The equation 9x = 27 has an answer of x = 3.
Write down Pive different equations with an answer of x = 3.

The rationalization the denominator of the given expression is [tex]\frac{5\sqrt{6}x^3 }{2\sqrt{y} }[/tex] .

We have given an expression [tex]\frac{5\sqrt{3}x^3 }{\sqrt{2y} }[/tex] .

The denominator of the expression is [tex]\sqrt{2y}[/tex] .

Multiply the fraction in the numerator and denominator by [tex]\sqrt{2y}[/tex] , we get

         [tex]\frac{5\sqrt{3}x^3\times\sqrt{2y} }{\sqrt{2y} \times\sqrt{2y} }=\frac{5\sqrt{6}x^3\sqrt{y} }{2y}[/tex]

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The radical expression 3√0.008 y^3 x^6 can be simplified into 0.2 y x^2.

Radical expression is an expression containing a √ symbol. It shows the nth root of a number or variable. This number or variable inside a radical expression is the nth power of another number. Radical expression can also be expressed in exponent notation such that the nth root of x is equal to x raised to 1 over n.

n √x = x^1/n

Expressing 3√0.008 y^3 x^6 into exponent notation:

3√0.008 y^3 x^6 = (0.008 y^3 x^6)^1/3

Applying the distributive property of exponents,

(0.008 y^3 x^6)^1/3 = 0.008^1/3 (y^3)^1/3 (x^6)^1/3

Using the Power Rule for Exponents which states that to raise a number with an exponent to a power, multiply the exponent times the power:

(a^m)^n = a^(m*n).

0.008^1/3 (y^3)^1/3 (x^6)^1/3 = 0.008^1/3 y x^2

Simplifying the constant,

0.008^1/3 y x^2 = 0.2 y x^2

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Answer:

b = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]\frac{3}{8}[/tex] = [tex]\frac{b}{2}[/tex] ( cross- multiply )

8b = 6 ( divide both sides by 8 )

b = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]

Answer:

b=3/4

Step-by-step explanation:

3/8=b/2

First you will need to cross multiply because apparently that's how we do things. To cross multiply, you would just have to take the bottom of the fraction from the LHS (left hand side) and times it with the top part of the fraction in RHS (right hand side). You do the same thing to the other side (take the top part of LHS and multiply it with the bottom of RHS). Make sure to keep the = sign in the middle.

8 x b = 3 x 2 (8 x b= 8b)

8b=6

Then, you would have to make the b on the LHS alone so you would have to divide the RHS by 8. (To move from one side to another, you would have to change it to the opposite of the sign like if it's -9, then to the other side it would be +9 and if it's x8 then the other side would be /8 and vice versa).

b=6/8

You will have to simplify unless the question asks you not to but I'll do it anyways. 2 goes into 6 and 8 as a common factor and so the answer should look like this:

b=3/4

If you have any further questions please ask me!

Answer:

QR = 3

Step-by-step explanation:

given Q is the midpoint of PR , then

PQ = QR , that is

3x = x + 2 ( subtract x from both sides )

2x = 2 ( divide both sides by 2 )

x = 1

Then

QR = x + 2 = 1 + 2 = 3

Answer:

QR = 3

Step-by-step explanation:

since Q is the midpoint, then PQ is the same as QR. so we equate the two as follows:

3x = x+2

then find x as shown below.

3x-x = 2 ( I grouped the like terms)

2x = 2. now divide by 2 to find x

x= 1,

since QR is x+2, now substitute x for 1

1+2 =QR

3 is the answer.

.thanks

The constant of variation is 1/4 .

The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity. That means if one value increases than another one will automatically decrease and vice versa.

Let say if x and y are two values and k is a constant value, then

According to inverse variation,

k = xy or y = k/x

In the given question,

Take the order pair  [tex](\frac{3}{8} ,\frac{2}{3} )[/tex]

As it is an inverse variation, we can substitute it

y=k/x  or k = xy

put the values from order pair

k = [tex]\frac{3}{8}[/tex] × [tex]\frac{2}{3}[/tex]

k = [tex]\frac{1}{4}[/tex]

Therefore, the constant of variation for order pair  [tex](\frac{3}{8} ,\frac{2}{3} )[/tex] is 1/4 .

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{-7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-7 - (-2)~~)^2 + (~~-7 - 3~~)^2} \implies d=\sqrt{(-7 +2)^2 + (-7 -3)^2} \\\\\\ d=\sqrt{( -5 )^2 + ( -10 )^2} \implies d=\sqrt{ 25 + 100 } \implies d=\sqrt{ 125 }\implies d\approx 11.18[/tex]

Exact Distance = [tex]\boldsymbol{5\sqrt{5}}[/tex] units

Approximate Distance = 11.1803 units

===================================================

Work Shown:

[tex](x_1,y_1) = (-2,3) \text{ and } (x_2, y_2) = (-7,-7)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-(-7))^2 + (3-(-7))^2}\\\\d = \sqrt{(-2+7)^2 + (3+7)^2}\\\\d = \sqrt{(5)^2 + (10)^2}\\\\d = \sqrt{25 + 100}\\\\d = \sqrt{125}\\\\d = \sqrt{25*5}\\\\d = \sqrt{25}*\sqrt{5}\\\\d = 5\sqrt{5}\\\\d \approx 11.1803\\\\[/tex]

The exact distance is [tex]5\sqrt{5}[/tex] units, which approximates to about 11.1803 units

I used the distance formula. Round the approximate value however your teacher instructs.

A slight alternative is to plot the two points to form a right triangle. The hypotenuse goes from (-2,3) to (-7,-7). Then use the pythagorean theorem.

You can use tools like WolframAlpha or GeoGebra to confirm the answer.

Answer:

74

Step-by-step explanation:

[tex]5(2(10)-5)-1 \\ \\ =5(20-5)-1 \\ \\ =5(15)-1 \\ \\ =75-1 \\ \\ =74[/tex]

A quadrilateral has four sides that are each an even number of meters long (in meters).Considering a 46 meter of perimeter, the value of the longest side length out of the four sides is 12.

Given that,

A quadrilateral has four sides that are each an even number of meters long (in meters).

Considering a 46 meter of perimeter.

We know that even numbers differ by 2 and are multiples of 2.

Thus, due to the four sides of quadrilaterals.

let those sides' lengths be

2x,2x+2,2x+4 and 2x+6

The perimeter of a quadrilateral's boundary as a whole is its perimeter. An irregular or regular four-sided polygon is referred to as a quadrilateral. A regular quadrilateral has sides that are all the same length and angles that are all the same measure; an irregular quadrilateral does not have equal sides and angles.

Perimeter of a quadrilaterals is

perimeter=sum of the 4 sides.

36=sum of the 4 sides.

Which we have taken 2x,2x+2,2x+4 and 2x+6.

2x+2x+2+2x+4+2x+6=36

8x+12=36

8x=36-12

8x=24

x=[tex]\frac{24}{8}[/tex]

x=3.

Now, we can find the sides by the x value which is 3.

1st side=2x=2[tex]\times[/tex]3=6

2st side=2x+2=2[tex]\times[/tex]3+2=8

3st side=2x+4=2[tex]\times[/tex]3+4=10

4st side=2x+6=2[tex]\times[/tex]3+6=12

Therefore, the value of the longest side length out of the four sides is 12.

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Answer:13

Step-by-step explanation:

x+x+1+x+2+x+3=46

4x+6=46

-6 -6

4x=40

4x/4=40/4

x=10

Longest side: x+3

=10+3

=13

Inverse of the give function F(x) = ( x + 4 )³ - 1 is F⁻¹(x) = [√( x + 1 ) ] - 4.

Given is a function of x, F(x) = ( x + 4 )³ - 1

These question can be solved by following 4 easy steps

Step 1 : Switch the F(x) with the variable y

This implies, F(x) = ( x + 4 )³ - 1 becomes y = ( x + 4 )³ - 1

Step 2 : Interchange the variable x and y in the above obtained equation

This implies, from the equation y = ( x + 4 )³ - 1, we get

x = ( y + 4 )³ - 1

Step 3 : Solve the new obtained equation for y

This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.

x = ( y + 4 )³ - 1

=> x + 1 = ( y + 4 )³

=>  (y + 4 )³ = x + 1

=> y + 4 = √( x + 1 )

=> y = √( x + 1 ) - 4

Hence we obtain the required equation.

Step 4 : Switch the variable y with F⁻¹(x)

This implies, y = √( x + 1 ) - 4 becomes F⁻¹(x) = √( x + 1 ) - 4

Therefore, we get the inverse of the give function F(x) = ( x + 4 )³ - 1 as F⁻¹(x) = [√( x + 1 ) ] - 4.

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Answer:

4 is 4 2/3

Step-by-step explanation:

3 can only go in 14 4 times with 2 leftover

The number of pairs of parallel sides the rotated figure have is 2

Parallel sides or lengths are line segments or lines in the same plane that extend on both sides without intersecting

The shape is given as:

Shape = Rhombus

Rotation= 90 degrees counterclockwise rotation about the vertex G

The rotation transformation is a rigid transformation

This means that when a shape is rotated by 90 degrees counterclockwise about a vertex (in this case, the vertex G), the image of the rotation would have the same properties as the preimage

A rhombus has 2 pairs of parallel sides

This means that the number of pairs of parallel sides the rotated figure have will also be 2 (same as the original shape)

Hence, the number of pairs of parallel sides the rotated figure have is 2

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The result of simplifying the number 4¹/₂ . 4¹/₂  using the properties of exponents is 4

To solve this exercise we have to resolve algebraic operations following the exponent properties.

4¹/₂ . 4¹/₂

Base= 4

Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:

(4) ⁽¹/₂ ⁺ ¹/₂⁾

(4) ⁽¹⁺¹⁾/₂

(4) ⁽²/₂⁾

(4)⁽¹⁾

4

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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The logarithm statement log_b x / log_b y = log_b x/y is a false statement as log_b x / log_b y = log_b x - log_b y.

We are given the logarithm as:

log_b x / log_b y = log_b x/y

We need to tell if it is true of not.

We get that, it is false statement.

We know that log a / log b = log a - log b

So, log_b x / log_b y = log_b x - log_b y

So, it is not equal to log_b x / y

Therefore, we get that, the logarithm statement log_b x / log_b y = log_b x/y is a false statement as log_b x / log_b y = log_b x - log_b y.

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The value of x when r(x) = -4 is 20/3.

Given, the function is r(x) = ₋2/3x ₊ 4

substitute r(x) = ₋4 in the value of r(x)

r(₋4) = ₋2/3(₋4) ₊ 4

r(₋4) = 8/3 ₊ 4

r(₋4) = 8 ₊ 12/3

r(₋4) = 20/3

hence we get the value as 20/3

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Answer:

7, 5

Step-by-step explanation:

Change the denominator to make the end result 0. Anything with a 0 denominator results in it being undefined.

The expression (10-t)/(t-7) is undefined when t=7.

The expression 10/(3t-15) is undefined when t=5.

To find the values of t for which the expressions are undefined, we need to look for any values of t that make the denominators equal to zero.

we know that dividing by zero is undefined.

For the expression (10-t)/(t-7),  the denominator is t-7.

So, this expression is undefined when t-7=0

To find the value of t that makes t−7=0, solve the equation:

t-7=0

t=7

So, the expression (10-t)/(t-7) is undefined when t=7.

For the expression 10/(3t-15), the denominator is t-7.

So, this expression is undefined when 3t-15=0

To find the value of t that makes 3t-15=0, solve the equation:

3t-15=0

Add 15 on both sides:

3t=15

Divide both sides by 3:

t=5

So, the expression 10/(3t-15) is undefined when t=5.

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Answer:

36 × 12 = 432

hopefully this helps :)

We will get [tex]\left\{\begin{array}{l}\log \cdot 33 \\-\log \cdot 99+\log \cdot 30\end{array}\right.[/tex] after simplifying the given expression

log 33,000- log 99+ log 30.

So,

Then,

[tex]\left\{\begin{array}{l}\log \cdot 33 \\000-\log \cdot 99+\log \cdot 30\end{array}\right.\\\left\{\begin{array}{l}\log \cdot 33 \\-\log \cdot 99+\log \cdot 30\end{array}\right.[/tex]

Therefore, we will get [tex]\left\{\begin{array}{l}\log \cdot 33 \\-\log \cdot 99+\log \cdot 30\end{array}\right.[/tex] after simplifying the given expression log 33,000- log 99+ log 30.

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Answer:

[tex]y=\frac{ac}{a-b-c}[/tex]

Step-by-step explanation:

[tex]y(a-b)=c(y+a) \\ \\ y(a-b)=cy+ac \\ \\ y(a-b)-cy=ac \\ \\ y(a-b-c)=ac \\ \\ y=\frac{ac}{a-b-c}[/tex]

Only the third statement (c)"To square a number multiply the number by itself" is true.

The square of any number is defined as the product of the number and itself .

Let us consider a number a , then the square of a is denoted by a² and  a² = a × a .

Let us take each statement and verify if they are true or false.

a)"To square a number, multiply the number by 2"

this is false as to square we have to multiply the number with itself.

example: 3²=9 but 3 × 2 = 6

b)The second statement is also false because square-root of a number is different than dividing a number by 2.

Example: √16=4 but 16÷2=8

c) "To square a number, multiply the number by itself."

This statement is true .

d) a perfect square is defined as a number whose square-root is an integer (both odd and even)

9 is a perfect square and √9=3 which is odd

Therefore the fourth statement is also false.

Hence only statement (c) is correct .

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The recursive equation here is; a_n = 3n - 1

Formula for the nth term of an arithmetic sequence is;

an = a + (n - 1)d

where;

a is first term

n is position of term

d is common difference

We are given that;

First term; a = 2

Second term; a2 = 5

Common difference; d = 3

Thus, recursive equation here is;

a_n = 2 + 3(n - 1)

a_n = 2 + 3n - 3

a_n = 3n - 1

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Answer in decimal form = -26.25

Answer as an improper fraction = -105/4

========================================================

Work Shown:

1/2 = 0.5

Replace every copy of x with 0.5 in the f(x) function.

f(x) = x-8

f(0.5) = 0.5-8

f(0.5) = -7.5

Repeat the same idea for the g(x) function

g(x) = x+3

g(0.5) = 0.5+3

g(0.5) = 3.5

Then multiply the results

f(0.5)*g(0.5) = (-7.5)*(3.5) = -26.25

Then optionally convert to an improper fraction following the steps shown below.

-26.25 = -(26.25)

-26.25 = -(26+0.25)

-26.25 = -(26+1/4)

-26.25 = -(26*(4/4)+1/4)

-26.25 = -(104/4+1/4)

-26.25 = -105/4

Answer:

x = 4

Step-by-step explanation:

[tex]\frac{x}{7}[/tex] = [tex]\frac{28}{49}[/tex] ( cross- multiply )

49x = 7 × 28 = 196 ( divide both sides by 49 )

x = 4

Answer: 0.004 = 4.0 x [tex]10^{-3}[/tex]

Step-by-step explanation:

Rules guiding exponential notation :

Writing numbers in exponential notations have some guiding rules. These include:

The base is always 10

The exponent cannot be zero and must be an integer. It can be positive or negative.

The coefficient can take any form - negative or positive, integer or decimal. All significant digits must be included after the decimal.

Following these rules :

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Answer:

[tex]48\sqrt 6[/tex]

Step-by-step explanation:

[tex]2\sqrt{8}=2(2\sqrt{2})=4\sqrt{2} \\ \\ 6\sqrt{12}=6(2\sqrt{3})=12\sqrt{3} \\ \\ (4\sqrt 2)(12\sqrt 3)=48\sqrt 6[/tex]

A parabola's maximum value is the y-coordinate of its vertex when it opens downward.

Therefore, a parabola's maximum value is the y-coordinate of its vertex when it opens downward.

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Answer:

1225

Step-by-step explanation: i did the tesr b

Answer:

D

Step-by-step explanation:

hope this works for you :)