Exponents power of power multiplication properties

(4a³b^4)³

[tex]\begin{cases} x = -3 &\implies x +3=0\\ x = 2 &\implies x -2=0\\ x = 4 &\implies x -4=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{ ( x +3 )( x -2 )( x -4 ) = \stackrel{0}{y}}\implies (x+3)(x^2-6x+8)=y \\\\\\ x^3-6x^2+8x+3x^2-18x+24=y\implies \boxed{x^3-3x^2-10x+24=y}[/tex]

Answer:

Step-by-step explanation: the value is 633.202 ft

Cosine is negative, we know that angle C is obtuse. Therefore, the triangle with sides 9, 15, and 19 is an obtuse triangle.

What is triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

To determine whether a triangle with sides 9, 15, and 19 is acute or obtuse, we can use the Law of Cosines, which relates the sides and angles of a triangle:

c^2 = a^2 + b^2 - 2ab*cos(C)

where a, b, and c are the side lengths, and C is the angle opposite side c.

In this case, we have:

a = 9, b = 15, c = 19

Using the Law of Cosines, we can solve for the cosine of angle C:

cos(C) = (a^2 + b^2 - c^2) / 2ab

cos(C) = (9^2 + 15^2 - 19^2) / (2915)

cos(C) = -0.283

Since, cosine is negative, we know that angle C is obtuse. Therefore, the triangle with sides 9, 15, and 19 is an obtuse triangle.

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Using the slope intercept form of the line, cost per night (m) is 75 and the initial fee (b) that the cabin charges is 50.

Equation of a line in slope intercept form is

y = mx + b

Here m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.

The cabin that Jake and his friends are staying at charges an initial fee plus the cost per night.

Given graph is a linear relationship between the total cost, y, and number of nights, x.

Let initial fee be b and cost per night be m.

So the equation will be of the form,

Total cost = Initial fee + (cost per night × number of nights)

y = b + mx

Comparing this with slope intercept form, initial fee is the y intercept and cost per night is the slope.

From the graph, we have a point (0, 50).

y intercept = 50

So initial fee = 50

Consider (0, 50) and (2, 200).

Slope = (200 - 50) / (2 - 0) = 75

So cost per night = 75

Hence cost per night is 75 and the initial fee is 50.

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By using the method of Normal Distribution, Marques made 4 three point shots and 4 free throws.

Let's denote the number of three point shots that Marques made as x and the number of free throws he made as y.

According to the problem, Marques made a total of 8 shots, so we have:

x + y = 8

And he scored a total of 12 points, which can be expressed as:

3x + y = 12

We now have a system of two equations with two unknowns:

x + y = 8

3x + y = 12

We can solve this system by either substitution or elimination. Here, we'll use the elimination method.

Multiplying the first equation by 3, we get:

3x + 3y = 24

Subtracting the second equation from this, we get:

2y = 12 - 3x

Dividing by 2, we get:

y = 6 - (3/2)x

We can substitute this expression for y into the first equation:

x + (6 - (3/2)x) = 8

Simplifying, we get:

(1/2)x = 2

x = 4

So Marques made 4 three point shots. We can substitute this value into either of the original equations to find y:

4 + y = 8

y = 4

So Marques made 4 free throws.

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Answer:

CFGGFF

Step-by-step explanation:

CGDF

[tex]x!/10^{(6x)}[/tex] diverges as x approaches infinity.

What is expression ?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can be as simple as a single number or variable, or they can be complex combinations of multiple variables and operations.

Examples of expressions include:

3 + 5

x - 2y

(a + b) * (c - d)

2x^2 + 3x - 5

sin(x) / cos(x)

Expressions can be evaluated to obtain a numerical value or simplified to make them easier to work with. For example, the expression 2x^2 + 3x - 5 can be simplified by factoring as (2x - 5)(x + 1) or by completing the square as 2(x + 3/4)^2 - 49/8.

Expressions are an important part of algebra and other branches of mathematics, where they are used to represent mathematical relationships and solve equations. They are also used in computer programming and other areas of science and engineering to represent mathematical models and calculations.

According to given condition :

The expression [tex]x!/10^{(6x)}[/tex] is a mathematical function that represents the factorial of x divided by 10 to the power of 6 times x. This expression diverges as x becomes large because the factorial function grows much faster than the exponential function.

As x increases, the value of x! grows very rapidly because x! is the product of all integers from 1 to x. In contrast, the value of 10^(6x) grows much more slowly because it is an exponential function with a fixed base of 10.

Therefore, as x gets larger, the value of [tex]x!/10^{(6x)}[/tex] grows very rapidly, eventually becoming much larger than any fixed value. This means that the expression diverges to infinity as x approaches infinity.

To see this more formally, we can use Stirling's approximation, which states that n! is approximately equal to [tex](n/e)^n * sqrt(2pin)[/tex] for large values of n. Substituting this into the expression for [tex]x!/10^{(6x)}[/tex], we get:

[tex]x!/10^{(6x)} ≈ [(x/e)^x * sqrt(2pix)] / 10^{(6x)}[/tex]

Taking the logarithm of both sides, we get:

[tex]ln(x!/10^{(6x)}) ≈ x * ln(x/e) + 0.5 * ln(2pix) - 6x * ln(10)[/tex]

As x approaches infinity, the first two terms on the right-hand side dominate, and the expression grows without bound.

Therefore, [tex]x!/10^{(6x)}[/tex]diverges as x approaches infinity.

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An expression to represent the perimeter is P = 2m + 2(m² + 11m + 28)/m

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

We are given that;

The expression m² + 11m + 28

Now,

Let's assume that the length of the rectangle is "m" and the width is "n".

The formula for the area of a rectangle is A = l × w. We are given that the area of the rectangle is m² + 11m + 28, so we can write:

A = m² + 11m + 28

Substituting the formula for the area, we get:

m² + 11m + 28 = m × n

We can rearrange this equation to solve for n:

n = (m² + 11m + 28) / m

The perimeter of a rectangle is given by the formula P = 2(l + w). Substituting the values of l and w, we get:

P = 2(m + n)

Substituting the value of n, we get:

P = 2(m + (m² + 11m + 28) / m)

P = 2m + 2(m² + 11m + 28) / m

Therefore, by the given area of rectangle perimeter will be 2m + 2(m² + 11m + 28) / m

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The inequality that shows how much can be added to the regular size for a drink that costs under $4.00 is given as follows:

2.25 + 0.25n < 4.

The drink costs $2.25, plus each of the n additionals cost $0.25, hence the total cost is given as follows:

T(n) = 2.25 + 0.25n.

For a cost under $4, the cost must be less than $4, hence the inequality is given as follows:

2.25 + 0.25n < 4.

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Answer: B) 37.68

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.

Plugging in the given radius of 6 centimeters, we get:

C = 2πr

C = 2π(6)

C ≈ 37.68

Answer:

Step-by-step explanation:

A

The box plot that represents the data-set is given as follows:

Option C.

From left to right, the five features of the box and whisker plot are listed as follows

The minimum and maximum values are given as follows:

The median is of 34 concerts for each (middle value of the ordered data-sets), hence the plot is given by option C.

The quartiles are the mean of each half of the ordered data-sets.

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The number of rhinestones per square centimeter on the surface of a disco ball is 448/274.167.

Suppose that radius of the considered sphere is of 'r' units.

Then, its surface area S would be:

[tex]S = 4\pi r^2 \: \rm unit^2[/tex]

Given;

A disco ball has a circumference of 16.558 centimeters

448 rhinestones on its surface.

Now,

2pi*r=16.558

r=8.279/pi

Surface area of sphere=4pi*r^2

=4*68.541841

=274.167

Here, 448/274.167

Therefore, the surface area per square cm will be 448/274.167.

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Answer: the answer for the second is b^x= bxb^y and b^y= b^6xb^x

For the first the answer is b^x=b^3/b^y and b^y= b^3/b^x

Step-by-step explanation: First we must get the x or the y alone. When completing this I believe you have to take into account the exponent rules if you're trying to simplify it fully.

Answer:

14.76

Step-by-step explanation:

Circumference = 2πr

Substitue the values into the formula

2(3.14) (2.35)=

Multiply pi by the radius

2(7.379)= 14.758

Round the answer to the hundreths place

14.76

Answer:

x = 3 ± 2[tex]\sqrt{6}[/tex]

Step-by-step explanation:

x² - 6x = 15

to complete the square on the left side

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3)x + 9 = 15 + 9

(x - 3)² = 24 ( take square root of both sides )

x - 3 = ± [tex]\sqrt{24}[/tex] = ± [tex]\sqrt{4(6)}[/tex] = ± ([tex]\sqrt{4}[/tex] × [tex]\sqrt{6}[/tex] ) = ± 2[tex]\sqrt{6}[/tex]

add 3 to both sides

x = 3 ± 2[tex]\sqrt{6}[/tex]

then

x = 3 - 2[tex]\sqrt{6}[/tex] , x = 3 + 2[tex]\sqrt{6}[/tex]

|t+4| ≤ 48 is the inequality that is used to find t, the number of tablespoons of flour actually used in a recipe.

What is inequality?

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.

Here, we have

Given: Henry's bread recipe calls for 3 cups of flour, with a variation of up to 4 tablespoons depending on the humidity level. There are 16 tablespoons in 1 cup.

We have to find inequality that is used to find t, the number of tablespoons of flour actually used in a recipe.

= 3×16 = 48

= |t+4| ≤ 48

Hence, |t+4| ≤ 48 is the inequality that is used to find t, the number of tablespoons of flour actually used in a recipe.

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Formula a = (v = 2 * pi * r / t)

Formula b = (v2 = g * m_central / r)

The scenario in context to formula a and formula b is given below:

Formula a = (v = 2 * pi * r / t)

It is used to calculate the velocity (v) of a circular object moving with a constant speed around a circle of radius (r) in time (t).

Example scenario: if you want to find the velocity of a moving object in a circular path, use formula a.

Suppose you want to find the velocity of a car moving in a circular path on a race track. The radius of the track is "r" and the time taken for the car to complete one lap is "t".

Using the equation (v = 2 * pi * r / t), we can calculate the velocity as follows:

Let's say the radius of the track is 100 meters and the time taken for the car to complete one lap is 60 seconds. Then, the velocity can be calculated as follows:

v = 2 * pi * (100 m) / (60 s)

v = 31.42 m/s

So, the velocity of the car moving in a circular path on the race track is 31.42 m/s.

Formula b = (v2 = g * m_central / r)

It is used to calculate the velocity squared (v^2) of an object moving under the influence of a central force (g * m_central) and is related to the radius (r) of its orbit.

Example scenario: If you want to find the velocity squared of an object under the influence of a central force, use formula b.

Suppose you want to find the velocity squared of a planet moving in a circular orbit around a star (a central force). The mass of the star is "m_central" and the distance of the planet from the star is "r".

Using the equation (v²  = g * m_central / r), we can calculate the velocity squared as follows:

v² = (6.67 x 10^-11 N m² /kg² ) * (m_central) / (r)

Let's say the mass of the star is 2 x 10^30 kg and the distance of the planet from the star is 1.5 x 10^11 m.

Then, the velocity squared can be calculated as follows:

v²  = (6.67 x 10^-11 N m² /kg² ) * (2 x 10^30 kg) / (1.5 x 10^11 m)

v²  = 2.22 x 10^20 m² /s²

So, the velocity squared of the planet moving in a circular orbit around the star is 2.22 x 10^20 m² /s² .

At, last we can say if you want to find the velocity of a moving object in a circular path, use formula a. If you want to find the velocity squared of an object under the influence of a central force, use formula b.

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Answer: 26

Step-by-step explanation: if each ride costs $.50 each, and admission costs $7, you multiply .50 by 26 and get 13. After you then add $13 and $7 and that equals $20. $13 dollars Jerold can spend

In a right angled triangle, the angles are given by the fοrmula:

Angle A + Angle B + Angle C = 180°Therefοre, x° = 131°.

Angle is a geοmetrical figure fοrmed by twο rays with a cοmmοn endpοint. It is measured in degrees οr radians and is used tο describe the amοunt οf turn between twο lines. It can alsο be used tο measure the size οf an angle in a triangle, the amοunt οf rοtatiοn οf a 3D οbject, and mοre. Angles are impοrtant in bοth mathematics and science as they're used tο calculate the amοunt οf fοrce needed tο mοve an οbject οr the amοunt οf energy needed tο keep an οbject in mοtiοn.

In a right angled triangle, the angles are given by the fοrmula:

Angle A + Angle B + Angle C = 180°

Given that FHG = 49°, we can calculate the οther angles:

Angle A = 180° - 49° = 131°

Angle B = 180° - 131° - 49° = 0°

Angle C = 180° - 131° - 0° = 49°

Therefοre, x° = 131°.

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The amount of water required to produce 1% sugar syrup from 12g sugar is 1.2L.

Volume is the amount of space occupied by an object, whereas capacity is the ability of an object to hold a substance, such as a solid, liquid, or gas.

The amount of water that must be added for a given weight of solution is expressed as weight by volume solution (w/v).

w/v (weight by volume percentage):

The grams of solute in 100 milliliters of solution are defined as the percent weight per volume.

This method determines the concentration of the solution.

The concentration given is 1%.

The sugar weight is 12g.

Solvent volume = weight/concentration

Volume  = 12/1 = 12 x 100 mL

Volume = 1.2 L

Hence, 1.2l of water is required to produce 1% sugar syrup from 12g of sugar

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Answer:

Yes.

Step-by-step explanation:

We need to make sure that we match up the right sides before checking for proportionality.

From the picture, we can see that SRT pairs with MLN.

It's easier to see if you draw a diagram of MLN on paper with the same orientation as SRT.

Were you to do this, you would see that as SR lies on the left side of SRT, so does MLN lie on the left side of ML.

Also, both ST of SRT and MN of MLN lie on the right side and RT of SRT and LN of MLN are the base.

Thus, the proportions are

[tex]\frac{SR}{ML}=\frac{ST}{MN}=\frac{RT}{LN} \\\\\\\frac{3.61}{5.415}=\frac{2}{3} \\\\\frac{9.71}{14.564}=\frac{2}{3}\\ \\ \frac{11.97}{17.955}=\frac{2}{3}[/tex]

Since all the ratios simplify to 2/3 and are equal, the sides are proportional.

The equation of the perpendicular bisector that goes through a segment with endpoints (2,1) and (6, -3) is y = x - 5.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of a line is

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

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:

An equation of the line that passes through the points (2,1) and (6, -3) is,

y - 1 = (-3 - 1)/(6 - 2)(x - 2)

y - 1 = -1(x - 2)

y - 1 = -x + 2

y = -x + 3

The slope of the perpendicular bisector that goes through the line y = -x + 3 is,

= -(1/-1)

= 1

And the required line passes through (2 + 6/2, 1-3/2) = (4, -1) and have slope 1,

So, the equation of the line is,

y + 1 = 1(x - 4)

y = x - 5

Therefore, the equation is y = x - 5.

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Since Nina made her career planning timeline in the year 2005, the year which Nina's timeline should start is: B. 2005.

A timeline can be defined as a list of important events or activities that are arranged in a chronological sequence, which is the order in which they happened (occurred).

we know that,

Chronology can be defined as the logical arrangement of events based on the order of their occurrence.

In this context, we can reasonably infer and logically deduce that the year which Nina's timeline should start is 2005 because Nina made her career planning timeline in the year 2005.

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Answer:y=-x/-+8

Step-by-step explanation:

Answer:

A. 1&3 are vertical

C. 1&3 are supplementary angles

The result of dilating a rectangle using a scale factor of 1/2 through point B will be a new rectangle with half the length and width of the original rectangle, centered around point B.

When a rectangle is dilated using a scale factor of 1/2, it means that the size of the rectangle is reduced by half.

This can be achieved by multiplying the dimensions of the rectangle by the scale factor. In the case of a dilation through point B, the new rectangle will be centered around point B and its length and width will be half of the original dimensions.

In mathematical terms, let's assume that the original rectangle has length "l" and width "w". The new rectangle after the dilation with a scale factor of 1/2 will have a length of (1/2)l and a width of (1/2)w.

To find the new coordinates of the rectangle, we need to subtract (1/4)l and (1/4)w from the original x and y coordinates respectively.

If the original rectangle has a length of 4 and a width of 2, then the new rectangle after the dilation with a scale factor of 1/2 will have a length of 2 and a width of 1.

The new x and y coordinates will be x-1 and y-0.5 respectively.

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The requried, for a user who uses 4 gigabytes of data in a month, the plan from Company C would be less expensive.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
The monthly cost of using 4 gigabytes of data on Company C's plan can be calculated using Rule C:

C(4) = $10 + $15 × 4 = $10 + $60 = $70

The monthly cost of using 4 gigabytes of data on Company D's plan can be calculated using Rule D:

D(4) = $80

So, in this case, C(4) is less than D(4), meaning that the monthly cost of using 4 gigabytes of data on Company C's plan is less than the monthly cost of using 4 gigabytes of data on Company D's plan.

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Step-by-step explanation:

Hello, So use the function p, to find the output

[tex]p(3) = - (3 - 4) {}^{2} + 10 = - 39[/tex]

[tex]p(5) = - (5 - 4) {}^{2} + 10 = 9[/tex]

Since p(4)>p(5) and p(3), p(4) is the maximum.

Also p is written in vertex form which is

[tex]a(x - h) {}^{2} + k[/tex]

Since a is negative, we will have a maximum vertex.

The answer is

Oriya has reasoned the vertex is a maximum because p(4) is the highest points compared to points near it such as p(3) and p(5).