Drag each equation to the correct location on the table. Determine which equations will result in extraneous solutions.

Answer:

  (a)  none

Step-by-step explanation:

A "hole" in the graph of f(x) is located at an x-value where the left limit of the function and the right limit are the same finite value, but the function is undefined at that value of x.

The function f(x) = (x -2)/(x -2) can be reduced to the function f(x) = 1, which is defined everywhere. That reduction occurs when the numerator factor (x-2) cancels the same binomial denominator factor. A graph of the original function will be a straight horizontal line with a "hole" at (2, 1).

The attachment shows a graph.

The given function can be reduced, but the reduced function remains undefined at x=1/2. Not all of the denominator factors are cancelled there. The function is graphed in the second attachment. At x=1/2, there is a vertical asymptote, not a hole.

  [tex]g(x)=\dfrac{(2x-1)(x+4)^2(x-1)(3x+2)}{3x(x-4)(2x-1)^3}\qquad x\notin \left\{0,\dfrac{1}{2},4\right\}\\\\g(x)=\dfrac{(x+4)^2(x-1)(3x+2)}{3x(x-4)(2x-1)^2}\qquad x\notin \left\{0,\dfrac{1}{2},4\right\}[/tex]

There are no holes in the function's graph.

__

Additional comment

A hole can occur for a variety of reasons. In the graph of a rational function, it will generally be found where numerator and denominator zeros cancel each other completely, and the function can be "reduced" to one that is define at the location of those zeros.

It can also occur in piecewise defined functions, where the pieces are defined on adjoining (half) open intervals. For example:

  [tex]f(x)=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x > 0\end{cases}[/tex]

has a hole at (0, 0).

The number of scores between 19.5 and 49.5 using the cumulative frequency is 16.

The cumulative frequency is the running total of frequencies over some class intervals.

The frequency refers to the number of elements in the set or class.

Therefore, the cumulative frequency is the sum of all previous frequencies up to the required point.

Scores on a Test

Class    Frequency   Cumulative Frequency

20–29         9                        9 (0 + 9)

30–39         4                       13 (9 + 4)

40–49         3                      16 (13 + 3)

50–59         2                      18 (16 + 2)

60–69        10                    28 (18 + 10)

Thus, the number of scores between 19.5 and 49.5 using the cumulative frequency is 16.

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Answer:

[tex]66\pi[/tex] ft²

Step-by-step explanation:

First find the area of the rectangle surrounding the cylinder.

Since the base diameter is 6 feet, the circumference [tex]=\pi d=6\pi[/tex].

Since the height is 8 feet, the area of the rectangle is [tex]6\pi\times8[/tex] or [tex]48\pi[/tex]

Now the area of the base circle [tex]=\pi r^2 = \pi\times\frac{1}{4}d^2=9\pi[/tex]

There are 2 base circles, so [tex]9\pi\times2=18\pi[/tex]

Surface area = [tex]18\pi+48\pi=66\pi[/tex] ft²

Answer:

Scalene Triangle

Step-by-step explanation:

Defn
When all the three sides of the triangle are of different measures, it is a scalene triangle.

Answer:

It is a scalene triangle since all sides have different measurements.

Step-by-step explanation:

The number of orders Michael, Rafael and Amanda served are 16.8, 33.6, and 41.6 servings

respectively.

x + 2x + (2x + 8) = 92

3x + 2x + 8 = 92

5x = 92 - 8

5x = 84

x = 84/5

x = 16.8 servings

Therefore,

Michael = x

= 16.8 servings

Rafael = 2x

= 2(16.8)

= 33.6 servings

Amanda = 2x + 8

= 33.6 + 8

= 41.6 servings

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El uso de las dadas operaciones es:

Para las operaciones "<", ">", y "=" uso es:

Entonces simplemente debemos comparar los dos números, si vemos al primer problema, por ejemplo:

3 ___ 17/2

Sabemos que 17/2 = 8.5

8.5 es más grande que 3, entonces el signo que debe ir ahi es:

3 < 17/2.

Todas las operaciones que estan colocados en la hoja ya son correctos.

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Any complex number [tex]z[/tex] can be written in trigonometric form as

[tex]z = |z| e^{i\arg(z)} = |z| \left(\cos(\arg(z)) + i \sin(\arg(z))\right)[/tex]

where [tex]|z|[/tex] is the modulus of [tex]z[/tex] and [tex]\arg(z)[/tex] is its argument, i.e. the angle [tex]z[/tex] makes with the positive real axis in the complex plane.

We have

[tex]|z| = \sqrt{3^2 + \left(\sqrt3\right)^2} = \sqrt{12} = 2\sqrt3[/tex]

and

[tex]\arg(z) = \tan^{-1}\left(\dfrac{\sqrt3}3\right) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) = \dfrac\pi6[/tex]

Then

[tex]3 + \sqrt3 \, i = \boxed{2\sqrt 3 \left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)}[/tex]

The simplified expression of [tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex] is [tex]\frac{9}{x^9}[/tex]

The expression is given as:

[tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex]

Divide 162 and 2 by 2

[tex]\sqrt{\frac{81x^9}{x^{27}}}[/tex]

Take the square root of 81

[tex]9\sqrt{\frac{x^9}{x^{27}}}[/tex]

Apply the quotient rule of indices

[tex]9\sqrt{\frac{1}{x^{27-9}}}[/tex]

Evaluate the difference

[tex]9\sqrt{\frac{1}{x^{18}}}[/tex]

Take the square root of x^18

[tex]\frac{9}{x^9}[/tex]

Hence, the simplified expression of [tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex] is [tex]\frac{9}{x^9}[/tex]

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Answer:

37,000

Step-by-step explanation:

10,867 rounds to 11,000 and 26,186 to 26,000. 11,000 + 26,000 = 37,000

The number of purple marbles in the bag are; 201 purple marbles

We are told that Two-fifths of the marbles are green, and the rest are purple.

A) The image attached shows the bar model where the shaded parts denote the purple marble while the unshaded parts denote the green marbles.

B) We are told that there are 134 green marbles.

If the total number of marbles are x. Then;

(2/5)x = 134

x = 134 * 5/2

x = 335 marbles

Thus;

Purple Marbles = (3/5) * 335 = 201 purple marbles

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d=r•t ,  formula show a joint variation ,  Option C is the answer.

The variation when a variable is dependent upon two or more variables and varies directly as either of them are taken constant is called Joint Variation.

According to the question , which among the options shows a Joint Variation.

Option 1  d = 50 t

It shows direct variation , as increase in t will directly increase d 50 times * the increase

Option 2 d = 16t²

It also shows direct square variation .

Option 3 d=r•t

In this variation d is dependent on two variables and so it is a joint variation.

Therefore Option C is the answer.

The complete question is ?

Which distance formula or formulas show a joint variation? d=50t, d=16t^2, d=r•t

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The expanded form of the expression; (-a)^3 is; (-a)(-a)(-a).

It follows from the task content that the expanded form of the expression given is to be written.

On this note, the expression (-a)³ can simply be rewritten in it's expanded form as; (-a)(-a)(-a).

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The inverse of the function are respectively; f⁻¹(3) = 2 and f⁻¹(8) = 8.5

The formula to find the equation of this function using two coordinates is;

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)

Using the first 2 coordinates, we have;

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

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

3y - 3 = 2x + 2

3y = 2x + 5

y = ¹/₃(2x + 5)

Thus, the inverse is;

f⁻¹(x) = (3x - 5)/2

Thus;

f⁻¹(3) = (3*3 - 5)/2

f⁻¹(3) = 2

Similarly;

f⁻¹(x) = (3x - 5)/2

Thus;

f⁻¹(8) = (3*8 - 5)/2

f⁻¹(8) = 8.5

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Answer:

[tex]\huge\boxed{\sf 5.6 \ miles}[/tex]

Step-by-step explanation:

Given that,

Rachel runs 7 miles in 80 minutes.

80 minutes = 7 miles

Using unitary method

Divide 80 to both sides

1 minute = 7/80 miles

1 minute = 0.0875 miles

Multiply 64 to both sides

64 minutes = 0.0875 × 64 miles

64 minutes = 5.6 miles

So, Rachel will run 5.6 miles in 64 minutes.

[tex]\rule[225]{225}{2}[/tex]

Using translation concepts, the graph of [tex]y = 2 - \sqrt{x}[/tex] is described as follows:

On a coordinate plane, a curved line approaches the grid line at (3, 0.3), and ends at (0, 2).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Function [tex]y = 2 - \sqrt{x}[/tex], in blue in the graph, is the function [tex]y = \sqrt{x}[/tex], in red, reflected over the x-axis and shifted 2 units, as shown in the graph.

Hence the correct statement is:

On a coordinate plane, a curved line approaches the grid line at (3, 0.3), and ends at (0, 2).

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The amount Anneliese started with before her deductions is -$235.00.

Total amount spent = $58.00 + $35.00

= $93.00

Amount left in her account = $-142.00

Amount Anneliese started with = -$93.00 - $-142.00

= -$235.00

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Answer:

2MN=RA+TP

13×2=x+18

26=x+18

26-18=x

8=x

Given that In 3 years, Dianna will be 4 times as old as she was 33 years ago, her present age is 45.

Given that, in 3 years, Dianna will be 4 times as old as she was 33 years ago.

Let x represent the age of Dianna presently.

Dianna's age in 3 years time will be: x + 3

Dianna's age 33 years ago is: x - 33

Since in 3 years, she will be 4 times as old as she was 33 years ago.

x + 3 = 4( x - 33 )

We solve for x

x + 3 = 4x - 132

3 + 132 = 4x - x

135 = 3x

x = 135/3

x = 45

Given that In 3 years, Dianna will be 4 times as old as she was 33 years ago, her present age is 45.

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Both the function have same vertical stretch of 1.5 , Option B is the correct answer.

A function is a law that relates a dependent and an independent variable.

The functions given in the question is

f(x) = 3/2 |(x -7)| -2

g(x) = 1.5 ln(x-2)+7

For a function f(x)

f'(x) = a f(x) represents the stretching of a function if a> 1

here the value of a = 1.5 for both the functions , so they have same vertical stretch of 1.5 .

Therefore from the options given , Option B is the correct answer.

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Answer:

Step-by-step explanation:

2cm = 5m, so we know that the length is 5m

4cm = 2cm * 2, so the width is 5m * 2, which is 10m.

Now, we multiply them together.

5*10 = 50

The backyard area is 50 meters

Answer:

50m^2

Step-by-step explanation:

Answer:

25-13=12 kokichi has 12 left

Step-by-step explanation:

hope it helps sorry if I'm wrong

Answer:

Basic math 25 - 13 =   12

Step-by-step explanation:

The function shows a horizontal shift of the function to the right by 3 units

Transformation is a techniques used to change the position of an object on an xy-plane. Given the parent function f(x) = x

The translated function g(x) = x + 3 shows a horizontal shift of the function to the right by 3 units

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Answer:

2347 elevated in the cube

Step-by-step explanation:

nashe

The weight of the math and the history book are 72 and 96 ounces respectively.

A history book weights 24 oz more than a math book.

Therefore,

let

x = weight of math book

weight of history book = 24 + x

The math book is 75% the weight of the history book.

Therefore,

math book weight = 75 / 100 (24 + x)

x = 75 / 100 (24 + x)

x = 1800 + 75x / 100

100x =  1800 + 75x

100x - 75x =  1800

25x = 1800

x = 1800 / 25

x = 72

Therefore,

weight of math book = 72 ounces

weight of history book = 72 + 24 = 96 ounces.

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The original price of a laptop that is 65% of the sales price is R3 1076923.07692

The sale price of a laptop is R3 700,00,which is only 65% of the original price.

Therefore,

let

x = original price

Hence,

700, 000 = 65% of x

700,000 = 65 / 100 of x

cross multiply

70000000 = 65x

divide both sides by 65

x = 70000000 / 65

x = 1076923.07692

Therefore, the original price of the laptop is R3 1076923.07692

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

Answer: [tex]64\pi[/tex]

Step-by-step explanation:

Area of the outer circle: [tex](\pi)(10^{2})=100\pi[/tex]

Area of the inner circle: [tex](\pi)(6^{2})=36\pi[/tex]

Subtracting these areas, we get the area of the shaded region is [tex]\boxed{64\pi}[/tex]