Write each equation in logarithmic form.
1/4=4⁻¹

According to the question, the given rational expression can be simplified as below:

Rational Expression = [tex]\frac{3x-3}{x^{2} -x}[/tex]

To simplify the given rational expression which are in the form of polynomial expression, calculate the factors of numerator and denominator. The divide it from each other.

Rational expression = [tex]\frac{3x-3}{x^{2} -x}=\frac{3(x-1)}{x(x-1)}=\frac{3}{x}[/tex]

Therefore, the final answer of the given expression is [tex]\frac{3}{x}[/tex].

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

To learn more about the polynomial expression from the given link:

https://brainly.com/question/1280754

#SPJ4

Answer:

Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:

Step-by-step explanation:

Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:

Step 1: Understand the problem.

Step 2: Devise a plan (translate).

Step 3: Carry out the plan (solve).

Step 4: Look back (check and interpret).

The example using the polya's 4-steps in problem solving is created along with the answer.

Let's apply Polya's 4-step problem-solving process to the following word problem:

Problem: Lily has twice as many apples as John. Together, they have 27 apples. How many apples does each person have?

Step 1 - Understand the Problem:

To solve this problem, we need to find the number of apples that Lily and John each have. We know that Lily has twice as many apples as John, and together, they have 27 apples. We need to determine the number of apples for each person.

Step 2 - Devise a Plan:

Let's use algebra to represent the number of apples. Let's say the number of apples John has is "x." Since Lily has twice as many apples as John, the number of apples she has is "2x." We know that together, they have 27 apples, so we can set up an equation:

x + 2x = 27

Step 3 - Execute the Plan:

Now, we'll solve the equation to find the value of "x."

3x = 27

x = 27 / 3

x = 9

So, John has 9 apples. Now, we can find the number of apples Lily has:

Lily's apples = 2 * 9 = 18

Step 4 - Review the Solution:

John has 9 apples, and Lily has 18 apples. Together, they have 9 + 18 = 27 apples, which matches the information given in the problem. Therefore, the solution is correct.

Answer:

John has 9 apples, and Lily has 18 apples.

Learn more about polya's 4-steps here:

https://brainly.com/question/28453190

#SPJ7

The statements and reasons to prove that line j is parallel to line k include the following:

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

A supplementary angle can be defined as two (2) angles or arc whose sum is equal to 180 degrees (180°).

Mathematically, a supplementary angle can be calculated by using this formula:

Q + R = 180

Where:

Q and R are measure of the angles subtended.

Read more on vertical angles theorem here: brainly.com/question/17876852

#SPJ1

Adding the additive inverse of B (that is, “-B” which must exist in every Vector Space . A+B-B = 0 -B A= -B

What is magnitude vector?

The magnitude of a vector is the square root of the scalar product of that vector by itself.

l A l  = [tex]\sqrt{A . A}[/tex]

l B l = [tex]\sqrt{B . B}[/tex]

l A + B l  = [tex]\sqrt{( A + B ) . ( A + B ) } = \sqrt{AA + AB + BA + BB}[/tex]

l A + B l = [tex]\sqrt{l A l^{2} + l B I ^{2} + 2 .l A l l B l cos (angle) }[/tex]

In case |A+B| = |A| + |B|

That is the same as the condition that the squares are equal.

l A + B l² = ( l A l + l B l)² =  l A l²  + l B l²  + 2|A||B|

|A||B| cos(angle)=|A||B|

|A||B|[cos(angle)−1]=0

This happens if and only if :

Either |A| or |B| or [cos(angle) - 1] must be zero.

In case |A| and |B| are not zero then cos(angle) = 1, that is : angle = 0

That means B = c*A where c is a positive constant. And, also when either A or B (or both) are the zero vector.

The second question is easier:

|A+B| = 0 implies A+B must be the zero vector.

A+B = 0

then, adding the additive inverse of B (that is, “-B” which must exist in every Vector Space)

A+B-B = 0 -B

A= -B

Learn more about magnitude

brainly.com/question/28173919

#SPJ9

Answer:

see explanation

Step-by-step explanation:

the closest perfect square to 86 is 81 , then

[tex]\sqrt{81}[/tex] = 9 ← estimate value

using the calculator

[tex]\sqrt{86}[/tex] ≈ 9.27 ( to 2 dec. places )

189 students are expected to ride the bus to school if there are 350 students.

An equation is an expression that shows the relationship between two or more numbers and variables.

A survey of 24 students found that 13 out of the 24 ride the bus to school. Hence:

Rate at which student ride bus = 13/24

if there are 350 students in middle school:

Number of students expected to ride bus = (13/24) * 350 = 189.58

189 students are expected to ride the bus to school if there are 350 students.

Find out more on equation at: https://brainly.com/question/13763238

#SPJ1

Answer:

7+5p+4r+6s

Step-by-step explanation:

the same thing cause their variables are different, you can't add if the variables are different

variables are those letters that are at the end of the coefficient

Answer:

2,000

Step-by-step explanation:

because the 8 in the hundreds place is more than 5 and allows the number to be rounded up

Answer: 2,000

Step-by-step explanation:

the 1 next to the 8 makes that 1 to round up to a 2 which makes it 2,000.

Answer:

Step-by-step explanation:

2 : 2, 3 : 3

If you randomly choose two cards from a thoroughly shuffled deck and if you put the first card back in the deck before you draw the second then the probability that the first card is an ace and the second card is a king is 0.59%.

The probability that the first card is an ace and the second card is a king can be calculated as follows,

Initially, divide the expected outcomes by the total possible outcomes

As a deck has a total of 52 cards, the total possible outcomes are considered to be 52

A deck consists of 4 aces and 4 king cards

Hence,

the probability that the first card is an ace = 4 / 52

the probability that the second card is a heart = 4 / 52

The probability that the first card is an ace and the second card is a heart can be determined by multiplying the probability of an ace with the probability of heart,

Probability = (4/52)(4/52)

Probability = 0.0059

Converting into percentage,

Probability = 0.0059 × 100

Probability = 0.59%

Hence the probability that the first card is an ace and the second card is a king is calculated to be 0.59%.

To learn more about probability, click here:

https://brainly.com/question/251701

#SPJ4

For the pair of functions, (g⁰f)(x) is - 6 x ² - 3 x + 22 and (f ⁰g)(x) is - 18 x ² + 7 x - 5

The given questions asks to find (g⁰f)(x) and (f ⁰g)(x), that is, function of g in terms of f(x) and function of f in terms of g(x).

To find : (g⁰f)(x)

Step 1 : Write g (x)

=> g (x) = - 3x -1

Step 2 : Put f (x) in place of x in g (x)

=> g (f(x) = -3 ( 2 x ² + x - 7 ) + 1

=> g (f(x) = - 6 x ² - 3 x + 21  + 1

=> g (f(x) = - 6 x ² - 3 x + 22

=> (g⁰f)(x) = - 6 x ² - 3 x + 22

Similarly,

To find : (f ⁰g)(x)

Step 1 : Write f (x)

=> f (x) = 2 x ² + x - 7

Step 2 : Put g (x) in place of x in f (x)

=> f (g(x) = 2 ( -3 x - 1 ) ² + x - 7

=> f (g(x) = 2 - ( 9 x ² + 1 + 3 x ) + x - 7

=> f (g(x) = - 18 x ² + 2 + 6 x + x - 7

=> f (g(x) = - 18 x ² + 7 x - 5

=> (f ⁰g)(x) = - 18 x ² + 7 x - 5

Therefore, we get for the pair of functions, (g⁰f)(x) as - 6 x ² - 3 x + 22 and (f ⁰g)(x) as - 18 x ² + 7 x - 5

Learn more about Polynomials here:

brainly.com/question/11536910?referrer=searchResults

#SPJ9

Two or more expressions separated with an equal sign is called as equation. y=24-x is the value for y of equation 4x-y=24.

Two or more expressions separated with an equal sign is called as equation.

The given equation is

4x-y=24.

In the given equation x and y are variables.

We are required to solve for y variable.

subtract both sides by -4x

4x-y-4x=24-4x

-y=24-4x

Multiply both sides by minus

y=-24+4x

y=4x-24

Therefore the solution for y is 4x-24.

To learn more on Equation click:

https://brainly.com/question/10413253

#SPJ1

Answer:

x² + 9x + 20

Step-by-step explanation:

f(x) = x² + 5x + 6

g(x) = x + 2

Now, let us find (f o g)(x)

 (f  o g)(x) =  f(g(x))

               = f(x+2)

               = (x + 2)² + 5(x +2) + 6

{Identity used: (a + b)² = a² + 2ab +b²}

               = x² + 2*x*2 + 2² +5*x +5*2 + 6

               =x² + 4x + 4 + 5x + 10 + 6        

               = x² + 4x + 5x + 4 + 10 + 6

Combine like terms,

               = x² + 9x + 20          

Answer: Reflect the shape A in the line: y = -1 An investment has been growing in value at a rate of 8% per year and now has a value of $8200. Find the value of the investment in 5 years. Step by St …

explanation:

For the pair of functions, (g⁰f)(x) is 4 x ² - 7 and (f ⁰g)(x) is 16 x ² + 8 x - 1

The given questions asks to find (g⁰f)(x) and (f ⁰g)(x), that is, function of g in terms of f(x) and function of f in terms of g(x).

To find : (g⁰f)(x)

Step 1 : Write g (x)

=> g (x) = 4 x + 1

Step 2 : Put f (x) in place of x in g (x)

=> g (f(x) = 4 ( x ² - 2 ) + 1

=> g (f(x) = 4 x ² - 8 + 1

=> g (f(x) = 4 x ² - 7

=> (g⁰f)(x) = 4 x ² - 7

Similarly,

To find : (f ⁰g)(x)

Step 1 : Write f (x)

=> f (x) = x ² - 2

Step 2 : Put g (x) in place of x in f (x)

=> f (g(x) = ( 4 x + 1 ) ² - 2

=> f (g(x) = 16 x ² + 1 + 8 x -2

=> f (g(x) = 16 x ² + 8 x - 1

=> (f ⁰g)(x) = 16 x ² + 8 x - 1

Therefore, we get for the pair of functions, (g⁰f)(x) as 4 x ² - 7 and (f ⁰g)(x) as 16 x ² + 8 x - 1

Learn more about Polynomials here:

https://brainly.com/question/11536910?referrer=searchResults

#SPJ9

[tex](-8)^\frac{1}{2} \neq -(8^\frac{1}{2})[/tex] because 8 is an odd power of 2 and [tex](-27)^\frac{1}{3} = -(27)^\frac{1}{3}[/tex] because 27 can be written with the power which a multiple of 3.

Consider [tex](-8)^\frac{1}{2}[/tex].

We know that 8 = 2³

So [tex](-8)^\frac{1}{2}[/tex] = [tex](-2^3)^\frac{1}{2}[/tex]

Also there is no real value for this expression. If 8 had an even power, then we would have got a real value. Because here 3 does not cancel with 2 completely.

Now for [tex]-(8^\frac{1}{2})[/tex] , this expression means the negative sign of the square root of 8. Even though 8 is not an perfect square, 8 has a real square root value. So this expression gives a real value. But the previous one does not.

Hence, [tex](-8)^\frac{1}{2} \neq -(8^\frac{1}{2})[/tex]

Consider [tex](-27)^\frac{1}{3}[/tex] = [tex](-3^3)^\frac{1}{3}[/tex] = -3, canceling out the 3 on the denominator with the power of (-3).

Also,  [tex]-(27)^\frac{1}{3}[/tex] =  [tex]-(3^3)^\frac{1}{3}[/tex] = -3 again.

Hence  [tex](-27)^\frac{1}{3} = -(27)^\frac{1}{3}[/tex] .

This is because the power was a multiple of 3.

Learn more about exponents at https://brainly.com/question/847241

#SPJ4

Answer:

No.

Step-by-step explanation:

The sides are not scaled evenly. For a scaled polygon, you would want all the sides to be multiplied by the same number.

Answer: No because they are different numbers that dont reach the amount of the last one, example: 8/ 5 doesn't match 6 no 4 yes the only one and 6/ 2 yes/ 3yes/ 4no so if they did all match up then yes but it would be no

Step-by-step explanation: They are different numbers that don't reach the amount of the last one, example: 8/ 5 doesn't match 6 no 4 yes the only one and 6/ 2 yes/ 3 yes/ 4 no so if they did all match up then yes but it would be no.

The equivalent expression of the expression given as −3/4÷(−8/12) is 9/8

The expression is given as

−3/4÷(−8/12)

Rewrite the expression properly as

−3/4 ÷ (−8/12)

Express the expression as a product

So, we have

−3/4 ÷ (−8/12) = −3/4 x −12/8

Divide the common multiples

So, we have

−3/4 ÷ (−8/12) = −3/4 x −3/2

Evaluate the products

−3/4 ÷ (−8/12) = 9/8

Hence, the equivalent expression of the expression given as −3/4÷(−8/12) is 9/8

Read more about equivalent expression at

https://brainly.com/question/2972832

#SPJ1

The linear equation passing through (1, 4) and (6, -1) is y = -x + 5.

Linear equation can be represented in slope intercept form.

The line passes through the points (1, 4) and (6, -1).

The equation of the line can be represented as follows:

y = mx + b

where

Therefore, let's find slope using (1, 4) and (6, -1)

m = -1  - 4 / 6 - 1

m = - 5 / 5

m = -1

Therefore, let's find the y-intercept using (1, 4)

y = -x + b

4 = -1 + b

b = 4 + 1

b = 5

Therefore, the linear equation passing through (1, 4) and (6, -1) is y = -x + 5.

learn more on linear equation here:https://brainly.com/question/16186187

#SPJ1

Answer:

x  = 3/10   OR WRITE   x = 0.3

Step-by-step explanation:

2 (8 x + 5)  - 11  +9x =  (5x + 2)     regroup  (16 x +10) -11 + 9 x = (15x + 2) = 25x -1       as ( we did 10 -11 also)    then    25x -1  =  15x + 2    =  25x  = 15x + 3 = 10x = 3   =  x  = 3/10  x = 0.3

If 6 different colored tiles are available to make a pattern in a row of floor tile. The number of  possible different 4-color patterns that are possible if no colors may be repeated is: 360.

Given:

Different colored tiles=6

Different color patterns=4

There are 6 different colored tiles if one colored tiles is pick there will be 5 colored tiles, if two colored tiles is pick there will be 4 colored tiles, if  three colored tiles is pick there will be only 3 colored tiles left.

Hence,

Possible different color patterns=(6×5×4×3)

Possible different color patterns=360 ways

Therefore If 6 different colored tiles are available to make a pattern in a row of floor tile. The number of  possible different 4-color patterns that are possible if no colors may be repeated is: 360.

Learn more about Possible different color patterns here:https://brainly.com/question/23637336

#SPJ1

  The value of the square root of the number 100 is 10.

  The square root is a mathematical operation considered the inverse of raising a number to a square power.

  To determine the square root of a number we must find a number that approaches the result with a square exponential operation or a product between itself, but in this case we will decompose into factors, since the root is not integer.

   If we want to determine the root of 100, we express:

√100, now we find a number that multiplied by itself gives us 100, and this numeor is the 10

√100 = √10² = 10

Learn more about square root in:

https://brainly.com/question/467099

#SPJ4

The solution for the given Logarithms equation  2 log₃x=54 is x = 3²⁷ in the nearest ten-thousandth =  7625597484987.

Exponential functions have logarithmic inverses. A log is thus an exponent! y=logbx if and only when by=x for all x greater than zero and 0b1.

Logarithms depict changes in terms of multiplication: each step in the preceding instances is 10x larger. Each step is "e" (2.71828...) times longer using the natural log. When dealing with such a sequence of multiplications, logarithms assist in "counting" them in the same way as addition assists us in counting when effects are added.

Given  2 log₃x=54

Divide both side by 2:

(2 log₃x)2 = 54/2

simplify.

log₃(x)  = 27

apply log rule:

x = 3²⁷

Decimal value of x = 3²⁷ = 7625597484987

The solution for the given Logarithms 2 log₃x=54 is x = 3²⁷ in the nearest ten-thousandth =  7625597484987

To know more about Logarithms visit:

https://brainly.com/question/24211708

#SPJ4

The probability that a cartridge is classified as not underfilled is 0.85, while the probability that a cartridge is either overfilled or underfilled is 0.55.

Probability is defined as the likeliness of an event to occur, and ranges from 0 to 1 or can be expressed as percentage.

(a) If a cartridge is classified as not underfilled, it means that it is either medium filled or overfilled. Then the probability of that is the sum of the probabilities of the two.

P(underfilled) = P(overfilled) + P(medium filled)

P(underfilled) = 0.40 + 0.45

P(underfilled) = 0.85

(b) If a cartridge is either overfilled or underfilled, then its probability is the sum of their probabilities.

P(either overfilled or underfilled) = P(overfilled) + P(underfilled)

P(either overfilled or underfilled) = 0.40 + 0.15

P(either overfilled or underfilled) = 0.55

Learn more about probability here: https://brainly.com/question/24756209

#SPJ4

Answer:

The length of a rectangle is 6 meters longer than three times its width. If the total perimeter is 468 meters, what are the dimensions of the rectangle?

the answer would be 177

The value of p is 54.

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called Substitution method.

The equation is given as:

3/2 p - 14 = p + 13

Now, We can solve the expression as;

3/2 p - 14 = p + 13

Add 14 in both side,

3/2 p - 14 + 14 = p + 13 + 14

3/2 p = p + 27

Subtract 'p' from both side,

3/2 p - p = p + 27 - p

3/2 p - p = 27

1/2 p = 27

Multiply 2 in both sides,

p = 54

Hence, The value of p is 54.

Learn more about the substitution method visit:

https://brainly.com/question/3774975

#SPJ1

Answer:

5y

Step-by-step explanation:

if you add 5+y then it'll be 5y, you just add the two terms together