Explain how the meaning of rational exponents follows from extending the properties of integer exponents to rational numbers, allowing for a notation for radicals in terms of rational exponents.

Answer:

Step-by-step explanation:

slope of line ⊥ to y=-8x+2

is -1/-8=1/8

eq. of line with slope 1/8 thro' (-4,1) is

y-1=1/8  (x+4)

8y-8=x+4

8y=x+4+8

8y=x+12

y=1/8 x+12/8

or

y=1/8 x+3/2

x y

2,0

1,-2

0,-4

-1,-6

-2,-8

Answer:

The given tessellated plane has translational and rotational symmetry. From the given options, we find that option A is correct.

Step-by-step explanation:

Concept: The symmetry has to be decided in such a way that when it applies to a figure, we get exactly the next figure. In the given figure, we have translational and rotational symmetries. We can translate the triangles to the next position and get the same triangle. Or we can rotate the triangle about the point of contact and get the same triangle.

For example, take the top left triangle. If it is translated towards approximately 30° direction, then we will get the triangle present at the top.

Or when we turn that triangle about the point of contact of that and the topmost triangle, then we can get the topmost triangle.

But there is no reflectional symmetry due to the absence of symmetry line.

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For [tex]x < -5[/tex]:

[tex]x-5 < 0 \Rightarrow |x-5|=-(x-5)=-x+5\\x+5 < 0\Rightarrow |x+5|=-(x+5)=-x-5[/tex]

So

[tex]|x-5|+|x+5|=-x+5-x-5=-2x[/tex]

Answer: 189/760

Step-by-step explanation:

The series can be represented in sigma notation as:

[tex]\sum^{18}_{n=1} \frac{1}{n(n+1)(n+2)}[/tex]

We can perform partial fraction decomposition as follows:

[tex]\frac{1}{n(n+1)(n+2)}=\frac{A}{n}+\frac{B}{n+1}+\frac{C}{n+2}\\\\ \implies 1=A(n+1)(n+2)+B(n)(n+2)+C(n)(n+1)[/tex]

If n = 0, then [tex]1=A(0+1)(0+2) \implies A=\frac{1}{2}[/tex]

If n = -1, then [tex]1=B(-1)(-1+2) \longrightarrow B=-1[/tex]

If n = -2, then [tex]1=C(-2)(-2+1) \longrightarrow C=\frac{1}{2}[/tex]

This means the series can be expressed as:

[tex]\sum^{k}_{n=1} \left(\frac{1}{2n}-\frac{1}{n+1}+\frac{1}{2(n+2)} \right)=\frac{k(k+3)}{4(k+1)(k+2)}[/tex]

Substituting in k=18,

[tex]\frac{18(21)}{4(19)(20}=\boxed{\frac{189}{760}}[/tex]

Answer:

Step-by-step explanation:

We have that O(n²) is the theta notation for 7n² + 4n + 2.

Let's give big-Oh a formal definition:

O(g(n)) = {the set of all f such that 0 [tex]\leq[/tex] f(n) [tex]\leq[/tex] cg(n) for any n >= n₀ fulfilling positive constants c and n₀}

To show this

We need to find c and n₀ such that:

7n² + 4n + 2 <= cn² for all n >= n₀ .

Divide both sides by n², getting:

7 + 4/n + 2/(n²) <= c for all n >= n₀ .

If we choose n₀ equal to 1, then we need a value of c such that:

7 + 4 + 2 <= c

We can set c equal to 13. Now we have:

7n² + 4n + 2 <= 13n² for all n >= 1 .

Hence, 7n² + 4n + 2=O(n²)

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Answer:

Speed of light 186000 miles/second.

it takes 500 seconds (approx 8 minutes) for light from the sun to reach Earth.

Step-by-step explanation:

Earth travels around the sun in a slightly oval-shaped orbit, known as an ellipse. Therefore, the planet's distance from the sun changes throughout the year.

However, the average distance from Earth to the sun is about 93 million miles (150 million kilometres). Scientists also call this distance one astronomical unit (AU).

A universe is a big place, and sometimes researchers use astronomical units to communicate how far celestial objects are separated from one another. For example, Jupiter orbits about 5 AU from the sun.

The distance between the earth and the sun d= velocity of light × time taken to reach light from the sun to earth

Distance from Earth to Sun=93000000 miles.

Speed of light = 186000 miles/second.

=>  [tex]\frac{93000,000}{186000}[/tex]

=> 500 seconds.

=> 8.333 minutes

it takes 500 seconds (approx 8 minutes) for light from the sun to reach Earth.

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Using subtraction of perfect squares, it is found that the factored expression is:

9t² - 4 = (3t - 2)(3t + 2).

It is given as follows:

a^2 - b^2 = (a - b)(a + b)

In this problem, the binomial is given as follows:

9t² - 4.

Hence:

Hence the factored expression is:

9t² - 4 = (3t - 2)(3t + 2).

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The cosine ratios which are correct for the ΔPQR are CosineP = r/q and CosineR = p/q.

We have,

Δ PQR,

Length of hypotenuse PR = q

The length of PQ = r,

And the length of QR = p

NOw,

We know that Trigonometric ratios of CosineΘ;

CosineΘ = Base/Hypotenuse

So,

CosineP = r/q

And,

CosineR = p/q

So, from the above find out values we can say that these values are given in option (a) and option (d).

Therefore, the cosine ratios which are correct for the ΔPQR are CosP = r/q and CosR = p/q.

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Answer:

the second option

Step-by-step explanation:

UV and AB are at a right Angie to reach other.

and

UV is parallel to ZY

The parabola has roots at x=3 and x=-1, so its vertex is halfway between those points, at x=1, and so the y-coordinate of the vertex is -(1-3)(1+1)=4.

Another point that lies on the parabola is (-1, 0).

Answer:

Important- not urgent

Step-by-step explanation:

The research paper is important but since Brandon has two weeks to decide it is not urgent.

Answer:

see the attachment photo!

The median of the distribution is 4.

A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.

The median is the number at the center of the data set.

Arranging the numbers in the histogram in ascending order is: 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 9, 10

1/2 x 22 = 11th number  4

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Step-by-step explanation:

hope you can understand

Answer:

x

Step-by-step explanation:

I got it right.........

The values of f(3.52)=26.61 and f(-8.77)=257.05

An assignment of an element from set Y to each element of set X constitutes a function from set X to set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The notation f: X→Y denotes a function, its domain, and its codomain. The value of a function at an element x of X, denoted by the symbol f(x), is referred to as the image of x under f or the value of f applied to the argument x.

The given function is f(x) = 3x²-3x =3x(x-1)

f(3.52)=3*(3.52)(3.52-1)

=26.61

f(-8.77)=3*(-8.77)(-8.77-1)

=257.05

Therefore, the values of f(3.52)=26.61 and f(-8.77)=257.05

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The positive number between every pair of distinct points is known as the distance and it can be found as the absolute value of the difference  between the corresponding real numbers.

The distance represents the space between a pair of distinct points. This is called the distance postulate.

In order to find the distance, you would need to solve for the absolute value of the difference between the real numbers that are at the two points.

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Answer:

The positive number between every pair of distinct points is known as the distance and it can be found as the absolute value of the difference  between the corresponding real numbers.

Step-by-step explanation:

The circle equation in polar coordinates is:

   [tex]r - 4*cos(\theta) + 4*sin(\theta) = 0[/tex]

Here we have the circle equation:

[tex](x - 2)^2 + (y + 2)^2 = 8[/tex]

First, we expand it to:

[tex]x^2 - 4x + 4 + y^2 + 4y + 4 = 8[/tex]

Now we can rewrite it as:

[tex]x^2 + y^2 -4x + 4y + 4 + 4 = 8\\\\x^2 + y^2 - 4x + 4y = 0[/tex]

Remember that:

[tex]x^2 + y^2 = r^2\\\\x = r*cos(\theta)\\y = r*sin(\theta)[/tex]

Replacing that, we get:

[tex]x^2 + y^2 - 4x + 4y = 0\\\\r^2 - 4r*cos(\theta) + 4r*sin(\theta) = 0[/tex]

That is the equation in polar form.

Now, because we can discard the solution r = 0, we can divide both sides by r to get:

[tex]r - 4*cos(\theta) + 4*sin(\theta) = 0[/tex]

To simplify it.

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C. e

Step-by-step explanation:

[tex] ln( {e}^{e} ) = e ln(e ) = e(1) = e[/tex]

The transformation of a function may involve any change in the initial function. The correct option is C.

The complete question is:

Each statement describes a transformation of the graph of y = log2x.

Which statement correctly describes the graph of y = log2(x + 3) - 9?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Vertical shift

Stretching:

Given the initial function y = log2x, now if the function is needed to be transformed to y = log2(x + 3) - 9, then the function is needed to be shifted left by 3 units and down by 9 units.

Hence, the correct option is C.

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Answer:

Using the ratio and proportion method, we find that on an average 1.875 rooms can be painted per gallon.

Step-by-step explanation:

Concept: Use the method of ratio and proportion.

In this method, if a relationship is given between two values, then using that relationship we can find another relationship with respect to another variable.

Given that for 2/5 gallons of paint, we can paint 3/4 of rooms. So, for one gallon of paint, divide 2/5 by 3/4.

2/5 gallons of paint = 3/4 rooms

1 gallon of paint = [tex]\frac{\frac{3}{4} }{\frac{2}{5} } = \frac{15}{8} =1.875[/tex] rooms

So, on an average they can paint 1.875 rooms per gallon.

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Answer:

6 and 4

Step-by-step explanation:

Let one number be x.

Then another will be : 4x - 20

In accordance with the question;

x + 4x - 20 = 10

5x = 10 + 20

x = 30/5

= 6

x = 6

4x - 20 = 4×6 - 20 = 4

So, the numbers are 6 and 4.

Answer:

look at the picture.

Step-by-step explanation:

look at the picture.

Answer:

8

Step-by-step explanation:

8*25=2.00

2.00+.90=2.90

Answer:

20 km

Step-by-step explanation:

So 1/3 = 2/6
2/6 = distance traveled by boat + 1/6 traveled by riding horses = 3/6 = 1/2

Meaning the 10 km by foot left is the other half

Answer:

O c. y-int y = 4 and No x-int

Step-by-step explanation:

In the slope-intercept equation y = -3x + 4, only slope and y-intercept are displayed as it is in slope-intercept format which is y = mx + b; m being the slope and b being the y-intercept.

There is no x-intercept present in a slope-intercept equation.

But due to the 4 being in the place of the y-intercept is the y-intercept of the graph and line depicted off this linear equation (slope-intercept equation).

Hence, the answer is C. Y-intercept = 4 and No x-intercept.

The probability that the results indicate a successful market for the product and the product is actually not successful is P=0.77.

Probability refers to a possibility that deals with the occurrence of random events.

Events are given:

S: success

F: failure

MS: market research forecast a success

MF: market research forecast a failure

we have given:

P(S)=0.70

P(F)=0.30

P(S | MS)=0.90

P(F | MS)=0.20

we can derive that P(F | MF)=0.80.

We also can conclude that P(S | MF)=0.10.

We can calculate the probability of having a forecast of a failure,

[tex]P(MF | F) =\dfrac{ P(F | MF)P(F)}{ P(F | MF)P(F) + P(S | MS)P(S) }[/tex]

P (MF | F) = 0.24 / 0.31

P (MF | F) = 0.77

The probability that the results indicate a successful market for the product and the product is actually not successful is P=0.77.

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Answer:

3

Step-by-step explanation:

374274 =3.74274 x 100000=3.74272x 10^5