The quotient property of radicals requires the indices of the radicals to be the same. Does this mean that it is not possible to write es002-1.jpg as a single radical? Explain.

Answers

Answer 1

The radicands are powers of the same base, so they can be written using rational exponents.

Simplify the quotient of the exponential expressions by getting a common denominator and subtracting exponents.

The simplified expression is the 4th root of y

Answer 2

The expression can be written as a single radical by covertong the expression to a rational format such that both the denominator and numerator have the same base as

Numerator = The 4th root of y³ = y¾

Denominator = squareroot of y = y½

Using indices :

Division sign signifies the powers should be subtracted

[tex] \frac{y¾}{y½} = y^{¾ - ½} = y¼[/tex]

Therefore, the expression can be written as a single radical thus

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Related Questions

WILL GIVE A BRAINLEST!!!!!!

Solve and check : c-4/c-2=c-2/c+2 - 1/2-c


The solution is c =

How many extraneous solutions are there?

Answers

[tex]c=14[/tex]

There is no extraneous solution because as we put the value of c in equation (1), it does not make the equation (1) not define.

Step-by-step explanation:

Given :

[tex]\dfrac {c-4}{c-2} = \dfrac {c-2}{c+2} - \dfrac{1}{2-c}[/tex]                   --------- (1)

Calculation :

[tex]\dfrac {c-4}{c-2} = \dfrac {(c-2)^2+(c+2)}{(c+2)(c-2)}[/tex]

[tex]c-4 = \dfrac {(c^2-4c+4)+(c+2)}{(c+2)}[/tex]

[tex](c-4)(c+2) = (c^2-3c+6)[/tex]

[tex](c^2-2c-8) = (c^2-3c+6)[/tex]

[tex]c=14[/tex]

There is no extraneous solution because as we put the value of c in equation (1), it does not make the equation (1) not define.

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Answer:

14 and Zero

Step-by-step explanation:

Daniel read 3 books in 2.5 weeks. which rate represents this situation

7.5 books/3 weeks

3 books/2.5 weeks

3 books/7.5 weeks

2.5 books/3weeks

Answers

3 books/2.5 weeks. Because it basically just says it in the sentence and its impossible for it to be any other one

Write an equation in point-slope form for the line through the given point with the given slope. (–3, –7); m = -6/5

Answers

Point slope form : y-y₁=m(x-x₁)

Goes through (-3, -7) and the slope = -6/5

Since we are given the slope and the x₁ as well as y₁, we can simply plug everything into the point slope formula.

y - (-7) = -6/5(x - (-3))

Simplify.

y + 7 = -6/5(x + 3) 

~Hope I helped!~

Construction is under way at an airport. This map shows where the construction is taking place. If Road A and Road B are parallel, what is the distance from P to Q on Road C?433 feet



975 feet



1,050 feet



1,477 feet

Answers

For this case we observe that we have a problem of similarity of triangles.
 We can then use the following relationship to solve the problem:
 [tex] \frac{650+x}{800+1200} = \frac{650}{800} [/tex]
 From here, we clear the value of x.
 We have then:
 [tex] 650+x = \frac{650}{800}(800+1200) [/tex]
 Rewriting we have:
 [tex] 650+x = \frac{650}{800}(2000) [/tex]
 [tex] 650+x = 1625 [/tex]
 [tex] x = 1625 - 650 [/tex]
 [tex] x = 975 feet [/tex]
 Answer:
 the distance from P to Q on Road C is:
 [tex] x = 975 feet [/tex]





Answer:

if your asking for plato it will be B

Step-by-step explanation:

got it correct just now

Write an inequality to represent the situation: The temperature stayed above -15 degrees. Help!

Answers

Answer:

Temperature t > -15 degrees.

Step-by-step explanation:

Let t denote the temperature.

The inequality sign for above or greater is >. The inequality sign for less than is <.

It is given temperature stayed above -15 degrees.

This can be written in inequality form as t> -15 °(degrees)

The inequality to represent the temperature is t > -15°C

Given data:

To represent the situation where the temperature stayed above -15 degrees, the inequality symbol used is ">".

In an inequality, the ">" symbol means "greater than." By using this symbol,  the temperature needs to be greater than -15 degrees.

The inequality representing this situation is:

Temperature > -15°C

So, t > -15°C

If the temperature is higher than -15 degrees, the inequality is true.

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If triangle ABC has sides of lengths 6,10,and x, between which two numbers must the value of x lie

Answers

The sum of two sides of a triangle must be more than the length of the third side. 6+4 = 10 so x must be greater than 4. 6 + 10 = 16, so x must be less than 16
4<x<16
x is between 4 and 16.

Find the area of a circle with a circumference of 2pi Either enter an exact answer in terms of 3.14 pi or as a decimal

Answers

C = 2 π r
2 π = 2 π r
r = 1
so
A = π r^2
A = 3.14 x 1^2
A = 3.14 

answer
A = 3.14

what is the approximate distance between the points (1 -2) and (-9 3) on a coordinate grid?

Answers

[tex]d= \sqrt{(-9-1)^2+(3-(-2))^2}= \sqrt{100+25}= \sqrt{125} \approx 11.18 \ \ \text{units}[/tex]

Answer:

11.18

Step-by-step explanation:

Jessica needs 54 cupcakes for her party. They come in packs of 10.how many packs does Jessica need ?

Answers

6 packs. there will be 6 extra cupcakes 

Follow below steps:

To determine the number of packs Jessica needs for 54 cupcakes:

Divide the total number of cupcakes by the number of cupcakes in each pack: 54 ÷ 10 = 5.4

Since Jessica cannot buy a fraction of a pack, she needs to round up to the nearest whole number. Therefore, Jessica needs 6 packs of cupcakes.

The area of a triangle is 1440 cm^2. the base of the triangle is 5 times the height. what is the height of the triangle?

Answers

height = "h"
Triangle Area = .5 * base * height
1,440 = .5 * 5h * h
1,440 = 2.5 h^2
576 = h ^2
height = 24 centimeters
and the base is therefore 120 centimeters

Double Check
base = 120  cm
height 24 cm
area = .5 * 120 * 24
area = 1,440



“How many times did you ride the Ferris wheel today?” Is the question a statistical question? Explain why or why not.

Answers

Well in a way...im not sure. lets see if we are dealing with statistical and last time i checked thats a part of math soo she/he is wondering how many TIMES the other person so...some part of be is saying Yes But then again no...you choose its your question xD (hope i helped somewhat)
"A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer. For example, "How many minutes do 6th grade students typically spend on homework each week?" is a statistical question." the first google result. not my work

Is the transformation a rotation about point j?

Answers

yes, if you rotated one of the figures at point B it would overlap the 2nd figure exactly.
Yes, it seems to have rotated about 90 degrees 

Choose the correct simplification of the expression a to the 9th power times b to the 10th power all over a to the 2nd power times b to the 7th power.

Answers

a^9 * b ^10
======
a^2 * b ^7

When you are dividing, then the powers are subtracted Top first, bottom second.
a^(9 - 2) b^(10 - 7)
a^7 b^3

the factors of m^2 + 12m + 35 are?

Answers

m^2 + 12m + 35

Factored:
(m+5)(m+7)

Check:
(m+5)(m+7)
(m*m) + (m*7) + (5*m) + (5*7)
m^2 + 12m + 35

Hope this helps! :)

Explain why 81 3/4 equals 27

Answers

81 to the 4th root is 3 and 3 cubed is 27.

General Idea:

There are few exponent rules that need to be used to simplify the rational exponent to get to the answer.

Exponent rules:

[tex] Rule\; 1: a \cdot a \cdot a \cdot a =a^4\\ \\ Rule\; 2: (a^m)^n=a^{m \times n} [/tex]

Applying the concept:

Rewriting 81 as a number with an exponent using prime factorization.

[tex] 81=3 \times 3 \times 3 \times 3 = 3^4\\ \\ Applying \; Rule \; 1, \; we\; get\; \\\\81^{\frac{3}{4}}=(3^4)^{\frac{3}{4}} \\ \\ Applying \; Rule \; 2,\; we\; get\\ \\ 3^{4 \times\frac{3}{4} } = 3^{\frac{12}{4} }=3^3=3 \times 3 \times 3 = 27 [/tex]

Conclusion:

The above explanation explains why [tex] 81^{\frac{3}{4}} =27 [/tex]

ASAP plz help fast thanks

Answers

Looks like A and D <<<<-===== short answer.
In order for lines to be perpendicular the slope of one line has to be the minus reciprocal (upside down) of the other. 
A
3x + y= 6
y = -3x + 6 So the second line has to be 1/3 Notice it is plus.

B
6x - 2y = 4
-2y = -6x + 4
y = (-6/-2)x + (4/-2)
y = 3x - 2

C
y = 3x - 2

D
y = 1/3 x +7

help me i need it asap ! please and be correct plz

Answers

The right triangles are congruent, so
.. 2x -14 = 37 -x
.. 3x = 51 . . . . . . . add x+14
.. x = 17 . . . . . . . . divide by 3

x = 17

Five is a solution of (Y < -3)

A.True

B.False

Answers

This is false. 

The integer '5' has a higher value than -3 as it leans on the right side of a number scale, while -3 sits on the left side.

I hope this helps!

PLEASE HELP SUPER EASY IM JUST STUPID

Which is the most accurate description of the polygon below?

Answers

It's a rhombus.
1. D
2. A
3. D
4. B
5. C

Answer:

It is a rhombus.

Step-by-step explanation:

To identify the type of polygon, we will first determine if the opposite sides are parallel.  To do this, we find the slope of each line segment.  (Parallel lines have the same slope.)

For WX, m = (5-2)/(1-5) = 3/-4 = -3/4

For XY, m = (2--1)/(5-1) = 3/4

For ZY, m = (2--1)/(-3-1) = 3/-4 = -3/4

For ZW, m = (2-5)/(-3-1) = -3/-4 = 3/4

Since the slopes of WX and ZY are the same, these two sides are parallel.  Since the slopes of XY and ZW are the same, these two sides are parallel.  Since opposite sides are parallel, the figure is a parallelogram.

In order to be a rectangle, the angles would have to be right angles.  Since perpendicular lines have slopes that are negative reciprocals of each other, the slopes of adjoining sides would have to be opposite signs and flipped.  This is not the case, so the angles are not right; this means it is not a rectangle.

The only other option for a parallelogram without right angles would be a rhombus.  This is the case if the length of each side is the same.  We will use the distance formula for this:

[tex]WX=\sqrt{(5-2)^2+(1-5)^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\\\XY=\sqrt{(2--1)^2+(5-1)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\\\\YZ=\sqrt{(2--1)^2+(-3-1)^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\\\ZW=\sqrt{(2-5)^2+(-3-1)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]

Since the length of each side is the same, this figure is a rhombus.

Suppose that G(x) = F(x - 8). Which statement best compares the graph of G(x) with the graph of F(x)? apex
A.The graph of G(x) is the graph of F(x) shifted 8 units to the right.
B.The graph of G(x) is the graph of F(x) shifted 8 units to the left.
C.The graph of G(x) is the graph of F(x) shifted 8 units up.
D.The graph of G(x) is the graph of F(x) shifted 8 units down.

Answers

Answer:

B

Step-by-step explanation:

The graph of G(x) = F(x - 8) is the graph of F(x) shifted 8 units to the right, option A.

When comparing the graph of G(x) = F(x - 8) with the graph of F(x), we note that there is a horizontal shift involved. Following the rules for transformations, subtracting a positive constant from the independent variable x results in shifting the graph to the right by that constant. Therefore, the statement that best compares the graph of G(x) with the graph of F(x) is: The graph of G(x) is the graph of F(x) shifted 8 units to the right, option A.

This is similar to the effect observed when comparing the functions f(x) and f(x - 2), where the latter's graph is a rightward shift of the former's graph by 2 units.

Complete the table. Original Price Percent 112 of Discount 32% Sale Price

Answers

I'm guessing you mean the original price is $112 and there is a discount of 32%. First you want to find how much the discount is, 32% of $112. 'of' means multiplication.

32% * 112

0.32 * 112

35.84

So there is a $35.84 discount, subtract this from the original price to find the price after discount:

$112 - $35.84 = $76.16

So the price after discount is $76.16.

Answer:

$76.16

Step-by-step explanation:

$76.16

Which of the following values is closest to the mean for the set of data shown below?
23, 32, 20, 43, 41, 66, 63, 59, 54, 36, 45, 61, 55, 44, 47
A.45.9 B.50 C.58 D.54.3

Answers

the answer b

hoped it helped!!!
ok so to find the mean u need to add all the numbers (689)
 then divide by how much numbers there are (49.9)
so your answer is b

please mark brainliest!

Someone please help, with a cherry on top?

View attached graph and find the approx. slope

THANK YOU SOOO MUCH!!!

Answers

your answer is 4.8. hope this helps

How to calculate linear distance between two points on circle circumference?

Answers

The distance between two points on the circumference of a circle is called the arc. If the arc length subtends an angle θ to the center of the circle and the circle has a radius r, then the length of the arc is calculated by the formula;
 θ/360 × 2πr.

Lisa made $286 for 13 hours of work. at the same rate, how many hours would she have to work to make $242 ?

Answers

Lisa wpuld have to work 11 hours to make $242

Rico travelled from the United States to the United Kingdom. Once Rico arrived, he converted his American dollars into British pounds (the currency in the U.K.). He gave the bank teller $500 and was given back 295 pounds. At the end of his vacation Rico had 75 pounds left over which he converted back into US dollars. How much money (in US dollars ) did Rico have when he got home? Round the answer to the hundredth.

Answers

105 us dollars is 75 pounds

Find the value of x in the triangle shown below?

A. 44°
B. 29°
C. 107°
D. 90°


Answers

c. 107 44+29=73 180-73= 107
The sum of All the internal angles of triangle equals to 180 degree
So you can sum the one that are given and subtract 180 from them to find x which is 107

telling a child that he won't amount to anything in life is a form of
(A)neglect
(B)emotional abuse
(C)physical abuse
(D)sexual abuse

Answers

Answer: Option B. Emotional abuse  
Emotional abuse, also called psychological violence, is a form of abuse where the person or sufferer is exposed to act which can result in psychological trauma and can include depression, anxiety, etc. So, this act of telling a child that he would not amount to anything is considered as emotional abuse.

How would you factor 4x^2 + 9?
I think the answer has imaginary numbers in it, but how would you get the solution?

Answers

The answer is it cannot be. It is because if you use the difference of two square, the operation used must not be addition, but it would be subtraction.
It can be factored out if you will find the factors of 4x^2 - 9 =0
So the factors will be(using difference of two perfect squares):
(2x+3)(2x-3)
Cause if you will use the factors (2x+3)(2x+3) or even the negative signs to it, it will give:
4x^2+12x+9 or 4x^2-12x-9 

so for the answer of your question, it is invalid.

helppppppppppppppppppppppppppppp

Answers

Answer:
x = 4

Explanation:
For the right hand side:
log base 9 of 8 + log base 9 of (x-2) = log base 9 (8*(x-2))
                                                          = log base 9 of (8x-16)
For the left hand side:
2*log base 9 of x = log base 9 of x^2

Now, equating the two sides and solving for x:
log base 9 of (8x-16) = log base 9 of x^2
This means that:
x^2 = 8x - 16
x^2 - 8x + 16 = 0
(x-4)^2 = 0
Therefore:
x = 4

Hope this helps :)
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