What is the definition of principal square root in math?

Answers

Answer 1

A square root of a number a is a number y such that y2 = a; in other words, a number y whose square (the result of multiplying the number by itself, or y⋅y) is a.[1] For example, 4 and −4 are square roots of 16 because 42 = (−4)2 = 16. Every nonnegative real number a has a unique nonnegative square root, called the principal square root, which is denoted by √a, where √ is called the radical sign or radix. For example, the principal square root of 9 is 3, denoted √9 = 3, because 32 = 3 • 3 = 9 and 3 is nonnegative. The term whose root is being considered is known as the radicand. The radicand is the number or expression underneath the radical sign, in this example 9.

Answer 2

Final answer:

The principal square root in math refers to the positive square root of a number. It is denoted as √x and is applicable to non-negative numbers.

Explanation:

The principal square root in math refers to the positive square root of a number. It is denoted as √x, where x is a non-negative number.

For example, the principal square root of 25 is √25 = 5 because 5 multiplied by itself equals 25.

The principal square root is only applicable to non-negative numbers, while negative numbers have no real square roots.

Related Questions

What value is added to both sides of the equation x^2 − 8x = −10 in order to solve by completing the square?
−8
16
−4
4

Answers

x^2-8x=-10
we need to get (x-a)^2 with x^2-8x to figure it out
using (x-4)^2=x^2-8x+16 we see to add 16
x^2-8x=-10
x^2-8x+16=6
(x-4)^2=6
x-4=sqrt6
x=4+sqrt6 to solve for x

Let's solve your equation step-by-step.x2−8x=−10Step 1: Subtract -10 from both sides.x2−8x−(−10)=−10−(−10)x2−8x+10=0Step 2: Use quadratic formula with a=1, b=-8, c=10.x=−b±b2−4ac2ax=−(−8)±(−8)2−4(1)(10)2(1)x=8±242x=4+6 or x=4−6Answer:x=4+6 or x=4−6

N equation of a line through (0, 2) which is perpendicular to the line y=3x+3y=3x+3 has slope

Answers

Something's not quite right here. What do you mean by "N?"

I could and will make assumptions regarding what you meant. (Feel free to correct me if need be.)

Find the equation of a line through (0,2) which is perpendicular to the line y=3x+3. To find the slope of this perpendicular line, take the negative reciprocal of 3 (the slope of the given line). It is -1/3.

Using the point-slope form of the equation of a straight line:

y = (-1/3)x + 2 (answer)

Devin made some mistakes. Identify where he made each mistake:

24 ÷ 6 x (5 – 1)

= 24 ÷ 6 x 4
= 24 ÷ 24
= 1

Answers

When doing the order of operations and you are put in a situation where you do two different operations, solve the problem from left to right.
In this case instead of doing 6*4 first do 24/6 first.

Liam's bookstore sold 40 notebooks and 20 newspapers for a total of $130. A day later, the bookstore sold 8 notebooks and 4 newspapers at the same prices, for a total of $28. How much does a notebook and a newspaper cost at Liam's bookstore?

Answers

The total sales will be calculated by adding up the revenue from the selling of the notebooks and that of the newspaper. For representation, we let x be the price of each of the notebook and y be the price of each of the newspaper. The equation that allows us to solve this item are,

40x + 20y = 130
and 8x + 4y = 28

With this, if we divide the left hand side by the left hand side of the equation number 2, we have 5. However, 130 divided 28 is not 5 but 4.64. Hence, the system does not have any solution.

Let us say that:

X = price of each notebook

Y = price of each newspaper

So from the problem statement we can create the following equations:

40 X + 20 Y = 130 --> eqtn 1

8 X + 4 Y = 28 --> eqtn 2

Divide both equations by the lowest coefficient to simplify:

Divide eqtn 1 by 20 => 2 X + Y = 6.5

Divide eqtn 2 by 4=> 2 X + Y = 7

So we can see that although both equations has equal left side, the right side do not match. Hence this problem is impossible to solve.

-> The given information describes an impossible situation.

My father is currently 13 times as old as my daughter. next year, my father will be 11 times as old as my daughter. how many years old is my father now?

Answers

suppose my daughter is x years old now, my father is 13x years old
next year my daughter will be x+1 years old, my father will be 13x+1, which is also 11(x+1)
so 13x+1=11(x+1)
13x+1=11x+11
2x+10
x=5
father is 13x=65 years old now.

Suppose you pay $21 for a pair of shoes that was originally $30. What was the percent of decrease in price for the shoes? Set up an equation, arrive at your answer, and check your work. Then clearly state your answer.

*SHOW WORK*

Answers

21 / 30 = X (Percentage paid of original price.) 21 / 30= 0.7 * 100 = 70% 100% - 70% = 30% $21 was 30% off the original price of $30

how do you do 36-7p=-7(p-5)

Answers

First, distribute the negative seven to the p and negative five in the parentheses. it should look like 36 - 7p = -7p + 35.

Next, add seven p to both sides and it cancels out. 36 -7p = -7p + 35.
+7p= +7p
Then minus thirty five on both sides. You get an inconclusive answer of 1=0

Final answer:

equation 36-7p=-7(p-5) simplifies to 36=35 after distributing and cancelling variables which results in an inconsistency. Therefore, this equation has no solutions.

Explanation:

The question involves working with linear equations. From the equation, 36-7p=-7(p-5), we will aim to isolate the variable, 'p'.

In this equation, start by distributing the -7 into the bracket. So, -7(p-5) becomes: -7*p + 7*5, which simplifies to: -7p + 35. Now, your equation should look like: 36 - 7p = -7p + 35.Next, let's cancel out -7p from one side by adding 7p to both sides. You get: 36 = 35.This is an inconsistency because 36 is not equal to 35. Therefore, this equation has no solution.

Learn more about Linear equations here:

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Five friends made 100 dollars working together.how much did each person make if the earnings are divded equally ?

Answers

• Divide: 100 ÷ 5 = 20

So each person made $20.00.

Hope this helps! :D

~PutarPotato

How can 32 over 6 be expressed as a decimal?

Answers

That would be 5.333333 reapeating

all i did is use a calculator and i got 5.33333333

What is the solution to –4|–2x + 6| = –24?

A.) x = 0
B.) x = 0 or x = –6
C.) x = 0 or x = 6
D.) no solution

Answers

What is the solution to –4|–2x + 6| = –24?

-4║-2x+6║=-24
-4/-4║-2x+6║=-24/-4 division property
║-2x+6║=6 simplified

Positive Negative
-2x+6=6 -2x+6=-6
-2x+6-6=6-6 -2x+6-6=-6-6 subtraction property
-2x=0 -2x=-12 simplified
-2/-2x=0/-2 -2/-2x=-12/-2 division property
x=0 x=6

C.) x = 0 or x = 6

If three people had three cookies how many ways can they distribute the cookie

Answers

The first cookie can be distributed in 3 ways to the first person.
The second cookie can be distributed in 2 ways to the second person.
There is only one way to give the last cookie to the third person.

Total number of ways = 3*2*1 = 3! = 6

Answer: 6

NEED ANSWER ASAP!!! a compound inequality is graphed, and its graph consists of all real number. which open sentence could have resulted in this solution set? A. r < 5 or r < -1 B. r < 5 or r > -1 C. r > 5 or r < -1 D. r > 5 or r > -1

Answers

When we join two inequalities with an “or,” we unite their graphs – we include all solutions to *both* inequalities. Let’s first look at graphs of each of the four inequalities first, and then we’ll see when we unite them.

r < 5 starts with a hollow circular mark on 5 (since 5 isn’t included in r), and includes everything from there to negative infinity

r > 5 starts with that same mark, but its solutions include everything from there to positive infinity (except 5)

r > -1 starts at -1 and includes everything from there to positive infinity (except -1), and r < -1 stretches to negative infinity (except -1).

We want to join together two inequalities so that their solutions span from negative to positive infinity (all real numbers); which of our options include negative infinity, and which include positive infinity?

Negative infinity: r < 5, r < -1
Positive infinity: r > 5, r > -1

We could try joining r > 5 and r < -1, but then we’d be exclude all of the real numbers between and including -1 and 5. The graphs of r < 5 and r > -1 pass right by each other and continue infinitely off to negative and positive infinity respectively, so all possible real numbers will be included in their combined range.

So, our solution is “r < 5 or r > -1”.

the answer is “r < 5 or r > -1”.

How do I write 6 x 3/20 as a fraction in simplest form?

Answers

first, you need to turn it into a fraction by doing the multiplication. 6/1 × 3/20 which is 18/20. then you simplify it to get 9/10. 9/10 is your answer

Final answer:

To simplify 6 x 3/20, we first perform the multiplication to get 18/20. Then, we divide both the numerator and denominator by their greatest common divisor, which is 2, resulting in 9/10.

Explanation:

Firstly, in the given expression, 6 x 3/20, the order of operations (BIDMAS/BODMAS) requires us to perform multiplication and division from left to right. So, we multiply 6 and 3 to get 18. This gives us a new expression, 18/20. Then, we simplify this fraction by finding the highest number that both the numerator (18) and denominator (20) can be divided by, which is 2. So we divide both by 2, getting us 9/10. So, 6 x 3/20 simplifies to 9/10 in its simplest form.

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According to the data reported by the new york state department of health regarding west nile virus for the years 2000-2004, the least squares line equation for the number of reported dead birds (x) versus the number of human west nile virus cases (y) is y = −10.2638 + 0.0491x. if the number of dead birds reported in a year is 748, how many human cases of west nile virus can be expected? (round your answer to the nearest whole number.)

Answers

Final answer:

Using the least squares line equation y = −10.2638 + 0.0491x and substituting 748 for x, the number of reported dead birds, we find the expected number of human West Nile virus cases to be approximately 26 when rounded to the nearest whole number.

Explanation:

The question asks to predict the number of human West Nile virus cases based on the number of reported dead birds using a least squares line equation provided. Given the equation y = −10.2638 + 0.0491x and the value x = 748, which represents the number of dead birds, we can substitute x into the equation to calculate y, the expected number of human cases.

The calculation is as follows:

y = −10.2638 + 0.0491 × 748

y = −10.2638 + 36.7268

y = 26.463

After performing the calculation, we round the result to the nearest whole number:

Expected number of human cases = 26

a model rocket launches into the sky. An observer on the ground measures the angle of elevation to the rocket at its peak height to be 67 degrees. How high did the rocket get if the observer was 100' away from the launchpad?

Answers

Use a right triangle and trigonometry.
The angle is 67 deg.
The adjacent leg is the 100 ft side of the triangle along the ground.
The opposite leg is the unknown height, h.

tan x = opp/adj

tan 67 = h/100

h = 100 * tan 67

h = 100 * 2.36

h = 236

Answer: 236 ft

To convert degrees Fahrenheit (F) into degrees Celsius (C) use the formula 2003-05-04-00-00_files/i0150000.jpg. Rewrite the equation to convert degrees Celsius to degrees Fahrenheit.

Answers

Here's the formula for both conversions:

To convert Celsius to Fahrenheit, use the formula [°F] = [°C] x 9/5 + 32. For example, a 16°C temperature would convert to approximately 60.8°F.

The formula you are looking for to convert degrees Celsius to degrees Fahrenheit is [°F] = [°C] x 9/5 + 32. To perform the conversion, you multiply the temperature in degrees Celsius by 9/5 (or 1.8) and then add 32 to the result. This will give you the temperature in degrees Fahrenheit.

For example, if you wanted to convert 16°C to Fahrenheit (perhaps for planning a trip to Spain), you would do the following calculation: [°F] = 16 x 9/5 + 32 = 28.8 + 32 = 60.8°F. Thus, a weather forecast predicting 16°C is approximately equivalent to 60.8°F.

The area of a rectangle is found by multiplying the length by the width: A = lw. A certain rectangle has an area of x 2 + 7x + 12. Factor the trinomial to find the length and width of the rectangle.

Answers

Since it is given that the formula for area is length times width and the area is already given, we are going to find out the value of the width and the length by factoring. The first thing we are going to do is to find first the factors of 12. The factor that can be used for this are 4 and 3. Then, continue with the solution.

So the correct answer for this would be the last option. l = x + 4; w = x + 3.

Please mark me Brainliest and hope this helps :)

Evaluate the expression choose the best answer 8P3

A. 6,720
B. 876
C. 1,680
D. 336

HELP!!!!!

Answers

8P3
= 8! / (8-3)!
= 8 x 7 x 6 x 5! / 5!
= 8 x 7 x 6
= 336

answer
D. 336

A quarter-circle with a diameter of 4 meters. What is the area?

Answers

First, just find the area of the whole circle:

πr²
π(2)²
4π

Now, just multiply by 1/4.

4π * 1/4
π

Hope this helps!

trigonometry word problem

Answers

Where’s the problem at??

Four friends compared there bike riding times. Jess rode 4.25 km in 20 min. Corey rode 3.75 km in 18 min. Mia rode 3.5 km in 17 min. Zoey rode 3.6 km in 16 min.

Who rode at the greatest rate of speed?

A.
Jess

B.
Corey

C.
Mia

D.
Zoey

Answers

Jess rode 4.25 km in 20 min.
Speed = 4.25: 20 = 0.212 km/min

Corey rode 3.75 km in 18 min.
S= 3.75 : 18= 0.208

Mia rode 3.5 km in 17 min.
S = 3.5 :17 = 0.205

Zoey rode 3.6 km in 16 min.
S= 3.6 :16 = 0.225

The greatest rate of speed : ZOE with 0.225 km/min

Simplifly by using the distributive property 4r+3(r-2)

Answers

7r-6 if you simplify that's the answer.

4r + 3(r - 2)

Let's focus on the 3(r-2)

In order to distribute this, we multiply 3 to r AND -2 each

After using the distributive property, we get the following

3(r - 2) = 3r - 6

Now, let's go back to the whole equation

4r + 3(r - 2)

= 4r + 3r - 6

Combine like terms

7r - 6

That's your answer.

Have an awesome day! :)

What is the value of x using the pythagorean theorem ?

Answers

side a is 49
side c is 121
121-49 is 72
72 squared is your x

check the picture below.

Factor completely. a 2 + 28a + 27 (a + 1)(a + 27) (a + 3)(a + 9) (a - 1)(a - 27)

Answers

Answer:

(a+1)(a+27)

Step-by-step explanation:

Trinomials are three term algebraic expressions typically featuring variables to exponent powers. To break these trinomials down we factor them using the diamond method or GCF. The diamond method states that for a trinomial [tex]Ax^2+Bx+C[/tex] multiply A*C then find two numbers which multiply to this number and add to B. When you find those numbers, write them as [tex](x-/+ number)(x-/+number)[/tex].

[tex]a^2+28a+27[/tex]

A=1, C=27

A*C=27 and add to B=28 which 1 and 27 satisfy

The factors are (a+1)(a+27)

What is the new price of s shirt that is on sale for 50% off and has an original price of $50?

Answers

50%=1/2 or 1 half. 50/2=$25

Final answer:

To calculate the new price of the shirt on a 50% sale off its original price of $50, divide the original price by 2, resulting in a new price of $25.

Explanation:

The question asks us to calculate the new price of a shirt that is on sale with a 50% discount from its original price of $50. To find the new price, you simply need to reduce the original price by the percentage of the discount. Since a 50% discount cuts the price in half, you divide the original price by 2.

Calculation:

Original price of the shirt: $50

Discount: 50% of $50 = $50 / 2 = $25

New price after discount: $50 - $25 = $25

Therefore, the new price of the shirt after a 50% discount is $25.

A color printer prints 27 pages in 9 minutes. how many pages does it print per minute?

Answers

27/9=3
The printer is printing 3 pages per minute

Evaluate (7² - 9 ) ÷ ( 55 - 35 ).
A: -34
B: 48
C: -4
D: 2

Answers

This answer is D, 2. Hope this helps

Choose the correct ordered pair !!

Answers

It is B.

x+y=3
y=9

To solve the equation you would substitute 9 in for y (in the first equation) and get
x+9=3
You would then subtract 9 from both sides of the equation to get
x=-6
B is the only choice where -6 is first in the ordered pair, but just to make sure, you could substitute -6 back in to the equation to get
-6+y=3
Add 6 to both sides to get y=9, and you know that the correct ordered pair is
(-6,9)

First, let's plug the information we have into the equation.
x + 9 = 3

Next, you would have to do is isolate the x. To do this, you would subtract both sides by 9.
x + 9 = 3
x = -6

So, this is what we know.
y = 9
x = -6

Now, all you would have to do is change them into coordinates. (x,y)
(-6,9)

Your answer would be B. (-6,9).

I hope this helps!

Please help with 2 questions thank you!

Show all work please!!

Answers

1:
1 - given
2 - defination of bisector
3 - reflexive
4 - given
5 - definition of bisector
6 - ASA congruence theorem

2: SQ = SQ would be the one I would use

Question 1:
1. Given
2. Definition of an angle bisector
3. Reflexive property
4. Given
5. Definition of an angle bisector
6. ASA congruence
(You might have to double check these)

Question 2:
SQ is the line segment that would prove the triangle congruent by HL, since it is a shared side.

Have an awesome day! :)

Triangles are congruent is they have the same ?

Answers

Shape and size. Hope this helped

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there

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