Expand the logarithm fully using the properties of logs. Express the final answer in terms of
log
⁡
x
logx.
log
⁡
7
x
3
log7x
3

The equivalent expression is (a)  1 + √5

From the question, we have the following parameters that can be used in our computation:

√5 + 1

The additive property of equality states that

a + b = b + a

using the above as a guide, we have the following:

√5 + 1 = 1 + √5

This means that the equivalent of √5 + 1 is 1 + √5

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Complete question

Which of the following is equivalent to √5 + 1

O A 1 + √5

OB. 1-√√5

O C. √5-1

OD √5-2

Answer: 3 dogs

Step-by-step explanation:

Each dog eats 1/6 cans of food

Stanley uses a total of 1/2 cans of food

[tex]\frac{1}{2}[/tex]  / [tex]\frac{1}{6}[/tex] = 1/2 * 6

= 3 dogs

Answer: It is equidistant from the segment's endpoints

Step-by-step explanation:  This can also be called "a locus of point" and this is now the perpendicular bisector theorem.

Answer:

14sin(55) and

14cos(35)

Step-by-step explanation:

Greetings!!

just remember trigonometric ratios which are

[tex]sin = \frac{opposite}{hypotenus} \\ cos = \frac{adjecent}{hypotenus} \: and \\ tan = \frac{opposite}{hypotenus} [/tex]

following that substitute given values to solve for x.

[tex]sin55 = \frac{x}{14} [/tex]

solve for x

[tex]x = 14 \sin(55) [/tex]

And

[tex] \cos(35) = \frac{x}{14} [/tex]

solve for x

[tex]x = \cos(35) [/tex]

Hope it helps!!!

1225 J is the Kinetic Energy of the football as it was traveling down the

field.

Calculate the Kinetic Energy (KE) of the football.

KE = 0.5 x 5 kg x (25 m/s)^2

Calculate the Kinetic Energy of the football in Joules (J).

KE = 0.5 x 5 kg x (25 m/s)^2 x 9.8 m/s^2

Calculate the Kinetic Energy of the football in Joules (J).

KE = 0.5 x 5 kg x (25 m/s)^2 x 9.8 m/s^2 = 1225 J

The energy an object has as a result of motion is known as kinetic energy in physics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity.

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The equation can be written as 6 + (-6y) = -6y - 1 + (7).

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

The given is an equation with missing parts.

The left hand side of the equation does not contain a term with variable, but the right hand side contains it.

Adding that term in the left hand side, we get, 6 + (-6y) in the left hand side.

So the right hand side must be equal.

So the expression in the right hand side is -6y - 1 + (7).

Hence the expressions are 6 + (-6y) on the left hand side and  -6y - 1 + (7) on the right hand side.

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well, let's find the equation of the line through those points then, and let's see

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-6}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-2)}}} \implies \cfrac{-6 }{0 +2} \implies \cfrac{ -6 }{ 2 } \implies - 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-2)}) \implies y = - 3 ( x +2) \\\\\\ y=-3x-6\implies \boxed{3x+y=-6} ~~ \ne ~~ 3x-y = 6[/tex]

Answer:

4x+6y = 46

Step-by-step explanation:

you just add by column

2x+2x

y+5y

9+37

Answer: 90200

Step-by-step explanation:

9020 x 10 = 90200.

Just add one more zero when multiplying by ten.

Answer:

x = 200

Step-by-step explanation:

[tex]\frac{x}{5} = \frac{120}{3}[/tex]

so you cross multiply

5 × 120 = 600

x × 3 = 3x

so

3x = 600

x = 200

Answer:

Step-by-step explanation:

Prime factorization is the process of expressing a number as the product of its prime factors. To find the prime factorization of a number, you can use the following steps:Divide the number by the smallest prime factor (2) and write the result.Divide the quotient from step 1 by the next smallest prime factor (3) and write the result.Repeat step 2 with each successive prime factor until the quotient is 1.For example, to find the prime factorization of 60:60 / 2 = 30 -> 2

30 / 2 = 15 -> 2 * 2 = 4

15 / 3 = 5 -> 4 * 3 = 12

5 / 5 = 1 -> 12 * 5 = 60The prime factorization of 60 is 2 * 2 * 3 * 5To find the greatest common factor (GCF) of two numbers, you can use the following steps:Write the prime factorization of each number.Write the GCF as the product of the prime factors that are common to both numbers, each raised to the lowest power that occurs in both factorizations.For example, to find the GCF of 24 and 40:Prime factorization of 24 = 2^3 * 3

Prime factorization of 40 = 2^3 * 5The GCF is 2^3 = 8To find the least common multiple (LCM) of two numbers, you can use the following steps:Write the prime factorization of each number.Write the LCM as the product of the prime factors of each number, each raised to the highest power that occurs in either factorization.For example, to find the LCM of 24 and 40:Prime factorization of 24 = 2^3 * 3

Prime factorization of 40 = 2^3 * 5The LCM is 2^3 * 3 * 5 = 120Alternatively, you can use the formula LCM(a, b) = (a * b) / GCF(a, b)Please note that this is a method for finding the prime factorization and GCF/LCM of small numbers. For larger numbers, it is more efficient to use a specific algorithm or software.

Answer:

(2,4)

Step-by-step explanation:

The point that's on the origin (0,0) goes to the right by 2 which is your x-axis and goes up 4 which is your y-axis.

Answer:

Translation: (2,4)

Step-by-step explanation:

The dot/point that's in the middle which is always (0,0) goes to the right by 2 (x-axis) meaning that the first coordinate would be 2. It then goes up 4   (y-axis) meaning that the second coordinate would be 4.

55 is the number of soda bottles the machine can make each minute.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, the graph shows the relationship between time and the number of soda bottles a machine can make. Use points ​(4​,220​) and ​(7​,385​)

Since this graph is a straight line graph and also it goes through the origin that means time is directly proportional to the number of soda can manufactures

To prove this theory

the ratio between cans to the time taken by machine = 220/4 = 385/7

Since the ratio is the same for two points.

Thus,

Soda machine makes in 4 hours = 220 cans

Soda machine makes in 1 hours = 220/4 = 55 cans

Therefore, the number of soda bottles the machine can make each minute is 55.

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The value of function fg(x) is -x^4-4x^3.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

given functions are f(x)=-x^3 and g(x)=x+4

        so,   fg(x)=f(x)*g(x)=-x^3(x+4)

Therefore, the value of

                fg(x)  = -x^4-4x^3

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The value of function fg(x) is -x^4-4x^3.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

given functions are f(x)=-x^3 and g(x)=x+4

       so,   fg(x)=f(x)*g(x)=-x^3(x+4)

Therefore, the value of

              fg(x)  = -x^4-4x^3

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The probability that the Texas Sharpshooters score exactly 1 goal next hockey game is 0.5

The following figure accurately depicts the table.

Experimental probability is the likelihood of a future event based on past happenings.

Experimental probability is equal to the ratio of good results to all possible results.

To calculate the likelihood that the Texas Sharpshooters will score precisely

Next hockey game: 1 goal

As displayed in the table:

a successful outcome is repeated four times.

So, positive results equal 4

8 total results

likelihood = 4/8 = 0.5

So, The probability that the Texas Sharpshooters score exactly 1 goal next hockey game is 0.5

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Answer:

0.50 (Choice C)

Step-by-step explanation:

Khan Academy told me.

The price for a children's ticket is $2.50

Now, According to the question:

A fundraising dinner was held on two consecutive nights.

Let the number of children's tickets be x.

Let the number of adults' tickets be y.

The total number of tickets sold is 937.50

On the first night, 100 adult tickets and 175 children's tickets

Therefore,

100x + 175y = $937.50

On the second night, 200 adult tickets and 316 children's tickets were sold for a total of $1790.

200x + 316y = $1790

Now, we have two simultaneous equations:

100x + 175y = $937.50 ----(1)

200x + 316y = $1790----(2)

Divide by 2 equation (2)

100x + 158y = $895----(3)

From the first equation, make y the subject of the formula:

100x = 937.50 - 175y

Put the value of 100x in equation (3)

937.50 -175y + 158y = $895

937.50 - 17y = $895

-17y = -42.5

y = 2.50

Hence, the price for a children's ticket is $2.50

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Answer: Solving a compound inequality in compact form is similar to solving a simple inequality in the sense that both involve isolating the variable on one side of the inequality and then using the same rules of inequality to find the solution set. Both compound and simple inequalities can be graphed as a line on a number line or coordinate plane, with the solution set being either all the numbers less than, greater than, or between two values, depending on the inequality sign.

However, solving a compound inequality in compact form is different from solving a simple inequality in that a compound inequality has two or more inequality statements combined using "and" or "or" connectors. When solving a compound inequality, we have to consider both inequalities together to find the final solution set. For example, when solving the inequality 3 < x < 5, we have to consider both 3 < x and x < 5, to find the range of x that satisfies both inequalities. And when we have a compound inequality with "or" connector like 3<x<5 or 6<x<8, we need to find the solution set for each inequality separately and then combine them.

So, the difference between solving a compound inequality and a simple inequality is that a compound inequality has multiple inequality statements that must be considered together to find the final solution set, while a simple inequality has only one inequality statement.

Step-by-step explanation:

The solution to the equation in the given interval is 2.365

From the question, we have the following parameters that can be used in our computation:

3sin(2x - 4) = 2

Divide both sides of the equation by 3

So, we have the following representation

sin(2x - 4) = 2/3

Take the arcsin of both sides

This gives

2x - 4 = 0.73

Evaluate the like terms

2x = 4.73

Divide by 2

x = 2.365

Hence, the value of x is 2.365

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A line of symmetry is the reflections map the figure onto itself.

A line of symmetry is, in other words, a line that splits a figure into two mirror representations. This line's reflection maps the figure onto itself. While some figures lack symmetry, others do feature one or more lines of symmetry. An example of a form having reflection symmetry is a rectangle.

The symmetry axes are shown and given the letters m and n. The figure will map to itself when reflected across either (or both) of the symmetry axes. It seems like you want to call those reflections...

Ra, where

a = m, and

Rb, where

b = n

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The probability that  randomly selected costume needs both shortened and taken in is 9/33

There are a total of n(T) = 33 costumes. Of these n(A) = 17 require alteration. The two sorts of change are shortening and taking in. n(S) = 15 costumes require shortening, and n(I) = 11 costumers require being taken in.

We are to determine the probability that a randomly selected costume requires both shortening and taken in.

The following is the formula for the union of sets.

P(S ∪ I) = P(S) + P(I) - P(S ∩ I)

∴ S ∪ I = A

∴ P(A) = P(S) + P(I) - P(S ∩ I)

∴ [tex]\frac{n(A)}{n(T)} = \frac{n(S)}{n(T)} + \frac{n(I)}{n(T)} - P(S \cap I)[/tex]

∴ [tex]P(S \cap I) = \frac{n(S)}{n(T)} + \frac{n(I)}{n(T)} - \frac{n(A)}{n(T)}[/tex]

Substituting the values:

∴ [tex]P(S \cap I) = \frac{15}{33} + \frac{11}{33} - \frac{17}{33}[/tex]

∴ [tex]\frac{26}{33} - \frac{17}{33}[/tex]

∴ [tex]\frac{9}{33}[/tex]

Therefore the probability that randomly selected costume needs both shortened and taken in is 9/33

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1. The probability of getting heads on the first two and then a tail on the third is 1/8.

2. The probability of not getting a clay pot or a cactus is  1/2.

3. The probability of getting the same number twice is 1/36.

4. The probability of getting at least two heads is

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

1. The probability of getting a head P(H) = 1/2 and the probability of getting a tail P(T) = 1/2.

Therefore, The probability of getting heads on the first two and then a tail on the third is,

= (1/2)×(1/2)×(1/2).

= 1/8.

2. The probability of getting a clay pot is 1/4 and the probability of getting a cactus is 1/4.

So, The probability of getting a clay pot or a cactus is 1/4 + 1/4.

= 2/4.

= 1/2.

Therefore, The probability of not getting a clay pot or a cactus is,

= 1 - 1/2.

= 1/2.

3. Suppose we get a number 1 on the first throw and we know its probability is 1/6,

Therefore, The probability of getting 1 again is also 1/6.

So, The probability of getting the same number twice is,

= (1/6)×(1/6).

= 1/36.

4. The probability of getting at least two heads is,

P(HHT) + P(HHH).

= (1/2)×(1/2)×(1/2) + (1/2)×(1/2)×(1/2).

= 1/8 + 1/8.

= 2/8.

= 1/4.

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Answer:

see below

Step-by-step explanation:

5000

60% = 3000 in stocks

year 1 gain 9% = 3000*1.09 =3270

year 2 loss 4% = 3270*(1-4%) =3139.2

40% = 2000 in savings

year 1 earn 4.9% = 2000*1.049 = 2098

year 2 earn 4.9% = 2098*1.049=2200.8

TOTAL in 2 years = 3139.2+2200.8 = 5340

so gain = 5340-5000 =340

if all only in savings:

5000*(1.049)² = 5502

Answer:1, 3, 9, 27

Step-by-step explanation:

The points G and H is the center of dilation from the points E, F, G, or H

What is Center of Dilation ?

The middle of a dilation is a hard and fast point inside the aircraft about which all points are increased or reduced in size. The middle is the handiest invariant (now not changing) factor below a dilation (k ≠1), and may be positioned inside, outdoor, or on a parent.

Given ,

In the Quadrilateral ABCD and its dilated image A′B′C′D′ are shown in the figure.

The points E, F, G, or H.

So, The center of dilation could be G and H .

Therefore, The points G and H is the center of dilation from the points E, F, G, or H

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If there are 5 girls, 6 boys and some adults in a classroom and probability that a girl is chosen is 1/3 , then the probability of an adult being chosen is  4/15 .  

The number of adults in unknown .

So let "n" denote the number of adults.

the number of girls in the room is = 5 girls ;

the number of boys in the group is = 6 boys ;

So , the total number of people to choose from will be =  5 + 6 + n  ;

= 11 + n ;

The probability of picking the girl from this group will be = 5/(11+n) ;

the probability of girl being selected is = 1/3,

Equating both the probabilities ,

we get ; 5/(11+n) = 1/3

On Cross multiplying we have :  11 + n = 15

which means ⇒ n = 4 and number of adults is = 4 ;

So ,the total number of people is = 11 + 4 = 15.

So , The probability of picking adult is = 4/15.

The given question is incomplete , the complete question is

There are 5 girls, 6 boys and some adults in a classroom. The probability that a girl is chosen is 1/3. What is the probability of an adult being chosen ?

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As per the concept of fraction, the amount time spend for each test is 1.67 hours

In math the term called fraction is known as  the number is expressed as a quotient in which the numerator is divided by the denominator.

Here we have know that Jordan spent 5 hours over the weekend studying for 3 tests.

In order to find the amount of time spend for each test, we have to divide the total number of subject by the time spend by him.

Here the value of total subjects = 5 and the amount of time spend by him is 3.

Then the amount of time time spend for each test is calculated as,

=> 5/3

=> 1.67 hours

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The original price of the house is 156,000

From the question,

The house was increased by 30% which leads to an increase to 156000

To get the original price of the house

Let the value of the house be x

We then multiply the original price of the house(x) by 30%

we have 0.30*x

0.30x = 156000

Divide both sides by 0.30

x = 520,000

Hence, 520000 is the original price of the house

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The length of string will be used to hang each pennant is 3.9 meters.

The term length in math is defined as the measurement or extent of something from end to end and it is used to identifying the size of an object or distance from one point to the other.

Here we have given that Ingrid has 14. 4 meters of string to hang 5 pennants and a banner at her school.

And here we have also know that she needs 0. 65 meter of string for the banner and the same length string for each pennant.

the length of the string needed for 5 pennants is calculated as,

=> 0.65 x (5 + 1)

=> 3.9 meter.

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The linear speed of the tip of this second hand as it passes around the clock face is 0.84 cm/ seconds

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

The formula and procedure we will use to solve this exercise is:

Where:

Information about the problem:

As the distance in the problem will be the circumference of the circle that second-hand makes in one complete revolution, we have:

Length of a circle = 2*pi*r

Length of a circle = 2*3.14*8

Length of a circle = 50.24 cm

The time it takes to complete one full revolution by second hand is 60 seconds, so applying the velocity formula with this time, we get:

speed = x /t

speed  = 50.24 cm/ 60 seconds

speed  =  0.84 cm/ seconds

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