rational equation $\sqrt{x+6}-4=x$ ; therefore, $x=-5$ is an extraneous solution of the equation.

We can conclude that even all the algebraic procedures of Israel are correct, he did not check for extraneous solutions.

An extraneous solution of an equation is the solution that emerges from the algebraic process of solving the equation but is not a valid solution of the equation. Is worth pointing out that extraneous solutions are particularly frequent in rational equation.

8 0

4 years ago

Find the probability of picking 3 consonants and 2 vowels when 5 letters are picked (without replacement) from a set of alphabet

schepotkina [342]

Step-by-step explanation:

picking 3 consonants and 2 vowels when 5 letters are picked (without replacement) from a set of alphabet tiles.

There are 26 letters in alphabet

number of consonants = 21 and number of vowels = 5

We need to pick 3 consonants from 21 consonants

Probability of picking 1 consonant from 26 alphabets = 21/ 26

after picking 1 consonant then number of consonant becomes 20

Probability of picking second consonant from 25 alphabets = 20/ 25

Probability of picking third consonant from 24 alphabets = 19/ 24

We need to pick 2 vowels from 5 vowels

Probability of picking 1 vowel from remaining 23 alphabets = 5/ 23

Probability of picking second vowel from remaining 22 alphabets = 4/ 22

Now multiply all the probabilities

$\frac{21}{26} *\frac{20}{25} *\frac{19}{24} *\frac{5}{23} *\frac{4}{22}$

= 0.02022

6 0

4 years ago

HELP PLEASEEEE!!

emmasim [6.3K]

31.0 degrees

TanX wich is 30/50

same thing as 30 divided by 50

7 0

3 years ago

A six-pack of soda costs $2.49, a 12-pack of soda costs $3.99, and a 24-pack of soda costs $5.49. Which pack has the lowest cost

Paladinen [302]

Solve:-

Find unit price per pack.

6-Pack:-

2.49 ÷ 6 = 0.41
$0.41 per can

12-pack:-

3.99 ÷ 12 = 0.33
0.33 per can

24-pack:-

5.49 ÷ 25 = 0.22
0.22 per can

The cheapest is 24-pack, because the unit price for that is the cheapest. After that pack is the 12-pack one because that is cheaper than the 6-pack. and last is the 6-pack.

8 0

4 years ago

Write a simplified polynomial expression in standard form to represent the area of the rectangle below. (2 points)

Drupady [299]

(2x-4)(x+5) expand with indicated multiplication...

2x^2+10x-4x-20

2x^2+6x-20 (it's the top one :P)

5 0

3 years ago

Read 2 more answers