Simplify each expression. (8x⁹y³ / 27x² y¹²)²/₃

If x=4, then substitute x for 4, multiply by 3 since 3 was being multiplied by x, then subtract 2, which gets you 10

Answer:

B. f - g = 17

The domain and range will be a set of all real numbers for all the odd positive integers.

We can write given equation as y² =n²x

if we Put even value of n then we get function similar to y²=x which does not match with the given question

If we put the odd value of n then we get function similar to y³ = x which match with the given question.

Hence the domain and range will be a set of all real numbers for all the odd positive integers.

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The estimate of the quotient 1624 divided by 23 using compatible numbers is 81

The quotient of numbers is the result of dividing the numbers

The statement is given as

1624 divided by 23 using compatible numbers

The expression can be represented as:

1624 ÷ 23

Using compatible numbers, 1624 can be estimated as 1620, while 23 can be estimated as 200:

So, the expression becomes

1624 ÷ 23 = 1620 ÷ 20

Next, we divide the estimated numbers

So, we have

1624 ÷ 23 = 81

Hence, the estimate of the quotient 1624 divided by 23 using compatible numbers is 81

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

Explanation:

The general quadratic ax^2+bx+c = 0 has these properties

For more information, check out Vieta's formulas.

If we flip the bx term to -bx, thereby getting ax^2-bx+c = 0, then we have these properties

We're told the sum and product of the roots are the same

b/a = c/a

b = c

Example:

The equation x^2-10x+10=0 has the sum of the roots equal to 10, and the product of the roots is also 10. You can use the quadratic formula to confirm this.

Answer:

12

Step-by-step explanation:

good right? if not then your question was wrong

Answer:

Step-by-step explanation:

The slope is defined as the ratio of the “rise” divided by the “run” between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line.

The inclination of a straight line is the angle that the line makes with the positive direction of the x-axis. The tangent of the angle that a line makes with the positive direction of the x-axis is called the slope or gradient of the line. The slope of a line is generally denoted by m.

Given two points (x1, y1) and (x2, y2) on a line, the slope m of the line is y = (y2 – y1)/(x2 – x1)

The slope-intercept form of a line is given by y = mx + b gives the slope of line m and the y-intercept of line b. The inclination of the line with the horizontal axis is called the slope of the line. The point at which the curve cuts or crosses the y – axis is called the y-intercept.

The solved logarithmic functions are log y = log 2 + 4 log x and log y = 2 log 2 - log x for y = 2x⁺⁴ and y - 4x⁻¹ = 0 respectively.

What is a logarithmic and exponential function?

Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet,  e. For example log 10 = 1 and e^2.

Solving the given expressions: y = 2x⁺⁴, y - 4x⁻¹ = 0

Applying given properties of logarithmic and exponential function;

log a + log b = log (ab)

4 log x = log x⁴

e^(log x) = 1

e^(x + y) = (e^x) × (e^y)

Take expression y = 2x⁺⁴

Applying log on both sides, we get,

log y = log (2x⁺⁴)

log y = log 2 + log x⁺⁴

log y = log 2 + 4 log x

To Check Results,

Taking exponential,

y = e^[log 2 + 4 log x]

y = e^(log 2) × e^[4 log (x)]

y = 2 × e^(log x⁴)

y = 2x⁴

Thus, the answer is verified.

Take expression y - 4x⁻¹ = 0

Applying log on both sides, we get,

log y = log (4x⁻¹)

log y = log 4 + log x⁻¹

log y = 2 log 2 - log x

To Check Results,

Taking exponential,

y = e^[2 log 2 - log x]

y = e^(2 log 2) × e^[-log (x)]

y = e^(log 4) × e^(log x⁻¹)

y = 4x⁻¹

y - 4 x⁻¹ = 0

Thus, the answer is verified.

Hence, the solved expression is log y = log 2 + 4 log x and log y = 2 log 2 - log x for y = 2x⁺⁴ and y - 4x⁻¹ = 0 respectively.

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The 32 feet of the material for the perimeter of the garden is not enough as the perimeter of the garden is 34.64 feet.

We are given that:

Area of a square garden = 75 feet²

Let the side of the square garden be x

x² = 75

x = √ 75

x = 5 √3 feet

Perimeter of the square garden = 4 × x feet

Perimeter = 4 × 5 √ 3 feet

Perimeter = 20 √ 3 feet

P = 34.64 feet.

Now, Tristan only has 32 feet of material.

So, the material is not enough.

Therefore, we get that, the 32 feet of the material for the perimeter of the garden is not enough as the perimeter of the garden is 34.64 feet.

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For the given points, As the distance of AB and CD is same, So AB and CD are congruent.

If and only if their lengths are identical, any two line segments are congruent. The length of the line segment AB is identical to the length of the line segment CD in the aforementioned representations. Consequently, the two line segments AB and CD are similar.

length of AB = √(2+2)² + (1-1)²  =  2

length of CD = √(3-3)² + (2+2)² = 2

As the value of AB = CD So, we can say that AB and CD are congruent.

Graph is attached at the end.

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Step-by-step explanation:

Answer:

(3x + 2y) (2x - 3y)

Step-by-step explanation:

Check it using the FOIL method - first times first, outer times outer, inner times inner, last times last

The value of radical expression 5√0.00032 x⁵ is (6.4e-5)x.

By considering the given radical expression

5√0.00032 x⁵

=(0.00032 x⁵ )^1/5

=(6.4e-5)x

A y-intercept, a horizontal asymptote, a domain (the range of x values at which the function exists), and a constant growth factor, b, are the four main characteristics of exponential functions.

An expression with a square root is referred to as a radical expression. Radicand: A value or phrase contained within the radical symbol. Equation with radical expressions and variables as radicands is referred to as a radical equation.

The 'V'-shaped portion of the radical symbol will have a superscript number when it is used to represent any root other than a square root. For instance, the expression 3(8) denotes the cube root of 8.

The radical symbol, which resembles a check mark, the index, a small number written outside the radical symbol, and the radicand, a quantity written beneath the horizontal bar of the radical symbol, are the three main components of the radical expression a^b.

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Answer:

[tex]\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

[tex]\sin 2x=2\sin x \cos x \\ \\ \sin 120^{\circ}=2\sin 60^{\circ} \cos 60^{\circ} \\ \\ =2(\sqrt{3}/2)(1/2) \\ \\ =\frac{\sqrt{3}}{2}[/tex]

Answer:

3+(4x)

Step-by-step explanation:

The algebraic expression will be written as:

x=jelly tots

The number of chocolates=3+(4×x)

=3+(4x)

The algebraic expression for the number of chocolates is 4n + 3 where n is number of packets of Jelly Tots.

Let's use variables to represent the number of Jelly Tots and chocolates:

Let "n" be the number of packets of Jelly Tots.

Now, the number of chocolates is three more than 4 times the number of Jelly Tots.

So, represent the number of chocolates as:

Number of chocolates = 4 * n + 3

4 * n represents 4 times the number of Jelly Tots.

Multiplying the number of Jelly Tots by 4 gives us the chocolates without the additional 3.

- +3 represents the additional chocolates.

Thus, the algebraic expression is 4n + 3.

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Hey there!

9 - 3x + x - 15

= 9 - 3x + 1x - 15

COMBINE the LIKE TERMS

= (9 - 15) + (-3x + 1x)

= (-3x + 1x) + (9 - 15)

= (-3x + x) + (9 - 15)

= -3x - x + 9 - 15

= -2x - 6

Therefore, your answer should be:

-2x - 6

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

y=x+9

Step-by-step explanation:

The general equation for a straight line is y=mx+c

1. first we need to find the gradient (m) to do this we do

4-5/-5-(-4)

which gives the answer of 1. This means or gradient (m) is 1. we can substitute this in our general formula y=mx+c which gives

y=1x+c this can also be written as y=x+c

2. we need to find the value of c. to do this we can sub in any co-ordinates from the question in this case we will be using (-4,5)

-4 is the x co-ordinate

5 is the y co-ordinate

5= -4+c

to get c we add 4 on each side we get

9=c

we can sub this into the equation we produced with the gradient giving us

y=x+9

3. the final answer is y=x+9

After the solution, the value of x for the equation √x+2 = x is 2.

So,

Given the equation: √x+2 = x

Then,

To get a quadratic, square it:

Quadratic formula:

However, when we square in our work, we must ensure that we haven't accidentally introduced extra roots.

In this case, -1 is not a solution to the original equation, whereas 2 is.

Therefore, after the solution, the value of x for the equation √x+2 = x is 2.

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The equation of the line in point-slope form is:

y - 8 = 3(x + 6) or y - 2 = 3(x + 8).

The equation, y - b = m(x - a), represents the equation of a line in point-slope form, where:

Given two points, (-8, 2) and (-6, 8), find the slope (m) of the line that passes through the two points:

Slope (m) = change in y / change in x = (8 - 2)/(-6 -(-8))

Slope (m) = 6/2

Slope (m) = 3

Substitute m = 3 and (-6, 8) into y - b = m(x - a):

y - 8 = 3(x - (-6))

y - 8 = 3(x + 6)

Or substitute m = 3 and (-8, 2) into y - b = m(x - a):

y - 2 = 3(x - (-8))

y - 2 = 3(x + 8)

Therefore, the equation of the line in point-slope form is:

y - 8 = 3(x + 6) or y - 2 = 3(x + 8).

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Answer:

Step-by-step explanation:

2x

The measure of the ∠PQS will be 71° , and the measure of the ∠PQR will be 142°.

What is an angle bisector ?

The angle bisector is the line or line segment that divides the angle into two identical portions.

Given that line, QS is bisecting the angle PQR into two angles RQS and PQS.

We know that the angle bisector bisects the two angles into two equal halves , i.e.,

∠ PQS = ∠ RQS

So ; the measure of ∠ PQS will be :

∠ PQS = 71°

So , if we want to calculate the measure of ∠PQR then it can be represented as the sum of two angles.

∠ PQR = ∠PQS + ∠RQS

or

∠PQR = 71° + 71°

or

PQR = 142°

Therefore, the measure of the ∠PQS will be 71° , and the measure of the ∠PQR will be 142°.

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The simplified expression after solving the given equation is 2 [tex]x^{6}[/tex] .

The given expression is,

[tex]\sqrt[3]{125}[/tex] x⁶ - [tex]\sqrt[3]{27}[/tex] x⁶                                          equation 1

Name the given expression as equation 1.

To simplify the given expression first we need to solve step wise,

[tex]\sqrt[3]{125}[/tex] = [tex]\sqrt[3]{25.25.25}[/tex] = 5

[tex]\sqrt[3]{27}[/tex] = [tex]\sqrt[3]{3.3.3}[/tex] = 3

Now, we need to substitute the above solved values in equation 1 and after substituting them we can write as follows:

[tex]\sqrt[3]{125}[/tex] x⁶ - [tex]\sqrt[3]{27}[/tex] x⁶  = 5[tex]x^{6}[/tex] - 3[tex]x^{6}[/tex]

On further simplifying, we will get

[tex]\sqrt[3]{125}[/tex] x⁶ - [tex]\sqrt[3]{27}[/tex] x⁶ = 2[tex]x^{6}[/tex]

Thus we can write that the simplified expression after solving the given equation is 2 [tex]x^{6}[/tex] .

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Answer: I can't see the answer choices but 98,673 divided by 222 is 444.5

hope this helps :)

It should be noted that converting 11/20 to a decimal through division will gives 0.55.

This can be illustrated as follows. It should be noted that the quotient is the value obtained by dividing one value by another. The quotient is 11.

The divisor is the value that divides. It should be noted that in this case, this is illustrated as 20.

It should be noted that 11 is the numerator and 20 is the denominator.

Therefore, it should be noted that converting 11/20 to a decimal through division will gives 0.55.

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Answer:

18 meters

Step-by-step explanation:

24 is dilated by 3/4

Which means 24 * 3/4 or 24 * .75  

i t h i n k

Answer:

You can use the definition of perfect square trinomials to find which of the given trinomials are perfect squares.

The trinomials which are perfect squares are:

Option B:

Option D:

What are perfect squares trinomials?

They are those expressions which are found by squaring binomial expressions.

How to find which of the given trinomials are perfect square trinomials?

Since the given trinomials are with degree 2, thus, if they are perfect square, the binomial which was used to make them must be linear.

Let the binomial term was am + b(a linear expression is always writable in this form where a and b are constants and m is a variable), then we will obtain:

Checking all options:

Option A:

Comparing it with the standard form we obtained, we have:

Option B:

Comparing it with the standard form we obtained, we have:

Thus, this trinomial is perfect squares trinomial.

Option C:

Comparing it with the standard form we obtained, we have:

Option D:

Comparing it with the standard form we obtained, we have:

Thus,   this trinomial is perfect squares trinomial.

Thus,

The trinomials which are perfect squares are:

Option B:

Option D:

Step-by-step explanation:

The answer is 77520.

How many different (ordered) playlists are possible?

Number of possible playlists = 77520

Explanation:

Total number of songs = 20

Songs in the playlist = 7

So, we need to select 7 songs out of 20. This can be done using combinations.

n = 20 , r=7

C( n , r ) = ?

C( n , r ) = C (20 , 7)

              = 20! / ( 7! (20-7)!)

              =  20! / ( 7! × 13! )

              = 77520

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after dilating the point ( 9 , 9 ), we get the point as ( 3 , 3 ) with the scale factor as 1 / 3.

We are given a point:

( 9 , 9 )

We have the scale factor as:

1 / 3

We need to dilate the point using the scale factor.

So, we get that:

( 9 × 1 / 3 , 9 × 1 / 3 )

= ( 3 , 3 )

Therefore, after dilating the point ( 9 , 9 ), we get the point as ( 3 , 3 ) with the scale factor as 1 / 3.

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Answer:

29

Step-by-step explanation:

to get from -16 to -7 you have to add 9

to get from -7 to 2 you have to add 9

to get from 2 to 11 you have to add 9

and the same thing for 11 to 20

Answer: The answer

is  29 because the pattern of the number is 999999

Step-by-step explanation:

The cost in dollars and cents for each dog pillow is $17.95

What is the total cost of  3 giant dog pillows?

The total cost of the  3 giant dog pillows is determined as the amount Amy gave the cashier minus the change the cashier handed to Amy, in essence, the cost in dollars and cents for each dog pillow can now be computed the total cost of the  3 giant dog pillows divided by the number of dog pillows purchased

total cost for  3 giant dog pillows=total cost of amount given to cashier change received

total cost of amount given to cashier=$60

change received=$6.15

total cost for  3 giant dog pillows=$60-$6.15

total cost for  3 giant dog pillows=$53.85

cost per dog pillow=total cost for  3 giant dog pillows/number of dog pillows purchased

cost per dog pillow=$53.85/3

cost per dog pillow=$17.95

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