3. Which word choice supports the idea that the author has a positive point of view of rollerskating?
A.been around since the early 1700s
B.loved winter ice-skating
C.hard to roll
D.more popular

The Answer to the about question rational exponents and radicals is given below.

To solve the first part Let us assume a expression (E) that contains rational exponents

E =  6² / ( 9[tex]\frac{2}{3}[/tex] × 3[tex]\frac{5}{3}[/tex] )

E =  6² / ( (3²)[tex]\frac{2}{3}[/tex] × 3[tex]\frac{5}{3}[/tex] )

E =  6²  / ( 3[tex]\frac{4}{3}[/tex] × 3[tex]\frac{5}{3}[/tex] )

E =   6² / 3[tex]\frac{9}{3}[/tex]

E =   6² / 3³

E = 36/27 = 4/3

E = 4/3

To solve the second part Let us assume a expression (F) that contains radicals.

F = 10 × √(∛(59 +5))

F = 10 × √(∛64)

F = 10 × √(∛(4×4×4))

F = 10 × √4

F = 10 × √(2×2)

F = 10 × 2

F = 20

Thus we have simplified the expression that contains rational exponents and also the expression that contains radicals also.

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To simplify an expression with rational exponents, we multiply the exponents together. To simplify an expression with radicals, we can find the square root of the number.

An expression with rational exponents that can be simplified further is:

To simplify this expression, we can use the rule that states when we raise an exponent to another exponent, we multiply the exponents together. Therefore, (161/4)3/2 = 161/4 * 3/2 = 163/8.

An expression with radicals that can be simplified further is:

To simplify this expression, we can find the square root of 32. The square root of 32 can be simplified as follows: √(32) = √(16 * 2) = √(16) * √(2) = 4√(2).

The length of piece of wire for square = 230 inches

The length of piece of wire for circle = 130 inches.

The given length of  wire = 360 inches

Now let it cuts into lengths r' and r

Therefore,

⇒ r' + r = 360   ...(i)

Now let with length r' square is formed

Therefore,

Area of square = r'xr'

                         = (r')²

And with length of r circle is formed,

Area of circle = π r²

According to the question

Both area are same,

⇒ (r')² =  π r²

Taking square root both sides,

⇒ r' = √π r    ......(ii)

Now from (i) and (ii);

⇒ √π r + r = 360

⇒ r(1 + √π) = 360

⇒      2.77 r = 360

⇒              r = 129.96 ≈ 130 in

Then r' = 360 - 130

            = 230

Hence length are 130 inches and 230 inches.

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A circle is defined as all co-planar points equidistant from a given point

A line segment is a piece of a line that has two endpoints.

It is a part of a line with one end point and proceeds on in one direction.

A line refers to collection of line along a straight path proceeding in opposite directions with no endpoints.

Level: Middle school

Subject: Geometry

Topic: Shapes and terms in geometry

The simplest form of 34 / 710 is 17 / 355.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.

Given that the expression 34 / 710.

Now to write the above expression in simple form, we divide the numerator and denominator by 2

34 / 710 = 34/ 2 ÷ 710 / 2

34 / 710 = 17 / 355

Now the above expression is not easily divisible by any number.

Therefore, The simplest form of 34 / 710 is 17 / 355.

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equation = g(x) = 2x-2

 when g(-3) replace x with -3

 so you get g(-3) = 2(-3)-2

2*-3 = -6-2 = -8

g(-3) = -8

Answer:

93 and 110 upper fourth

Step-by-step explanation:

Q3 is at 93 and the max number is at 110 so the upper fourth should fall between 93 and 110, the middle half of the responses  will fall between 70 and 93 and the lower fourth of the responses will fall between 40 and 70

Answer:

D.Non negtaive rational numbers.

Step-by-step explanation:

Given

A store sells self serve frozen yogurt and weight of yogurt taken in ounces.

The function C(w) represents the cost , in dollars .

The given yogurt can be  measured  in gram or kilogram or ounces etc.

The quantity of yogurt can not be negative  because  quantity  is always a positive number . So it can not be a negative number

The quantity is defined as the  amount of  any material or substance .

The quantity is always a positive number . It can not be negative value of a number.

Here, the quantity is taken in ounces  so it is a positive number .

The quantity of any material can be natural number or  positive rational  number .

Hence,the domain for the function C(w)  are non negative rational numbers.

An appropriate domain for the function would be non negtaive rational numbers .

Therefore, the correct answer is option D.

Actually the real answer is:

-1.

Answer:  The slope of the tangent line at the point (3, 2) is [tex]\dfrac[4}{9}.[/tex]

Step-by-step explanation:  We are given to find the slope of the line tangent to the following curve at the point (3, 2).

[tex]3y^2-2x^2=6-2xy~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that the derivative of a function at any given point is equal to the slope of the tangent at that point.

Now, differentiating both sides of equation (i) with respect to x, we have

[tex]\dfrac{d}{dx}(3y^2-2x^2)=\dfrac{d}{dx}(6-2xy)\\\\\\\Rightarrow 6y\dfrac{dy}{dx}-4x=0-2\left(y+x\dfrac{dy}{dx}\right)\\\\\\\Rightarrow 2x\dfrac{dy}{dx}+6y\dfrac{dy}{dx}=4x-2y\\\\\\\Rightarrow \dfrac{dy}{dx}=\dfrac{4x-2y}{2x+6y}\\\\\\\Rightarrow \dfrac{dy}{dx}=\dfrac{2x-y}{x+3y}.[/tex]

So, at the point (3, 2), we get

[tex]\dfrac{dy}{dx}=\dfrac{2\times3-2}{3+3\times2}=\dfrac{6-2}{3+6}=\dfrac{4}{9}.[/tex]

Thus, the slope of the tangent line at the point (3, 2) is [tex]\dfrac{4}{9}.[/tex]

The slope of the tangent at point (3,2) will be ([tex]5\div 18[/tex]) and it can be evaluated by differentiating the given equation of curve.

Given :

To determine the slope of the tangent, differentiation of the given equation of curve is carried out.

Differentiating equation (1) with respect to x.

[tex]\dfrac{d}{dx}(3y^2-2x^2) = \dfrac{d}{dx}(6-2xy)[/tex]

[tex]6y \dfrac{dy}{dx}-4x = 0-2y-2x\dfrac{dy}{dx}[/tex]

Now, further simplification of the above equation gives:

[tex]\dfrac{dy}{dx}(6y+2x)=4x-2y[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{4x-2y}{6y+2x}[/tex]

Now, at point (3,2) the slope of the tangent will be:

[tex]m = \dfrac{4\times 3-2\times 2}{6\times 2+2\times3}[/tex]

[tex]m = \dfrac{5}{18}[/tex]

So, the slope of the tangent at point (3,2) will be ([tex]5\div 18[/tex]).

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In rectangle ABCD, the value of x, given that the lengths of the diagonals BD and AC are expressed as 10x + 8 and 9x + 20 respectively, is 12.

In a rectangle, the diagonals are equal in length. This gives us the following equation,

10x + 8 = 9x + 20, where BD and AC represent the lengths of the diagonals respectively.

To solve this for x, we subtract 9x from both sides, which gives: x + 8 = 20. Then, subtracting 8 from both sides of the equation gives: x = 20 - 8 = 12.

So, the value of x that suits this rectangle is 12.

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I can confirm that Option C is correct, just finished the assignment.

Final answer:

Since no candidate won an absolute majority in the Texas Democratic Primary for governor, a runoff election is necessitated between Candidate X and Candidate Y, the top two vote-getters, to ensure the nominee is chosen by a majority.

Explanation:

In the scenario where Candidate X wins 45% of the vote, Candidate Y receives 30%, and Candidate Z wins 25% in the Texas Democratic Primary for governor, no candidate has achieved an absolute majority, as required by Texas law to win the primary outright. An absolute majority means that a candidate must have more than 50% of the votes, specifically fifty percent plus one vote. Since this did not happen, a runoff election is triggered.

The runoff will take place between the two candidates who received the most votes, which in this case, would be Candidate X and Candidate Y. This runoff ensures that the final nominee for governor from the Democratic Party will have the support of a majority of its voters, reflecting a more democratic outcome. The system prevents a candidate from winning the primary nomination with only a plurality of the vote, which could be less representative of the party's voters as a whole.

Answer:

Step-by-step explanation:

Given system of linear equations:

y=-1/2x + 4 and

x + 2y=-8.

Let us convert second equation in slope intercept form too.

x + 2y=-8

Subtracting x from both sides, we get

x -x+ 2y=-8-x

2y = -x-8

Dividing both sides by 2, we get

2y/2 = -x/2-8/2

y = -1/2 x - 4.

Let us find slope and y-intercept of each of the equation.

Slope-intercept form of a linear equation is y = mx+b, where m is the slope and b is y-intercept.

On comparing first equation y=-1/2x + 4 by slope-intercept form y = mx+b slope is -1/2 and y-intercept is 4.

For the second equation y = -1/2 x - 4 slope is -1/2 and y-intercept is -4.

Therefore, correct option is 3rd option: