(100 POINTS) HELP ASAP
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents.

y to the three fourths power, all over y to the one half power

the eighth root of y to the third power
the square root of y to the three fourths power
the fourth root of y
the square root of y

The coordinates of each image are G'(-2,9), and H'(1,-3).

What are the coordinates?

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).

Here, we have

R₍₁₈₀°,₀ (GH)

H(-1,3)

G(2,-9)

Now we need to the rotation of 180°  about the origin.

By following the rule, we get,

(x , y) ⇒ (-x , -y)

After solving,

G(2,-9) ⇒ G'(-2,9)

H(-1,3)  ⇒ H'(1,-3)

Hence, the coordinates of each image are G'(-2,9), and H'(1,-3).

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Answer:

m=18

Step-by-step explanation:

There are 39% of all the people on the trip are female students on a school trip.

One to fifteen teachers are assigned to every hundred students.

and there are 7:5 more female students than male students.

Let's say there are x teachers. Students multiply by 15 as a result.

Take the ratio of male to female as 7 years for the male and 5 years for the female.

The total student trip is made up of both male and female pupils.

Thus,

15x = 7y + 5y

15x = 12y

5x = 4y

x = 4/5y  ...eq 1

Then, the percentage of the female students.

5y/(x + 5x)×100

5y/16x ×100

Put the value of x from eq 1

625/ 16 = 39%

Thus, there are 39% of all the people on the trip are female students.

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The total cost for an order of 30 copies is $17.50.

So, calculate the total cost as follows:

We have:

Here, x implies a number of orders of copies and in question, it says the order of 30 copies.

So, Substitute x=30 in equation 1,

Hence, the total cost for an order of 30 copies is $17.50.

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By using the concept of law of exponents,the required answers are: 5)  [tex]e^{-1} f^{-1}[/tex] and 8) [tex]b^{3}[/tex]

According to this law of exponents, exponents of numbers are added, subtracted, multiplied, and divided when numbers get multiply, divide, and number raised by another exponents.

Exponents are the power of numbers, which tells us how many time a number multiply by itself.

we have,

5)   [tex]\frac{ef^0}{e^2f}[/tex]

⇒  [tex]e^{1-2}f^{0-1}[/tex]

⇒  [tex]e^{-1} f^{-1}[/tex]

8)  [tex]a^{0}b^{6} b^{-3}[/tex]         ( [tex]a^{0}[/tex]=1 )

⇒  [tex]b^{6-3}[/tex]

⇒  [tex]b^{3}[/tex]

Hence, final answer are [tex]e^{-1} f^{-1}[/tex] and [tex]b^{3}[/tex]

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The distance that Evan has left to hike is 13/30 mile.

From the information, Eva is hiking a real that has a length of 5/6 miles.

He has also hiked 2/5 miles. Therefore, in this situation, the distance that he has left will gotten by subtracting the fractions.

This will be:.

Distance left = Total distance - Distance hiked

Distance left = 5/6 - 2/5

= 25/30 - 12/30

= 13/30

The distance is 13/30 miles.

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Answer:

(9,1), Z(5,1)

Step-by-step explanation:

Looking at the triangles, the information needed to prove that ABC∼△DEF is AC = 10

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

AB and DE, BC and FE, then AC and DF

The solution is worked out using sides BC and FE, then AC and DF

BC / AC = FE / DF

8 / AC = 16 / 20

reducing the fraction 16/20 gives

8 / AC = 8 / 10

hence  AC = 10

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a) x = -6 to x =4

[tex](x_{1} , y_{1} ) (x_{2} , y_{2} ) = (-6,1) (4,3)[/tex]

Slope(m)[tex]= \frac{Y_{2}-Y_{1}}{x_{2}-x_{1}}[/tex]

               [tex]= \frac{1-3}{-6-4-}[/tex]

               [tex]= \frac{-2}{-10}[/tex]

               [tex]m = \frac{1}{5}[/tex]

Slope (m) of the function is 1/5.

b) x = -2 to x = 2

[tex](x_{1} , y_{1} ) (x_{2} , y_{2} ) = (-2,-1) (2,-3)[/tex]

slope (m)[tex]= \frac{Y_{2}-Y_{1}}{x_{2}-x_{1}}[/tex]

[tex]= \frac{-3-(-1)}{-2-2}[/tex]

[tex]= \frac{-2}{-4}[/tex]

slope(m) [tex]= \frac{1}{2}[/tex]

Slope(m) of the given function is 1/2.

What is fraction ?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

In a simple fraction, both are integers.

A complex fraction has a fraction in the numerator or denominator.

In a proper fraction, the numerator is less than the denominator.

Define slope(m)?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

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The equation representing the cost is y = 0.15x + 3 where x ix the number of copies and y is total cost.

Cost for 250 copies is $40.5

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a printing company charges $0.15 per copy in addition to a service fee of $3,

Therefore, according to question, the total cost y for printing x copies is,

y = 0.15x + 3

For x = 250

y = 0.15*250 + 3

y = $40.5

Hence, The equation representing the cost is y = 0.15x + 3 where x ix the number of copies and y is total cost.

Cost for 250 copies is $40.5

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The value of the shorter base which is x is 8 feet.

A trapezium is a quadrilateral with exactly one pair of opposite sides parallel to each other. The trapezium is a two-dimensional shape that appears as a table when drawn on a sheet of paper.

It has four sides and four vertices.

The trapezium is made of a rectangle and triangles.

Area of a trapezium = 1/2 (a + b ) h

where a = small base, b = big base and h = height.

from the above, b = 24 feet, h = 6 feet, a = x and area = 96 square feet

substituting the above into the equation

1/2 ( 24 + x) x 6 = 96

6(24 + x) = 96 x 2

6(24 + x ) = 192

multiplying the terms by 6

144 + 6x = 192

6x = 192 - 144

6x = 48

x = 48/6

x = 8 feet

In conclusion, the value of x is 8 feet

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Answer:25256

Step-by-step explanation:

The value of x in the angle illustrated as (5x + 2)° and (4x + 6)° is 4

It is important to note that line m and line n are parallel. In the diagram, they also intersect each other.

Therefore, it should be noted that according to angle rule, (5x + 2) and (4x + 6) are alternate angles. In this case, they're equal.

These will be illustrated as:

5x + 2 = 4x + 6

Collect like terms

5x - 4x = 6 - 2

x = 4

Therefore, x is 4°.

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=> Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3.

=>  Reflect figure A across the y-axis, and dilate it by a scale factor of 4.

Given,

In the question:

Figure A is a polygon that has been graphed on a coordinate grid.

To select the option:

Which of the following transformations will result in a similar image to figure A?

Now, According to the question;

The correct options are:

=> Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3.

=>  Reflect figure A across the y-axis, and dilate it by a scale factor of 4.

{If the two figures are similar, then their angles are not changed. The ratio of length are the same.}

Hence, => Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3.

=>  Reflect figure A across the y-axis, and dilate it by a scale factor of 4.

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The statements is true of the function f(x)= x^2 + 6x^3 - 4 + 2x^5 is C.the graph has exactly one x-intercept

It is shown that the function has one intercept in the x direction by plotting the graph of the polynomial

The graph showed one x intercept is at the coordinate (0.778, 0)

x intercept refers to the value of x when y is zero

The graph is plotted and attached

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Answer:

ye it is I can't help sorry I need the points

3.  3.8 ft

5.  28

7.  .1

Step-by-step explanation:

5/20.5=15.5/x

solve for x

3.8

7/14=14/x

28

10/x=1/100

.1

Answer:

We can do it by using the format tab

Step-by-step explanation:

We can change the background of a group of cells by selecting the cell or range of cells we want to format. We should Click Home > Format Cells dialog launcher, or press Ctrl+Shift+F from the keyboard. Then on the Fill tab, under Background Color, we pick the color we want. To use a pattern with two colors, we pick a color in the Pattern Color box, and then pick a pattern in the Pattern Style box. In this tab we can also select gradient or single color

The steps and reason to prove the angle theorems is; Table 3

The internal angles of the given triangle are given as;

a, b, c and d.

Now, we know that the sum of interior angles in a triangle is equal to 180°;

∠a + ∠b + ∠c = 180°

Now, ∠c and ∠d are angles that form a straight line and as such they sum up to 180° as they are supplementary angles.

∠c + ∠d = 180°

Thus, by transitive properties, we can say that;

∠a + ∠b + ∠c = ∠c + ∠d

Therefore by subtraction property of equality we have;

∠a + ∠b = ∠d

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The curve -3[tex]x^{2}[/tex] + 18x +3 has a maximum value of 30 at x = 3

In mathematics, a point at which a function’s value is greatest. If the value is greater than or equal to all other function values, it is an absolute maximum. if it is merely greater than any nearby point, it is a relative, or local, maximum. In calculus, the derivative equals zero or does not exist at a function’s maximum point.

Differentiate f(x) =  -3[tex]x^{2}[/tex] + 18x +3 ,

we have dy/dx = -6x + 18.

at turning point, dy/dx = 0

-6x + 18 = 0

6x = 18

x =18/3

x = 3

to check if x = 3 is a minimum or maximum point, we take the second derivate

which is  [tex]\frac{d^{2}y }{dx^{2} }[/tex] = -6

since  [tex]\frac{d^{2}y }{dx^{2} }[/tex] < 0

F(x) is a maximum,

so maximum value of x, we substitute x = 3 into the function

f(x)  = -3[tex](3)^{2}[/tex] + 18(3) + 3

f(x) = 30

In conclusion, the maximum value for the function is 30 at x = 3

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Answer:

Step-by-step explanation:

Equation are true:

C.

(3⁴)·(3⁵) = 3⁽⁴⁺⁵⁾ = 3⁹

D.

[tex]( 8^6 = \frac{1}{8^{-6}} )[/tex]

Answer:

C and D

Step-by-step explanation:

Steps for C:

Step 1: Combine exponent terms on left side
[tex]4+5=9[/tex]

Leave the base the same.

[tex]3^9=3^9[/tex]

[tex]True[/tex]

Steps for D:

Step 1: Simplify left side

[tex]\frac{1}{8^{-6} }=\frac{1/1}{262144} =262144[/tex]

Step 2: Simplify right side

[tex]8^6=262144[/tex]

[tex]262144=262144[/tex]

[tex]True[/tex]

Hope this helps :)

The least sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 5 minutes will be 416.16.

A normal distribution is a data set design in which the majority of values cluster around the middle of the range and the remainder taper off symmetrically toward either end. Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central location, with values decreasing as one moves out from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same. The normal distribution, like any other probability distribution, defines how the values of a variable are distributed. Because it properly captures the distribution of values for many natural occurrences, it is the most important probability distribution in statistics.

Here,

The z value at the 90 percent confidence interval is 1.645.

t ≥ z*s/√n

5≥1.645*62/√n

√n≥20.398

√n≥20.4

n≥416.16

The smallest sample size required to ensure that the sample mean does not deviate from the population mean by more than 5 minutes with 90% confidence is 416.16.

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Answer:

x = -6

Step-by-step explanation:

x - 2 = x (4) + 16

x - 2 = 4x + 16

4x - x = -2 - 16

3x = -18

3/3 x = -18/3

x = -6

Answer: “y is a function of x.” The letter x represents the input value or independent variable. The letter y, or f(x), represents the output value, or dependent variable.

Step-by-step explanation:lol i have no idea

By using the concept of straight angle, the value of x obtained is 17°

What is straight angle?

At first it is important to know about angle

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle

Straight angle is the angle whose measure is 180°

Here,

[tex]m\angle 1 =(4x +2)\\m\angle 2 = 110\\[/tex]

[tex]\angle 1 \ and \ \angle 2[/tex] forms a straight angle

[tex]m\angle 1 + m\angle 2 = 180[/tex] [Angle on a straight line]
[tex]4x + 2 + 110 = 180\\4x +112 = 180\\4x =180-112\\4x = 68\\x = \frac{68}{4}\\x = 17[/tex]

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The measure of missing line segments will be:

DG = 26; GE = 26; DF = 15; CH = 14; CE = 28

The centroid of a triangle is the place where the three medians of the triangle connect. It is sometimes defined as the point at where the three medians cross. A median line connects the middle of a side to the opposing vertex of a triangle. The centroid of a triangle is the point at where the triangle's three medians coincide (each median connecting a vertex with the midpoint of the opposite side).

Here,

IF If J is the centroid of CDE, this means that J divides CG, FE, DC, CE and DH into two equal parts.

The following expressions are therefore true

DG + GE = DE and DG = GE

Substituting

DG + DG = DE

2DG = DE

Given DE = 52

2DG = 52

DG = 52/2

DG = 26

Since DG = GE, hence GE = 26

Also DF + FC = DC and DF = FC

Since FC = 15, hence DF = 15

Also CH + HE = CE and CH = HE

Since HE = 14, hence CH = 14

CE = 14+14

CE = 28

The missing line segment count will be: DG = 26; GE = 26; DF = 15; CH = 14; CE = 28.

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Answer:

 50 people

Step-by-step explanation:

Solution

25% as a fraction is 25/100 which reduces down to 1/4. What this tells you is that 1/4 of the people asked want the hotel

1/4 * 200 = 50

50 people want the hotel.

Answer:

First step, correct answer is (3,1)

Step-by-step explanation:

1.it should be x+2(3x-8)=5

2. x+6x-16=5

3.7x=21

4. 7x/7=21/7

5. x=3

then you can eitheir take x+2y=5 or y=3x-8 i suggets taking second option as it is easier, just input values for x in

)  3x-8=y

6. 3(3)-8= 1

7. x=3, y=1

(4i+1)² can be simplified to 8i-15

A complex number is a number of the form a + bi, where a and b are real numbers

Given expression is (4i+1)²

four times of i plus one whole square.

(4i+1)² can be expanded by using algebraic identity

(a+b)²=a²+b²+2ab

(4i+1)²

Now put a as 4i and b as 1

(4i+1)²=16i²+1+2(4i)(1)

Where i²=-1

=-16+1+8i

=8i-15

Hence (4i+1)² can be simplified to 8i-15

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The nearest whole number to the number 5.2 is 5.

Given number:

= 5.2

we can determine the whole number of any decimals using the properties that is,

if decimal part < .5 its nearest whole number is 0.

example = 0.5 whole number is 0.

if decimal part  >  0.5 its nearest whole number is 1.

In this case,

= 5.2

decimal part  = 0.2 < 0

so the nearest whole number is 5.

Therefore the nearest whole number to the number 5.2 is 5.

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