What is the quotient in the simplest form?

Please i need help When is the product of the square root of a prime number and a nonzero rational number a rational number?

lidiya [134]

Answer:

The product of the square root of a prime number and a nonzero rational number is a irrational number.

Step-by-step explanation:

Given that,

When is the product of the square root of a prime number and a nonzero rational number a irrational number.

We know that,

Prime number :

Prime number is that number whose has a two factor. first factor is one and second is themselves.

The square root of a prime number is irrational number.

Rational number :

Rational number is that number which is in fraction form.

For example : $\dfrac{p}{q}$

Here, p and q are integers

We need to proof the product of the square root of a prime number and a nonzero rational number is a rational number

Using given data

Suppose, the square root = √5

Rational number = $\dfrac{2}{3}$

We need to calculate the product of the square root of a prime number and a rational number

Using formula of product

$R=P\timesQ$

Where, P = square root of a prime number

Q= rational number

Put the value into the formula

$R=\sqrt{5}\times\dfrac{2}{3}$

$R=\dfrac{2\sqrt{5}}{3}$

Hence, The product of the square root of a prime number and a nonzero rational number is a irrational number.

3 0

3 years ago

Solve the equation.<br><br> 89=x+1/3(7)

ser-zykov [4K]

89=x+1/3(7)
89=x+7/3
267/3=x+7/3
260/3=x
86 2/3=x. Hope it help!

7 0

3 years ago

−2(x+1/4)+1=5 PLEASE HELP

PilotLPTM [1.2K]

Answer: x=−9/4

Step-by-step explanation:

Let's solve your equation step-by-step.

−2(x+14)+1=5

Step 1: Simplify both sides of the equation.

−2(x+14)+1=5(−2)(x)+(−2)(14)+1=5(Distribute)−2x+

−1

2

+1=5

(−2x)+(

−1

2

+1)=5(Combine Like Terms)

−2x+

1

2

=5

−2x+

1

2

=5

Step 2: Subtract 1/2 from both sides.

−2x+

1

2

−

1

2

=5−

1

2

−2x=

9

2

Step 3: Divide both sides by -2.

−2x

−2

=

9

2

−2

x=

−9

4

7 0

3 years ago

Read 2 more answers

For a standard-position angle determined by the point (x, y), what are the values of the trigonometric functions?

Travka [436]

The measure of the cscθ and secθ are 5/4 and 5/3 respectively option (A) is correct.

<h3>What is trigonometry?</h3>

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have a standard-position angle determined by the point (x, y).

The point is (9, 12)

From the Pythagoras theorem, we can find the hypotenuse(h):

h = √(9²+12²)

h = 15

cscθ = hypotenuse/opposite = 15/12 = 5/4

secθ = hypotenuse/adjacent = 15/9 = 5/3

Thus, the measure of the cscθ and secθ are 5/4 and 5/3 respectively option (A) is correct.

Learn more about trigonometry here:

brainly.com/question/26719838

#SPJ1

4 0

3 years ago

Jesse asked how many magazine subscriptions each

torisob [31]

Answer:

Interquartile range of the data is:

IQR = 2

Step-by-step explanation:

First lets rearrange the data in ascending order:

0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4

<h3>Find Median:</h3>

Median = (No. of terms +1) / 2 (when n = odd number)

Median = 14/2 (th term)

Median = 7th term

Median = 1

<h3>Find Upper and Lower Medians:</h3>

As the number of total terms is odd (n=13) , we omit the median and form upper and lower sets and find their medium

0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4

Remove the median

0, 0, 0, 1, 1, 1 | 2, 2, 2, 3, 4, 4

Calculate the median of lower portion

0, 0, 0, 1, 1, 1

For even numbers

Lower Median = (0+1)/2

Lower Median = 0.5

Calculate the median of upper portion

2, 2, 2, 3, 4, 4

Upper Median = (2+3)/2

Upper Median = 2.5

<h3>Interquartile Range:</h3>

It is the difference between Upper and Lower Median

IQR = 2.5 - 0.5

IQR = 2

4 0

4 years ago