I need assistance; on question #1

The given expression can be written in its simplest form by solving the exponents.

There are two types of exponent rules that will be applied to the expression. First, we will solve the negative exponent then we will multiply the exponents.

According to the negative exponent rule: x^-n=1/x^n.

Hence, applying the rule to the base term in the denominator, 1/y^⁻³/₄= y^³/₄

Therefore, x^¹/₄ / y^⁻³/₄= x^¹/₄ y^³/₄

According to the multiplication of exponent rule: (x^n)^m=x^nm

Hence, applying the rule to the expression,

(x^¹/₄ y^³/₄)^12=x^¹/₄*12 y^³/₄*12

Multiplying the powers and simplifying,

x^¹/₄*12 y^³/₄*12=x^3y^9

The simplest form of the expression (x^¹/₄/y^⁻³/₄)^12 is x^3y^9.

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The transformation of pentagon Q to pentagon Q' is a clockwise rotation of 180° about the origin.

A transformation is a general term for four specific ways to manipulate the shape or position of a point, a line, or a geometric figure.

We have,

Coordinates of a pentagon Q.

(2, 4), (3, 7), (7, 5), (5,4), and (4,2).

Coordinates of pentagon Q'.

(-2, -4), (-3, -7), (-7, -5), (-5,-4), and (-4,-2).

We see that the coordinates of each point of the pentagon Q have changed their position as negative coordinates in pentagon Q'

The coordinates of pentagon Q are in (x, y) which can be assumed to be in the first quadrant of the coordinate plane.

The coordinates of pentagon Q' are in (-x, -y) which is in the 3rd quadrant.

From the first quadrant to 3rd quadrant there is a rotation of 180°.

Thus the transformation of pentagon Q to pentagon Q' is a clockwise rotation of 180° about the origin.

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Answer:

Step-by-step explanation:

no because perenthesis

Answer:

No it is not equivalent because the parenthesis

Step-by-step explanation: When it comes to parenthesis you have to do the problem in them, so you would do 33x33 rather than the whole problem at once. no idea if that makes sense bff it sounded right in my head

20 people likes movies, such that  12 of these also like music, then the probability is just the quotient between:

Q = 12/20 = 0.6

The probability that a person likes music given that he/she lies movies is 0.6 or 60%

Notice that there are 5 + 7 common elements between movies and music, and a total of 20 people likes movies, such that 5 + 7 = 12 of these also like music, then the probability is just the quotient between the numbers of total people that likes movies which we know is 20, and the people that likes movies and also music.

So the quotient between 12 and 20, that will gave us the probability we want to find.

The probability that a person likes music given that he/she lies movies is 0.6 or 60%

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[tex]25^{2x+1}=144[/tex] => x = 0.272, by properties of logarithm.

Given: [tex]25^{2x+1}=144[/tex]

Taking logarithm on both sides:

log ([tex]25^{2x+1}[/tex]) = log (144)

=> (2x + 1) log (25) = log (144) (As [tex]log_b(a)^m = m (log_b(a))[/tex])

=> 2x + 1 = [tex]\frac{log144}{log25}[/tex]

=> 2x + 1 = [tex]\frac{2.158}{1.397}[/tex]

=> 2x + 1 = 1.544

=> 2x = 0.544

=> x = 0.272

Hence, [tex]25^{2x+1}=144[/tex] => x = 0.272, by properties of logarithm.

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Answer:

Rate of change in y is -6

-3-6 = -9

-9-6=-15

-15-6=-21

Rate of change in x is 1

1+1=2

2+1= 3

3+1 = 4

4-1=5

........And so on

The linear function f(x) with a slope of -8 and that f(1) = 2 is f(x) = 10 -8x

From the question, we are find a linear function with slope of -8 and that f(1) = 2

If f(1) = 2, then the line passes through the point (1, 2)

Using the point-slope form of the equation of a straight line

y - y₁ = m(x - x₁)

Where m is the slope

Then,

y - 2 = -8(x - 1)

Simplify

y - 2 = -8x + 8

y = -8x + 8 + 2

y = -8x + 10

∴ f(x) = -8x + 10

f(x) = 10 - 8x

Hence, the linear function is f(x) = 10 -8x

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Answer:

The transformation from the parent function is a translation of 3 units left, a vertical stretch of scale factor 2, and a reflection in the x-axis.

Step-by-step explanation:

Given function:

[tex]\text{g}(x) = -2|x+3|[/tex]

Parent function:

[tex]\text{f}(x) = |x|[/tex]

A parent function is the simplest form of a family of functions.

The graph of g(x) is related to the graph of f(x) by a series of transformations.  To determine the series of transformations, work out the steps of how to go from f(x) to g(x).

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]

[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]

[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]

[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]

[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]

Step 1

Translation left by 3 units:

[tex]\implies f(x+3) =|x+3|[/tex]

Step 2

Stretch in the direction of the y-axis (vertically) with scale factor 2:

[tex]\implies 2f(x+3) =2|x+3|[/tex]

Step 3

Reflection in the x-axis:

[tex]\implies -2f(x+3) =-2|x+3|[/tex]

Conclusion

The transformation from the parent function is a translation of 3 units left, a vertical stretch of scale factor 2, and a reflection in the x-axis.

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When -46 decreased by the difference between -23 and -61, the number becomes -18.

Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign that is used to represent subtraction is -.

According to mathematical rules, when two negative signs are multiplied by each other, the number becomes positive.

The difference between -23 and -61: -61 - (-23)

-61 + 23 = -38

-46 - (-38)

-46 + 28 = -18

Here is the complete question:

-46 decreased by the difference between -23 and -61. What is the value of the number?

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Answer: f(-2) = - 4

Step-by-step explanation:

Answer: f(x) and g(x) both represent y of the equations

Step-by-step explanation: f(x) and  g(x) both represent the y of the equation for example f(x)=mx+b or g(x)+mx+b both would be to find y of that specific equation and that would also make them inverses because you could use the table to label the inverses on a graph.

The dimensions of the drawing of the rectangular plot using the scale of 1in.:5yd is; 24 inches by 10.6 inches

We are told that the dimensions of the rectangular plot of land is 120yd x 53yd.

Now, you want to draw this rectangular plot on a scale of 1 inch : 5 yards. This means that 1 inch will represent 5 yards.

Thus, for the side of 120 yards, using the scale gives us;

1/5 * 120 = 24 inches

For the side of 53 yards, using the scale gives us;

1/5 * 53 = 10.6 inches

Thus, the dimensions of the drawing of the rectangular plot using the scale of 1in.:5yd is; 24 inches by 10.6 inches

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The fourth point of the parallelogram is (10, -3).

What is Parallelogram?

A Parallelogram is a quadrilateral with opposite sides parallel.

Given that;

Three points of a parallelogram are (4,3), (-4,3) and (2,-3).

Now, Take Two points at one diagonal of parallelogram are (4, 3) and

(2, -3).

Let fourth point of a parallelogram is (x, y).

Take (-4,3) and (x, y) on the another diagonal of a parallelogram.

Since, Midpoint of both diagonal is same.

Hence, Midpoint of (4, 3) and (2, -3) is calculated as;

(4+2/2, 3+(-3)/2) = (6/2, 0/2) = (3, 0)

So, Midpoint of (4, 3) and (2, -3) = (3, 0)

And, Midpoint of (-4,3) and (x, y)  = (-4+x/2, 3+y/2)

Since,  Midpoint of both diagonal is same.

Hence, (-4+x/2, 3+y/2) = (3, 0)

Equating coordinates we get;

⇒-4+x/2 = 3

⇒ -4 + x = 6

⇒ x = 6 + 4

⇒ x = 10

And, 3+y/2 = 0

    ⇒3 + y = 0

    ⇒y = -3

So, The fourth point of the parallelogram is (10, -3).

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The required value of x using the properties of exponents and logarithm is 6.362.

What are the various properties of the logarithm?

Out of several properties of logarithms, some of the main properties are given below:

Product Rule

log (ab) = log a + log b

Change of base

log ₇ x = log x / log 7

Power Rule

log a² = 2 log a

Quotient Rule

log (a / b) = log a - log b

Solving the given equation for x

We are given a logarithmic expression: log (1 + 3x) = 3

On applying exponent both sides, we get,

e^[log (1 + 3x)] = e^3

Using the properties of exponents and logarithm, we get,

1 + 3x = 20.0855

3x = 19.0855

x = 6.362

Hence, the required value of x can be 6.362.

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the logarithm function ( log ₂ 4 ) is not a common logarithm function as it does not have a base 10.

In mathematics, the common logarithm is the logarithm with base 10.

It is also known as the decadic logarithm and as the decimal logarithm function.

Here, we have the logarithm function as:

( log ₂ 4 )

Now, we can see that:

It has a base of 2.

So, it will not be a common logarithm function as having base 10 is an important characteristic of a common logarithm function.

Therefore, we get that, the logarithm function ( log ₂ 4 ) is not a common logarithm function as it does not have a base 10.

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Answer:

C and B

Step-by-step explanation:

Evaluate g(5) then substitute the value obtained into f(x)

g(5) = [tex]\sqrt{5-1}[/tex] = [tex]\sqrt{4}[/tex] = 2 , then

f(2) = 3(2) + 1 = 6 + 1 = 7

-----------------------------------------------------------------------------

f(x) = [tex]\frac{x^2+3}{(x-4)(x+8)}[/tex]

the denominator of f(x) cannot be zero as this would make f(x) undefined.

equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.

(x - 4)(x + 8) = 0

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 8 = 0 ⇒ x = - 8

the vertical asymptotes are x = 4 and x = - 8

The simplest form of the following are -

a) 4/7 / (1 3/4) = 16/49

b) 5 3/5 / (2 2/3) = 21/10

The word simplify means to make something easier to do or understand. So, reducing or simplifying fractions means we make the fraction as simple as possible. We do this by dividing the numerator and the denominator by the largest number that can divide into both numbers exactly.

We have been given that

a) 4/7 / (1 3/4)

Rewrite as -

= (4/7) / (1× 3/4)

= (4/7) / (7/4)

= (4/7) × (4/7)

= 16/49

b) 5 3/5 / (2 2/3)

Rewrite as -

= (5× 3/5) / (2× 2/3)

= (5× 3/5) / (8/3)

= (28/5) / (8/3)

= (28/5) × (3/8)

= 7/5 × 3/2

= 21/10

= 2.1

Thus , the following are in order of simplicity:

a) 4/7 / (1 3/4) = 16/49

b) 5 3/5 / (2 2/3) = 21/10

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Answer:

Step-by-step explanation:

Devon will be able to cover 71.25 ft² of flower bed.

The number of bags of soil Devon has = [tex]4\frac{3}{4}[/tex]

Converting mixed fraction to fraction

Number of bags of soil = (4×4+3)/4

Performing multiplication and addition in numerator to find the number of bags of soil with Devon

Number of bags of soil = 19/4

Now, it is stated that area covered by 1 bag = 15 ft²

So, 19/4 bags will cover area = 15×(19/4)

Performing multiplication and division to find the area covered by the bags of soil

Area covered by bags of soil Devon has = 71.25 ft²

Hence, the area covered by bags of soil Devon has is 71.25 ft²

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The complete question is -

Devon has 4 3/4 bags of soil to put in his flower bed. Each bag will cover 15 ft2. How many square feet will he be able to cover?

We know that the measures of dispersion tend to see how numbers are scattered around the mean. In this case, we are asked to find three of the measures of dispersion which are; range, variance and standard deviation.

We first have to arrange the data in the proper order as follows;

20.1, 21.7, 23.2, 24.0, 30.9, 33.5, 58.4, 60.0, 74.8, 110.8

It is now easier for us to find the range of the data set as the difference between the largest and the smallest value; 110.8 – 20.1 = 90.7

The mean of the dataset is = 20.1 +  21.7+  23.2 + 24.0 + 30.9 + 33.5 + 58.4 + 60.0 + 74.8 + 110.8/10

= 45.74

Now;

Variance = (20.1 - 45.74)^2 + (21.7 - 45.74)^2 + (23.2 - 45.74)^2 + (24.0 - 45.74)^2 + (30.9 - 45.74)^2 + (33.5 - 45.74)^2 + (58.4 - 45.74)^2 + (60.0 - 45.74)^2 + (74.8 - 45.74)^2 + (110.8 - 45.74)^2/10

= 657.4 + 577.9 + 508.1 + 472.6 + 220.2 +149.8 + 160.3 + 203.3 + 844.5 + 4233/10

= 802.71

Standard deviation = √variance = √802.71

= 8.96

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The domain of the relation: {0, 1, 2, 3, and 4}

The range of the relation: {0, -1, -4, -9, -16}

The graph for the relation is in the attachment.

A domain of a relation can be defined as the set of x-values or inputs of a relation.

The set of all output or y-values that correspond to the x-values in a set of ordered pairs.

Given the relation, {(0, 0), (1, -1),(2, -4), (3,-9), (4, -16)}

The domain of the relation is: {0, 1, 2, 3, and 4} (these are all the input of the relation)

The range of the relation is: {0, -1, -4, -9, -16} (these are all the output of the relation)

The graph for the relation is in the attachment.

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Answer: Emily's in total journey is 15.045 kilometers.

Step-by-step explanation:

Given data,

Emily traveled a certain distance on a horse = 10.98 kilometers

Emily traveled a certain distance on a bike = 4.06 kilometers

The overall distance traveled by Emily on her horse and bike needs to be determined.

For "Total Distance" , we will use addition operation:

So, Total distance covered by Emily's journey is given by equal to

Emily traveled a certain distance on a horse + Emily traveled a certain distance on a bike

Let us assume,

Total distance covered by Emily's journey is represented by 'x'

Then we can write,

                          x = 10.981 kilometers + 4.064 kilometers

                          x = 15.045 kilometers

Therefore, Emily's in total journey is 15.045 kilometers.

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The percent error is 56. 9%

Percent error is defined as the difference between the estimated value and the actual value in comparison to the actual value.

The formula for percent error is expressed as;

Percent error = [tex]\frac{|VA - VE|}{VE}[/tex] × 100/1

Where;

Substitute the values

Percent error = | 612 - 390| / 390 × 100/ 1

Percent error = 222/ 390 × 100/ 1

Percent error = 0. 56 × 100

Percent error = 56. 9%

Thus, the percent error is 56. 9%

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The truth value of the conditional statement is false

The conditional statement is given as

“If a number is greater than -500, then the number is greater than 500.”

The above conditional statement is false

This is so because

Not all numbers greater than -500 are greater than 500

Take for instance 499 is greater than -500, but less than 500

Hence, the truth value of the conditional statement is false

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Answer:

y20=225x or y225+x20 ir can be

Answer:

the answer is 1

Step-by-step explanation:

trust mehhhh

The solution to the equation √x+4=√3 x is x = 2(1 + √3) or x = 2(1 - √3).

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] is called a quadratic equation.

The formula for the roots of the quadratic equation is found by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

It is given that:

The equation is:

√x + 4 = √3 x

√x = √3 x - 4

Squaring both sides:

x = (√3 x - 4)²

x = 3x² - 8√3 x + 16

2x² - 8√3 x + 16 = 0

x² - 4√3 x + 8 = 0

After solving with the quadratic formula:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\rm x = \dfrac{-(-4\sqrt3) \pm\sqrt{(-4\sqrt3)^2-4(1)(8)}}{2(1)}[/tex]

x = 2(1 + √3) or x = 2(1 - √3)

Thus, the solution to the equation √x+4=√3 x is x = 2(1 + √3) or x = 2(1 - √3).

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7/4 miles distance  does that person walk.

What is distance?

We can use a ratio to solve

1 mile           x miles

----------------= ---------------

1 hour           1 3/4 hours

Changing to improper fractions

1 mile           x miles

----------------= ---------------

1 hour         7/4 hours

Using cross products

1 * 7/4 = 1 * x

7/4 = x

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No extraneous solution to the equation.

The equation is

[tex](x + 5)^{1/2}[/tex] - [tex](5 - 2x)^{1/4}[/tex] = 0

To know whether the equation is an extraneous solution we first need to find the value of x.

So we have,

[tex](x + 5)^{1/2} = (5 - 2x)^{1/4}[/tex]

Multiply both sides with the power of 4, then we have

[tex]((x+ 5)^{1/2})^{4}[/tex] = [tex]((5 - 2x)^{1/4} )^{4}[/tex]

[tex](x+ 5)^{2}[/tex] = 5 - 2x

[tex]x^{2}[/tex] + 10x + 25 = 5-2x

[tex]x^{2}[/tex] + 12x + 20= 0

[tex]x^{2}[/tex] + 10x + 2x + 20 = 0

x(x + 10 ) + 2(x + 10) = 0

(x + 10)(x+2) = 0

x = -10, -2

Now we have to put the value of x in the equation

x = -10

[tex](-10 + 5 )^{1/2}[/tex]-[tex](5 - 2 * -10)^{1/4}[/tex] = 0

[tex](-5)^{1/2}[/tex] - [tex]25^{1/4}[/tex]= 0

[tex](-5)^{1/2}[/tex] - [tex]5^{1/2}[/tex] = 0

Which has not possible as we don't have negative number in the square root.

x = -2

[tex](-2 + 5)^{1/2}[/tex] -[tex](5-2*-2)^{1/4}[/tex]=0

[tex]3^{1/2}[/tex]- [tex]9^{1/4}[/tex]=0

[tex]3^{1/2}[/tex]- [tex]3^{1/2}[/tex]=0

0 = 0

Therefore there is no extraneous solution to the equation

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