2 3 + x = 3 what is X solved for

To solve the logarithmic equation with different bases, one must recognize the importance of base conversion and utilize logarithmic properties to guide conversion or comparison, not just directly equate the logarithmic arguments, which was a misunderstanding.

To solve the equation log_4(x + 3) = log_2(2 + x), we need a system that represents this equation effectively by considering logarithmic properties and base conversion.

Steps for Solving the Equation

Recognize that both sides of the equation are logarithms, which implies their arguments must be equal if their outputs are equal. Thus, it means x + 3 = 2 + x.

This simplification does not directly solve our original equation due to the different bases of the logarithms. We utilize the property that allows us to convert between bases: log_a(b) = log_c(b) / log_c(a), specifically focusing on changing base 4 logarithm to base 2.

We apply this to convert log_4(x + 3) to a base 2 logarithm, yielding a new equation: log_2(x + 3)/log_2(4) = log_2(2 + x).

Since log_2(4) = 2, the equation simplifies to 0.5 * log_2(x + 3) = log_2(2 + x).

This step reveals that the initial transformation inadvertently simplified through a direct comparison, which doesn't correctly express the conversion between bases or the nature of the original problem.

To correctly translate the given logarithmic equation into a system of equations, acknowledge that the original task was misunderstood in Step 1, as it did not account for the different log bases and their properties.

Instead, consider equations that capture the essence of converting bases or applying logarithmic identities to derive a solution.

A more accurate representation would involve recognizing the base conversion and understanding that without a direct means of converting or equating the logarithms due to their different bases and the variables involved, it does not straightforwardly lead to a solvable system without further information or manipulation that squarely addresses the base disparity.

You want the formula for conditional probability.

P(X | B) = (X and Y)/P(Y)

Final answer:

P(X | Y) = P(X and Y) / P(Y).

Explanation:

The formula P(X | Y) represents the probability of event X occurring given that event Y has already occurred.

This concept is often used in the context of conditional probability, which differs from the calculation of independent events where the probability of both events X and Y occurring is simply the product of their individual probabilities, denoted as P(X) · P(Y).

When events are not independent, to find the conditional probability P(X | Y), you would typically use the formula

P(X | Y) = P(X and Y) / P(Y),

where

P(X and Y) is the joint probability of events X and Y occurring together, and

P(Y) is the probability of event Y occurring.

Hello!

Answer:

[tex]\boxed{x=4, x=-7}\checkmark[/tex]

Step-by-step explanation:

First, expand.

[tex]x^2+3x-10=18[/tex]

Then, subtract by 18 both sides.

[tex]x^2+3x-10-18=18-18[/tex]

Simplify and solve.

[tex]x^2+3x-28=0[/tex]

Therefore, the solution to this equation is x=4, and x=-7.

x=4 and x=-7 is the correct answer.

Hope this helps you!

Have a nice day! :)

Thank you!

Answer:

Solution of the given equation: [tex]x=4 , -7[/tex]

Step-by-step explanation:

An equation is a mathematical statement that states that two things are equal to each other.

A linear equation in one variable is of the form [tex]ax^2+bx+c=0[/tex] where a,b,c are coefficients and x is variable .

Here. given: [tex](x-2)(x+5)=18[/tex]

Using rule (Multiplication is distributive over addition) : [tex]a(b+c)=ab+ac[/tex] ,

we can write this equation as,

[tex](x-2)(x+5) =18\\ x(x+5)-2(x+5) =18\\ x^2+5x-2x-10 =18\\ x^2+3x-10-18 =0\\ x^2+3x-28 =0\\[/tex]

On comparing this equation with [tex]x^2[/tex] - (sum of roots)[tex] x [/tex]+(product of roots) = 0, we get

sum of roots=3 (7-4)

product of roots = -28 [tex]\left ( 7\times -4 \right )[/tex]

Using this fact , we can write this equation as ,

[tex]x^2+7x-4x-28=0\\x\left ( x+7 \right )-4\left ( x+7 \right )=0\\\left ( x-4 \right )\left ( x+7 \right )=0\\\Rightarrow x=4\,,\,x=-7[/tex]

Answer:

Step-by-step explanation:

[tex]Domain:\\\\2g+8\neq0\ \wedge\ g^2-16\neq0\\\\g\neq-4\ \wedge\ g\neq4\\====================\\\\\dfrac{3}{2g+8}=\dfrac{g+2}{g^2-16}\qquad\text{cross multiply}\\\\3(g^2-16)=(2g+8)(g+2)\\\\\text{use the distributive property}:\ a(b+c)=ab+ac\\\text{and}\ FOIL:\ (a+b)(c+d)=ac+ad+bc+bd\\\\(3)(g^2)+(3)(-16)=(2g)(g)+(2g)(2)+(8)(g)+(8)(2)\\\\3g^2-48=2g^2+4g+8g+16\qquad\text{subtract}\ 2g^2\ \text{from both sides}\\\\g^2-48=12g+16\qquad\text{subtract}\ 12g\ \text{and}\ 16\ \text{from both sides}[/tex]

[tex]g^2-12g-64=0\\\\g^2+4g-16g-64=0\\\\g(g+4)-16(g+4)=0\\\\(g+4)(g-16)=0\iff g+4=0\ \vee\ g-16=0\\\\g+4=0\qquad\text{subtract 4 from both sides}\\g=-4\notin D\\\\g-16=0\qquad\text{add 16 to both sides}\\g=16\in D[/tex]

The Punic Wars led to demographic changes in Rome, with soldiers returning to find their lands claimed by others, resulting in their migration to the city and growth in the proletariat. This growth contributed to Rome's population reaching over one million by the first century BCE. The wars' aftermath also brought political upheaval that contributed to the fall of the Republic.

The Punic Wars significantly affected the demographic and social structure of Rome. Initially, Roman citizens were predominantly engaged in operating small family farms, with property ownership being a prerequisite for military service. Due to extended military campaigns during the Punic Wars, many soldiers found their lands neglected or in the hands of others upon their return. Consequently, this led to a mass migration of disenfranchised veterans and their families to Rome, swelling the ranks of the proletariat. The city's population ballooned, by some estimates reaching over one million by the first century BCE.

Additionally, the influx of wealth and resources from victories over Carthage markedly altered the political landscape. Disagreements on the distribution of wealth created political factions, primarily the Populares, who championed the cause of the common people, and the Optimates, who defended the interests of the elite. These developments precipitated deep social and political fractures, contributing to the eventual fall of the Roman Republic.

Answer:

The answer is (B)

Step-by-step explanation:

It would not be a, the maximum score is 180, so it would be less than or equal to.

It is (B), since they need to sell at least 40 bags a day, and max is 180.

Hope this helps!

Answer with explanation:

The two linear Inequality given below is:

  1.→ 4 x + 5 y < 180

  2.→x + y > 40

We have to express this inequality into a Situation.

→Representation of Option A in terms of equation

     x=Question which has 4 points

      y=Question which has 5 points

1. x +y =40

2. 4 x +5 y ≤ 180

→→→→Representation of Option B in terms of equation

x=Number of 4 pound bag

y=Number of 5 Pound bag

1. 4 x +5 y < 180

2. x +y > 40

→Representation of Option C in terms of equation

x=Number of cotton balls which are sold at $ 4

y=Number of cotton balls which are sold at $ 5

1. 4 x +5 y < 180

2. x +y > 40

3. 4 x < 180

4. 5 y <180

→Representation of Option D in terms of equation

x=Number of notebooks in a set of Notebooks which contain 4 notebook

y=Number of notebooks in a set of Notebooks which contain 5 notebook

1. 4 x +5 y < 180

2. x +y > 40

3. 4 x < 180

4. 5 y < 180

Option B ,is most Appropriate representation of the situation.

Answer:

Solve the equation inside the parentheses

-3(28) = -30

Multiply the constants

-84 = -30

The equation is false because  -84 ≠ -30. So, the equation is false

Answer:

this is the diagram

Step-by-step explanation:

Answer:

11 has 85° because it is opposite to 9

Step-by-step explanation:

Answer:

Hi there!

The answer is: 2 and -2

Step-by-step explanation:

Case 1: An absolute value of positive number will still be a positive number

so absolute value of 2 is 2

Case 2: An absolute value of negative number will be positive number so absolute value of -2 is 2

Answer:

The Absolute Value of Both 2 and -2 is 2

Step-by-step explanation:

An Absolute Value (abs) is the non-negative value of that number or to put it in other words, it is the amount of space between that number and 0 on a number line. Every Absolute Value other than 0 has two values (a positive and a negative) since the Absolute Value is always a positive. For Example,

abs(-2) = 2 = abs(2) ......The Absolute Value of both 2 and -2 is 2

abs(-75) = 75 = abs(75) .... The Absolute Value of both 75 and -75 is 75

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

5, − one third , one half

Step-by-step explanation:

If the number 'n' is a zero of f(x), then f(n)=0.

We could solve this problem by factorizing the polynomial, but the quickest way is by plugging the options into the equation.

We know that f(x) = 6x3 − 31x2 + 4x + 5.

Then:

Then, the correct option is: 5, − one third , one half.

Finally, the factorized form is: (x−5)(2x−1)(3x+1). If you expand it, you will get the original polynomial.

Answer:  The correct option is

(B) 5, − one third , one half.

Step-by-step explanation:  We are given to select the correct option that represents the zeroes of the following cubic function :

[tex]f(x)=6x^3-31x^2+4x+5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

if for any number a, the function f(x) is zero at x =a , then x = a is a zero of the function f(x).

We have, for the given function, at x = 5,

[tex]f(5)\\\\=6\times5^3-31\times5^2+4\times5+5\\\\=125\times6-31\times25+20+5\\\\=750-775+25\\\\=0[/tex]

So, x = 5 is a zero of the function f(x).

Now, we have

[tex]f(x)\\\\\=6x^3-31x^2+4x+5\\\\=6x^2(x-5)-x(x-5)-(x-5)\\\\=(x-5)(6x^2-x-1)\\\\=(x-5)(6x^2-3x+2x-1)\\\\=(x-5)(3x(2x-1)+1(2x-1))\\\\=(x-5)(3x+1)(2x-1)[/tex]

The zeroes of f(x) are given by

[tex]f(x)=0\\\\\Rightarrow (x-5)(3x+1)(2x-1)=0\\\\\Rightarrow x-5=0,~~3x+1=0,~~2x-1=0\\\\\Rightarrow x=5,-\dfrac{1}{3},\dfrac{1}{2}.[/tex]

Thus, the zeroes of f(x) are 5, -one-third, one half.

Option (B) is CORRECT.

Answer:

Step-by-step explanation:

[tex]\sqrt{x+4}-1=8\\\\\text{Domain:}\ x+4\geq0\to x\geq-4\\\\\sqrt{x+4}-1=8\qquad\text{add 1 to both sides}\\\\\sqrt{x+4}=9\qquad\text{square both sides}\\\\\left(\sqrt{x+4}\right)^2=9^2\\\\x+4=81\qquad\text{subtract 4 from both sides}\\\\x=77\in D[/tex]

Answer:

c is the answer. (Assuming that's a positive 5)

Step-by-step explanation:

You would use the slope formula: (y1 - y2)/(x1-x2).

Plugging in gives

(3--2)/(2-1)

(3+2)/(2-1)

which simplifies to:

5/1

= 5

Hope this helps!

Answer:

The correct option is C.  5

Step-by-step explanation:

Points to remember

slope of the line  passing through the point (x₁, y₁) and (x₂, y₂) is given by

Slope m = (y₂ - y₁)/(x₂ - x₁)

To find the slope of the given line

Here (x₁, y₁) = (2, 3)  and (x₂, y₂) = (1, -2)

Slope m = (y₂ - y₁)/(x₂ - x₁)

 = (-2 - 3)/(1 - 2)

 = (-5)/(-1)

 = 5

Therefore the slope of given line is 5

The correct option is C.  5

Answer:

9 boxes were packed. 10 brownies were left over.

Step-by-step explanation:

127 ÷ 13 =  9 R10

13 x 9 = 10 x 9 + 3 x 9 = 90 + 27 = 117

127 - 117 = 10

The sum of -2 and -18 is -20.

When you add two negative numbers together, you're essentially combining their magnitudes while keeping the negative sign. In this case, you're adding the magnitudes of 2 and 18, which equals 20, and since both numbers are negative, the sum retains the negative sign. So, -2 plus -18 equals -20.

Answer:

x = 7

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Hence

[tex]log_{x}[/tex] 343 = 3 ⇒ 343 = x³

Take the cube root of both sides

x = [tex]\sqrt[3]{343}[/tex] = 7

Answer: Congruent

Step-by-step explanation:

Congruent describes the shapes below that are the same shape but not the same size.

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.

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Answer:

Part 1) see the procedure

Part 2) [tex]4.95x+49.95 < 9.95 x[/tex]

Part 3) [tex]x > 9.99\ months[/tex]

Part 4) The minimum number of months, that he needs to keep the website for site A to be less expensive than site B is 10 months

Step-by-step explanation:

Part 1) Define a variable for the situation.

Let

x ------> the number of months

y ----> the total cost monthly for website hosting

Part 2) Write an inequality that represents the situation.

we know that

Site A

[tex]y=4.95x+49.95[/tex]

Site B

[tex]y=9.95x[/tex]

The inequality that represent this situation is

[tex]4.95x+49.95 < 9.95 x[/tex]

Part 3) Solve the inequality to find out how many months he needs to keep the website for Site A to be less expensive than Site B

[tex]4.95x+49.95 < 9.95 x[/tex]

Subtract 4.95x both sides

[tex]4.95x+49.95-4.95x < 9.95 x-4.95x[/tex]

[tex]49.95 < 5x[/tex]

Divide by 5 both sides

[tex]49.95/5 < 5x/5[/tex]

[tex]9.99 < x[/tex]

Rewrite

[tex]x > 9.99\ months[/tex]

Part 4) describe how many months he needs to keep the website for Site A to be less expensive than Site B.

The minimum number of months, that he needs to keep the website for site A to be less expensive than site B is 10 months

To make Site A less expensive than Site B, James needs to host his website there for at least 10 months.

Let's define m as the number of months James would host his website. We write an inequality that represents the situation: $4.95m + $49.95 <= $9.95m. This represents the total cost of Site A being less than or equal to Site B.

To solve the inequality, subtract $4.95m from both sides of the equation: $49.95 <= $5m. Dividing both sides by 5 gives: m >= 9.99, which we round up to 10 because we can't have a fraction of a month.

So, James would need to keep his website hosted on Site A for at least 10 months to be less expensive than Site B.

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Answer:

Step-by-step explanation:

you first have to find the slope by make it rise over run.

rise over run would be 6-4/-4-8. this is the slope or m in the equation y=mx+b. this means that the slope is -1/6

Answer:

a) The equation to find the elevation of Mt. Wilson is [tex]28,784.31=x+11,510.21[/tex]  

b) The elevation of Mt. Wilson is [tex]17,274.10\ ft[/tex]  

Step-by-step explanation:

Let

x ----> represent the elevation of Mt. Wilson

y ----> represent the elevation of Snow Crest

we know that

[tex]y=x+11,510.21[/tex] ----> equation A

we have

[tex]y=28,784.31\ ft[/tex]

Substitute the value of y in equation A and solve for x

[tex]28,784.31=x+11,510.21[/tex]  

[tex]x=28,784.31-11,510.21[/tex]

[tex]x=17,274.10\ ft[/tex]  

The elevation of Mt. Wilson is 17,274.1 feet.

To find the elevation of Mt. Wilson, you can set up an equation based on the information given. You're told that Snow Crest is 11,510.21 feet higher than Mt. Wilson, so you can write the equation as follows:

Elevation of Snow Crest = Elevation of Mt. Wilson + 11,510.21

Now, you can plug in the elevations you have:

Elevation of Snow Crest = 28,784.31 feet

Elevation of Mt. Wilson = x (since you're using x to represent the elevation of Mt. Wilson)

So, the equation becomes:

28,784.31 = x + 11,510.21

Now, you need to solve for x, which represents the elevation of Mt. Wilson. To isolate x, you can subtract 11,510.21 from both sides of the equation:

x = 28,784.31 - 11,510.21

x = 17,274.1

So, the elevation of Mt. Wilson is 17,274.1 feet.

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Answer:

Value of a = 7/6 and a = -1/5

Step-by-step explanation:

We need to solve the equation

30a^2 -7 = 29a

Adding -29a on both sides

30a^2-29a-7=0

Solving the quadratic equation using quadratic formula.

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

here a= 30, b =-29 and c=-7

Putting values, and finding the value of a

[tex]a=\frac{-(-29)\pm\sqrt{(-29)^2-4(30)(-7)}}{2(30)}\\a=\frac{29\pm\sqrt{841+840}}{60}\\a=\frac{29\pm\sqrt{1681}}{60}\\a=\frac{29\pm41}{60}\\a=\frac{29+41}{60} \,\, and \,\,a=\frac{29-41}{60}\\a=\frac{70}{60} \,\, and \,\,a=\frac{-12}{60}\\a=\frac{7}{6} \,\, and \,\,a=\frac{-1}{5}[/tex]

So, value of a = 7/6 and a = -1/5

Answer:

Make a proportion

X/8 = 16.5/6

Solve for X

X = 22

ANSWER

all real numbers

EXPLANATION

The given absolute value function is

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

This function is obtained by shifting the graph of

[tex]y = |x| [/tex]

to the left by 2 units.

Since the domain of the parent function is all real numbers, the domain of the transformed function is also all real numbers because the shifting the parent function horizontally or vertically does not affect the domain.

Answer:

C ) Inverse variation  .

Step-by-step explanation:

Given  : Graph.

To find : What type of variation do the adjacent side lengths exhibit.

Solution : We have given graph between width and height of the rectangle .

Width shown by the x axis  .

Height shown by the y axis .

Coordinates are ( 1, 4) ( 2,2) ( 8 ,0.5) ( 16 ,0.25) .

We can see from the given coordinates :

As the values of width coordinates increases , the values of height coordinates is decrease .

That mean width and height are inverse of each other .

Therefore, C ) Inverse variation  .

A type of variation which the adjacent side lengths exhibit is an: C. inverse variation.

An inverse variation can be defined as a type of proportionality which shows the relationship between two (2) variables, wherein, as the value of one variable increases, the value of the other variable decreases.

Based on the graph, we can logically deduce that there is an inverse variation between the height and width of this rectangle because they are inversely proportional.

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Answer:

(0,0) (-6,0), (-2,0)

Step-by-step explanation:

Answer:

The correct choice is A. (-6,0), (-2,0) and (0,0).

Step-by-step explanation:

Consider the provided information:

The provided function f(x) is an even function and has 5 x-intercept.

Therefore,

f(x) = f(-x)

Thus, there will be positive and negative pairs of zeros.

As it is given that the x intercept is at (6,0). Therefore, the another x intercept will be on (-6,0).

If there are an odd number of intercepts and function is even then, (0,0) will be the x intercept because of its own negation.

The only choice with (-6,0) and (0,0) is A.

Therefore, the correct choice is A. (-6,0), (-2,0) and (0,0).

Answer:

3/-2

Step-by-step explanation:

(3x) km/3 -2x=4 (x3) times 3 on both sides because you need to get the x by itself and your dividing so the opposite of dividing is multiplying.

9km - 2x = 12

-9               -9 subtract on both sides

-2x = 3

-2      -2 divide on both sides.

so x= 3/-2

I'm in algebra too, and i'm relearning it, so hope i have helped you in anywy and if i haven't I'm sorry.

Answer: 90°

Step-by-step explanation:

The two arcs made by the angle will add up to twice the value of the angle in degrees

89 * 2 = 178

178 - 88 = 90

Answer:

F(x) = 2.15(2x^2-4x-6)

x=9

F(x)= 2.15[2(9)^2 - 4(9) - 6

F(x)=258

$258

Your answer is B.

The complementary angle for 45 degrees is 45 degrees.

Given,

An angle = 45 degree

We need to find the measure of a complementary angle.

When the sum of two angles is 90 degrees the angles are called complementary angles.

Find complementary angles of 45 degrees.

Let. x be the complementary angle for 45 degrees.

x + 45 = 90

Subtracting 45 on both sides

x = 90 - 45

x = 45 degrees

We see that the required complementary angle is 45 degrees

Thus the complementary angle for 45 degrees is 45 degrees.

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