Scarlett is deciding between two parking garages. garage a charges an initial fee of $11 to park plus $5 per hour. garage b charges an initial fee of $8 to park plus $6 per hour. let a a represent the amount garage a would charge if scarlett parks for t t hours, and let b b represent the amount garage b would charge if scarlett parks for t t hours. write an equation for each situation, in terms of t , t, and determine the hours parked, t , t, that would make the cost of each garage the same.

The value of the variable x in the equation 2log₂(x) - log₂(2x) = 3 is x =16

The equation is given as

2log₂(x) - log₂(2x) = 3

Apply the power rule of logarithm

So, we have

log₂(x²) - log₂(2x) = 3

Apply the quotient rule of logarithm

So, we have

log₂(x²/2x) = 3

Apply the change of base of logarithm

So, we have

x²/2x = 2^3

Evaluate the exponent

So, we have

x²/2x = 8

Evaluate the quotient

So, we have

x/2 = 8

Multiply both sides by 2

So, we have

x =16

Hence, the value of the variable x in the equation 2log₂(x) - log₂(2x) = 3 is x =16

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The value of the expression log 10,000 is 4.

The logarithmic function is the inverse of the exponential function. This means that the logarithm of a given number, say x, is the exponent to which another fixed number that is the base b, must be raised, so as to produce that number x.

Log a to the base b can be written as- log a/ log b.

Moreover, log [tex]a^{k}[/tex] = k log a, for all non negative values of a

Here, we are given a logarithmic expression- log 10,000

As the base is not given, we always assume it to be 10.

We can expand this as-

log 10,000 = log 10,000/ log 10

= log [tex]10^{4}[/tex]/ log 10

= 4 log 10/ log 10

= 4

Thus, the value of log 10,000 is 4.

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The quotient should have four significant digits, which is the number of significant digits required to divide the numbers into equal parts.

Consider the two numbers,

2.058 × 10⁹ and 3.0571 × 10⁻⁴

Now, let x = 2.058 × 10⁹ and;

y = 3.0571 × 10⁻⁴

When we dived these two equations.

( x / y) = [ 2.058 × 10⁹ / 3.0571 × 10⁻⁴ ]

The significant digits in the number with the smaller number of significant digits should be used to determine the number of significant digits in a quotient where two numbers are divided by one another.

Here, 2.058 × 10⁹ is the figure with the fewer significant digits.

Since 0 comes after non-zero numerals, this number has four meaningful digits.

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Answer:

No

Step-by-step explanation:

If you substitute, you get

2(5) - 10 >= 3

10 - 10 >= 3

0 >= 3, which is false!

If the inverse of f exists, it is represented by f⁻¹ and exists only if f is a bijective function.

The value of this function is h⁻¹(4) = 2.

The inverse function of a function f is a function that reverses the operation of f. The inverse of f exists if and only if f is bijective, and it is denoted by f⁻¹ if it exists.

Because they allow mathematical operations to be reversed, inverse procedures are essential for solving equations. When introducing a mathematical procedure, one of the most important questions is how to invert it.

Inverse operations are mathematical manipulations in which one operation reverses the action of the other, such as addition and subtraction, multiplication and division. In most cases, the inverse of a number is its reciprocal, i.e. x - 1 = 1 / x. A number and its inverse (reciprocal) product equals one.

Let the function be h(x)= 1/x+2  

h(x) = 1/x + 2 then

y = 1/x + 2

x = 1/y + 2

simplifying the equation, we get

x-2 = 1/y

x-2 = y⁻¹

h⁻¹(x) = x - 2

substitute the value of x = 4,

h⁻¹(4) = 4 - 2

h⁻¹(4) = 2

The value of this function is h⁻¹(4) = 2.

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I think the answer is x=4

Answer: x=4

Step-by-step explanation:

2x+3(5x-7)=47

2x+15x-21=47

17x-21=47

  +21  +21

17x= 68

17     17

x=4

Answer:  115

Step-by-step explanation: because   if you subtract 120 - 5 you get 115 so its 115

After solving the given equation log₃x = 4, the value of x = 81.

So,

Then,

Therefore, after solving the given equation log₃x = 4, the value of x = 81.

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The value of logarithmic expression 1/2 (logx4 + logx y) - 3 logx z as a single logarithm is (log4x^2y)^1/2/logx z^3

By considering the given  logarithmic expression

1/2 (logx4 + logx y) - 3 logx z

=1/2 (log4x^2y)-3 logx z

=(log4x^2y)^1/2- logx z^3

=(log4x^2y)^1/2/logx z^3

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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Answer:

its b:0.0333! (srry if its wrong)

Step-by-step explanation:

We're given:

First, we must identify the pattern:

This is our written pattern statement. To convert this into an expression, we can use the following format:

[tex]mn+b[/tex]

In this case, m is 6, and b is 2 - 6, or -4. Plug these numbers into the expression:

[tex]6n+(-4)\\6n-4[/tex]

To find the 42nd term, plug in 42 as n:

[tex]6n-4\\6(42)-4\\248[/tex]

The 42nd term is 248.

a₄₂= 248.

An arithmetic progression or arithmetic sequence (AP) is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.

If the initial term of an arithmetic progression is a and the common difference of successive members is d, then the n-th term of the sequence  

This is an arithmetic sequence since there is a common difference between each term. In this case, adding

6

to the previous term in the sequence gives the next term. In other words,

aₙ= a₁+ d (n-1)

substitute  in the values of a₁=2 and d=6

simplify each term

aₙ= 6n-4

substitute and calculate you will get

a₄₂= 248.

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If a 2 N and 6 N pull on an object to the right and a 4 N force pulls to the left a 0.5 kg object. The net force on the object  is: 4N.

First step is to calculate the force to the right

Force to the right = 2N+6N

Force to the right = 8N

Second step is to calculate the net force on the object using this formula

Net force= Force to the right- Force to the left

Where:

Force to the right = 8N

Force to the left = 4N

Let plug in the formula

Net force= 8N - 4N

Net force= 4N

Therefore if a 2 N and 6 N pull on an object to the right and a 4 N force pulls to the left a 0.5 kg object. The net force on the object  is: 4N.

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The solution of the given equation by rounding off it to the nearest ten-thousandth is 0.5185.

What is a round-off of the digit?

In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.

For eg: 13.58 ~ 13.6

Solving the given equation 9²x = 42

As given equation is 9²x = 42

81x = 42

x = 42 / 81

= 14 / 27

= 0.5185

Hence, the solution of the given equation is 0.5185.

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Answer:

CD ≈ 10.8

Step-by-step explanation:

calculate the distance using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1} )^2 }[/tex]

with (x₁, y₁ ) = C (- 5, 4 ) and (x₂, y₂ ) = D (5, 8 )

CD = [tex]\sqrt{(5-(-5)^2+(8-4)^2}[/tex]

     = [tex]\sqrt{(5+5)^2+4^2}[/tex]

     = [tex]\sqrt{10^2+16}[/tex]

     = [tex]\sqrt{100+16}[/tex]

     = [tex]\sqrt{116}[/tex]

     ≈ 10.8 ( to the nearest tenth )

Answer:

8,1 is the correct answer

Answer:

your question is empty please give right questions to get answers

The inverse of the function will be:

if x is an integer, then f⁻¹ (x) = x - 1

for all other x , f⁻¹ (x) = x - 2

We are given the function as:

if x is an integer, then f (x) = x + 1

for all other x , f (x) = x + 2

Now, we need to find the inverse of the function.

We will do it in 2 parts.

First we will find the inverse of f (x) = x + 1 and then of f (x) = x + 2.

For f (x) = x + 1:

y = x + 1

y - 1 = x

x = y - 1

f⁻¹ (x) = x - 1

For f (x) = x + 2

y = x + 2

y - 2 = x

x = y - 2

f⁻¹ (x) = x - 2

Therefore, the inverse of the function will be:

if x is an integer, then f⁻¹ (x) = x - 1

for all other x , f⁻¹ (x) = x - 2

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Tt would take 15 minutes for there to be exactly 60 gallons in the hot tube.

Proportion can be defined as the mathematical comparison of two numbers.

It is also known as an equation defining that the two given ratios are equivalent to each other.

From the information given, we have the following deductions;

To determine the time taken for 60 gallons to be left in the hot tube, we have to subtract the number from the total number of gallons, we have;

= 150 - 60

Find the difference

= 90 gallons

Now,

If 6 gallons are drained in 1 minute

Then 90 gallons are drained in x minutes

cross multiply

x = 90/ 6

x = 15 minutes

Thus, it would take 15 minutes for there to be exactly 60 gallons in the hot tube.

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Answer:

If the state is 0, then Alberto's is -3 and Rebecca's is +2 or 2

The distance between Alberto's and Rebecca's: 2 - (-3) = 2 + 3 = 5

Step-by-step explanation:

If the state is 0, then Alberto's is -3 and Rebecca's is +2 or 2

The distance between Alberto's and Rebecca's: 2 - (-3) = 2 + 3 = 5

No extraneous solutions to this equation.

The equation is

[tex](5x- 4)^{1/2}[/tex] - x = 0

To find the value of x

[tex](5x- 4)^{1/2}[/tex] = x

Now square on both sides of the equation.

We get

5x - 4 =[tex]x^{2}[/tex]

[tex]x^{2}[/tex] - 5x + 4= 0

[tex]x^{2}[/tex] - 4x - x + 4 =0

x( x -4 ) - 1 ( x - 4) =0

( x- 4 ) ( x - 1)= 0

x = 4, 1

We get the value of x as 4 and 1

Now we have to put the value of x in the equation

First, put 4

[tex](5x - 4)^{1/2}[/tex] -x =0

[tex](5 * 4 - 4)^{1/2}[/tex] - 4= 0

[tex](20 - 4)^{1/2}[/tex] - 4 =0

[tex]16^{1/2}[/tex] - 4 = 0

4-4 =0

0 = 0

Now put 1

[tex](5 * 1 - 4)^{1/2}[/tex] - 1 = 0

[tex](5 -4)^{1/2}[/tex] - 1=0

1 - 1=0

0=0

Hence we get that both the value of x is not an extraneous solution.

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The quadratic function of graph given characteristics vertex(1,\9); passes through (4,\6) is y=1/3x2+2/3x+26/3.

A quadratic function is a polynomial function with one or more variables where the highest exponent of the variable is two. Due to the fact that the biggest degree term in a quadratic function is of second degree, it is sometimes referred to as the polynomial of degree 2. There must be a quadratic function with at least one second-degree term. It performs algebraic operations.

Assum:y=ax2+bx+c

Point (1,9)(4,6) into it:{9=a+b+c/6=16a+4b+c} (point 1and 2)

Therefore, vertex(1,9) –b/2a=1→-b=2a

Point 3 into 1 and 2={9=-a+c/b=8a+c}

a=1/3, b=2/3, c=26/3

y=1/3x2+2/3x+26/3

For: y=ax2+bx+c

The graph intersects the x axis at x1 and x2,

X1= -b+√b2-4ac/2a , X2= -b-√b2-4ac/2a

The x-coordinate of the vertex must be in the middle of x1 and x2.

Assume the x-coordinate of the vertex as x

So : x=x1+x2/2 = -b+√b2-4ac/2a + -b-√b2-4ac/2a / 2 = -b/2a

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Answer: 1 and 7 over 10

Step-by-step explanation:

Answer:

[tex]\frac{1}{10}[/tex]

Step-by-step explanation:

[tex]\frac{9}{10} + ( -\frac{4}{5} )[/tex]

change the fraction  [tex]( -\frac{4}{5} )[/tex] to[tex]( -\frac{8}{10} )[/tex]

I multiplied both the denominator and numerator by 2

[tex]\frac{9}{10} + ( -\frac{8}{10} )[/tex]

simplify the negative

[tex]\frac{9}{10} -\frac{8}{10}[/tex]

subtract the numerator not the denominator

[tex]\frac{1}{10}[/tex]

Answer:

8.25 Hours she worked last week

Step-by-step explanation:

The possible pairs when rewriting the position and sequence values are (d) (1, 1), (2, 4), (3, 9), (4, 16), (5, 25)...

The sequence is given as

1, 4, 9, 16, 25...

The position and sequence values of the above sequence are

1, 2, 3, 4, 5...

1, 4, 9, 16, 25...

When represented as an ordered pair, we have

(1, 1), (2, 4), (3, 9), (4, 16), (5, 25)....

Hence, the possible pairs when rewriting the position and sequence values are (d) (1, 1), (2, 4), (3, 9), (4, 16), (5, 25)....

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Answer:

p = 2/5

Step-by-step explanation:

[tex]7p+8=12-3p \\ \\ 10p+8=12 \\ \\ 10p=4 \\ \\ p=2/5[/tex]

Answer: I think this is it

Step-by-step explanation:

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list. This is what is most often meant by an average. The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Given:

y = x³ + 2x +5

z = x² + 7x + 1

To find: Value of 2y + z in terms of x

Finding:

Now, 2y = 2 (x³ + 2x + 5) = 2x³ + 4x + 10

Then, 2y + z =  2x³ + 4x + 10 + x² + 7x + 1

=> 2y + z = 2x³ + x² + 11x + 11

Hence, Option C is the correct option.

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