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kakasveta [241]
3 years ago
9

PLZ HELP ME !!!! Which expressions below equal a rational number ? Choose ALL that apply !

Mathematics
2 answers:
WINSTONCH [101]3 years ago
8 0

Answer:

The correct option is are 2, 3 and 4.

Step-by-step explanation:

Rational number: If a number can be defined in the form of p/q where, p and q are integers and q≠0, then it is known as rational numbers. For example: 0.2, 1/3 and 1 etc.

Irrational number: If a number can not be defined in the form of p/q where, p and q are integers and q≠0, then it is known as irrational numbers. For example: 0.222..., √2 and π etc.

\pi\sqrt{36}=6\pi

It is an irrational number because π is an irrational number.

7\sqrt{5}-\sqrt{245}=7\sqrt{5}-7\sqrt{5}=0

It is a rational number.

\frac{4}{5}+\frac{3}{8}=\frac{32+15}{40}=\frac{47}{40}

It is a rational number.

(4\sqrt{7})(2\sqrt{7})=(4\times 2)(\sqrt{7\times 7})=8(7)=56

It is a rational number.

\sqrt{100}+\sqrt{5}=10+\sqrt{5}

It is an irrational number because sum of a rational and an irrational number is always an irrational number.

Therefore the correct option is are 2, 3 and 4.

Yakvenalex [24]3 years ago
4 0

(From top to bottom) wrong, right, right, right, wrong. This is because a irrational*an irrational number is rational, but a rational*an irrational is an irrational number

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Which is equivalent to V180x11 after it has been simplified completely?
inna [77]

Question:

Which is equivalent to \sqrt{180x^{11}} after it has been simplified completely?

Answer:

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

Step-by-step explanation:

Given

\sqrt{180x^{11}}

Required

Simplify

We start by splitting the square root

\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}

Replace 180 with 36 * 5

\sqrt{180x^{11}} = \sqrt{36 * 5} *  \sqrt{x^{11}}

Further split the square roots

\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} *  \sqrt{x^{11}}

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{11}}

Replace power of x; 11 with 10 + 1

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10 + 1}}

From laws of indices; a^{m+n} = a^m * a^n

So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x^1}

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x}

Further split the square roots

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10}} * \sqrt{x}

From laws of indices; \sqrt{a} = a^{\frac{1}{2}}

So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{10*\frac{1}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{\frac{10}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{5} * \sqrt{x}

Rearrange Expression

\sqrt{180x^{11}} = 6 *  x^{5} * \sqrt{5} * \sqrt{x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}

From laws of indices; \sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}

So, we have

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

<em>The expression can no longer be simplified</em>

Hence, \sqrt{180x^{11}} is equivalent to 6x^{5}\sqrt{5x}

7 0
3 years ago
Read 2 more answers
If f(x) = 2x - 9, which of the following are correct? Select all that apply. f(-1) = -11 f(2) = 5 f(3) = -3 f(0) = -9 f(-3) = 15
Yuri [45]

f(-1) = -11 and f(3) = -3 . these functions are true .

What does a math function mean?

  • A relationship between a group of inputs and one output each is referred to as a function.
  •  A function is an association between inputs in which each input is connected to precisely one output.
  • A domain, codomain, or range exists for every function. f(x), where x is the input, is a common way to refer to a function.
  • In mathematics, a function is an expression, rule, or law that establishes the relationship between two variables (the dependent variable).

given function  f(x) = 2x - 9

   f(-1) = -11 ⇒ x = -1 put in function

                       f( -1 ) = 2 * -1 - 9  ⇒ - 11

    f(2) = 5   ⇒ x = 2 put in function

                    f( 2 ) = 2 * 5 - 9 = 1

    f(3) = -3  ⇒  x = 3 put in function

                     f ( 3 ) = 2 * 3 - 9 = -3

       f(-3) = 15   ⇒  x =  -3 put in function

                     f( -3) = 2 * -3 - 9 = - 15

Learn more about function

brainly.com/question/21145944

#SPJ13

3 0
1 year ago
What is the value of the expression shown below?
o-na [289]

Answer:

B

Step-by-step explanation:

1.6/0.2=8

10⁵-10²=10³

3 0
3 years ago
How to write 5x - 7y = 14 in function form
Slav-nsk [51]
5x-7y=14
-5x -5x
^
Subtract 5x from both sides

-7y=-5x+14
Divide by -7 by all of the numbers

y=-5/7x-2
7 0
3 years ago
The angles of a quadrilateral measure 80° 100° 100° and 80° In this order what kind of quadrilateral has this shape?
NemiM [27]

Answer:

The answer is a isosceles trapezoid.

Hope this helps!

brainliest? :)

8 0
3 years ago
Read 2 more answers
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