Find the inverse of each function. Is the inverse a function?
y=3 x+1

Answer:

0.2075

Step-by-step explanation:

Or $0.2075 per oz

The answer for the given logarithmic function is 5/2

Logarithm is a mathematical tool used to make high value calculations simple.

It is the exponent to the power of which a number must be raised to give a certain result.

Some of the important formulas in logarithm are:

loga where a is considered as base of the logarithm and b is the argument

is given as nlogab

when base and the argument is same , log is given as 1

logabc where a is the base is given as logab+logc

loga b/c where a is the base is given as logab-logac

Now it is given to us to find the value of log₄32

where 4 is the base and 32 is the argument

We know that logₐb can be written as log₂b/log₂a

using this identity of logarithm,

our question becomes log₂32/log₂4

32 = 2x2x2x2x2 which is

hence  can be written as 2^5

Thus the logarithmic function becomes

log₂2^5/log₂2^2=5log₂2/2log₂2

thus it becomes 5/2

Aa log2/log2 becomes 1

Thus log₄32= 5/2

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Step-by-step explanation:

5 minus 5 is 0,then 3 minus 2 is 1,therefore the answer is 1xy

The radius is 169 inches.

As per the known fact, the radius and area of circle are related by the formula -

Area = πr²

So, rewriting the expression in equation -

r=√(A/π)²

As mentioned, r is the radius and A is the area of the circle and π is constant

Keep the value of A in the above mentioned rewritten equation to find the value of radius of circle.

r = √(169π/π)²

On solving the above equation we get the new equation, which is as follows -

r = 169π/π

Cancelling π as it is common in both numerator and denominator

r = 169 inches

Hence, the radius of circle is 169 inches.

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Answer:

36

Step-by-step explanation:

3/4x = 18  multiply both sides by 4/3

(4/3)(3/4)x = (18/1) (4/3)

x = 24  There are 24 boys in the class.

2/3x = 24  Multiply both sides by 3/2

(3/2)(2/3)x = (24/1)(3/2)

x = 36

By solving a linear equation , we get the total number of students in the class are 36

An linear equation is a mathematical statement consists of expressions of only one variable that too with power 1 and constants and  compares two such expressions by equating them.

Standard form of  linear equation in one variable : ax +b = c

x = (c-b)/a

Let the total number of students in the class are  x

Given that 2/3 of the students in a class are boys

∴ The number of boys = 2/3(x) =(2x)/3

Then given that 3/4 of the boys are right handed and there are 18 right-handed boys

∴ 3/4( no of boys ) =18

⇒3/4 *(2x/3) =18

⇒(3*2x)/(4*3) =18

⇒x/2 =18

Multiplying both sides by 2

⇒x = 2*18 = 36

Therefore, the total number of students in the class are 36

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When all the four operations namely addition, subtraction, multiplication and division are involved in a problem, we perform the operations in the following sequence from left to right i.e. division, multiplication, addition and subtraction, remember the order as DMAS.

Easy and simple way to remember PEMDAS rule!!

P → Parentheses first

E → Exponent (Powers, Square Roots, Cube Roots, etc.)

MD → Multiplication and Division (start from left to right)

AS → Addition and Subtraction (start from left to right)

Note:

(i) Start Multiply/Divide from left side to right side since they perform equally.

(ii) Start Add/Subtract from left side to right side since they perform equally.

For Example; (7 + 8) × 3

First solve inside ‘parentheses’ 7 + 8 = 15, then 15 × 3 = 45.

Next solve the mathematical 'Exponent'.

For Example; 32+ 5

First solve ‘exponent’ part 32= 3 × 3 = 9, then 9 + 5 = 14.

Next, the part of the equation is to calculate 'Multiplication' and 'Division'.

We know that, when division and multiplication follow one another, then their order in that part of the equation is solved from left side to right side.

For Example; 21 ÷ 7 × 12 ÷ 2

‘Multiplication’ and ‘Division’ perform equally, so calculate from left to right side. First solve 21 ÷ 7 = 3, then 3 × 12 = 36, then 36 ÷ 2 = 18.

In the last part of the equation is to calculate 'Addition' and 'Subtraction'. We know that, when addition and subtraction follow one another, then their order in that part of the equation is solved from left side to right side.

For Example; 9 + 11 - 13 + 15

‘Addition’ and ‘Subtraction’ perform equally, so calculate from left to right side. First solve 9 + 11 = 20, then 20 - 13 = 7 and then 7 + 15 = 22.

These are simple rules need to be followed for simplifying or calculating using PEMDAS rule.

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Answer:

1/4

Step-by-step explanation:

or 90/360

Answer:

Step-by-step explanation:

No, They do not.

Answer:

All sides of a parallelogram have the same length.

Step-by-step explanation:

A parallelogram can have one pair or two pairs of parallel sides. All sides of a parallelogram have the same length. All angles of a parallelogram have the same measure.

Expression as a single natural logarithm. 1/3(ln x+ln y)-4 ln z is

[tex]ln( xy^{1/3})[/tex] -[tex]ln (z^{4} )[/tex]

[tex]ln (xy^{1/3} /z^{4} )[/tex]

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

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Answer:

Below in bold.

Step-by-step explanation:

7x - 2 + 9x - 2 + 2(5x) = 2(5x + 5) + 2(4x)

7x + 9x + 10x - 4 = 10x + 10 + 8x

7x + 9x + 10x - 10x - 8x = 10 + 4

8x = 14

x = 14/8 = 7/4

So, ST = 5*7/4 + 5

           = 55/4

           = 13 3/4

Answer:

ST = 13.75

Step-by-step explanation:

The perimeter of a trapezium is calculated with the following formula:

P = a + b + c + d (a, b: bases, c, d: sides)

The perimeter of a rectangle is calculated with the following formula:

P= 2(a + b) (a: base, b: side)

we will write the following equation to find the length of ST

7x - 2 + 9x - 2 + 5x + 5x = 2(5x + 5 + 4x) first do the inside the parenthesis

2(9x + 5) = 18x + 10

Now,

7x - 2 + 9x - 2 + 5x + 5x = 18x + 10 add like terms on the left side of the equation

26x - 4 = 18x + 10 transfer like terms to the same side of the equation

26x - 18x = 10 + 4 add/subtract

8x = 14 divide both sides by 8

x = 1.75 replace x with this to calculate the lentgh of ST

5x + 5 = 5*(1.75) + 5 and ST = 13.75

Answer: GCF = 6

Step-by-step explanation:

The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54

Then the greatest common factor is 6.

The equation will be 3 y = 2 x + 12 for the graph given.

We are given a graph of the equation.

We need to find the equation of the graph.

Now, first we will see the x and y intercept of the graph.

So, we get that:

x intercept:

( - 6 , 0)

y intercept:

(0 , 4)

Now, we know that equation of the line is given by:

y = a x + b    … (1)

Put the points in the equation:

for (-6 , 0)

0 = - 6 a + b

6 a = b     … (2)

for (0 , 4)

4 = b

Put in (2)

6 a = 4

a = 4 / 6

a = 2 / 3

Put in equation (1):

y = 2 / 3 x + 4

y = ( 2 x + 12 ) / 3

3 y = 2 x + 12

Therefore, we get that, the equation will be 3 y = 2 x + 12 for the graph given.

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Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

now we also know that

length = 1/3 × width + 5

so, when we bring this into the main equation for the perimeter :

2× (1/3 × width + 5) + 2×width

2/3 × width + 10 + 2×width

2/3 × width + 10 + 6/3 × width

8/3 × width + 10

The average number of miles he would have to ride each day to meet his goal is 8 miles

From the question, we are to write an equation that can be used to determine m, the average number of miles he would have to ride each day to meet his goal

From the given information,

Landon wants to ride his bicycle 36 miles this week and he has already ridden 4 miles.

The average number of miles, m, he would have to ride for 4 more days to meet his goal is

m = (36-  4)/4

This is the equation that can be used to determine m, the average number of miles he would have to ride each day to meet his goal

Now, determine m

m = (36 - 4)/4

m = 32/4

m = 8

Hence, the average number of miles he would have to ride each day to meet his goal is 8 miles

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Answer:

6

Step-by-step explanation:

2,4,6,8,10

6,12,18,24

The least number that is on both lists is 6

Answer:

7.5 × 10[tex] {}^{2} [/tex] (scientific notation)

Step-by-step explanation:

➟ 750 = 7.5 × 10[tex] {}^{2} [/tex] (scientific notation)

Answer:

28/5

Step-by-step explanation:

7 x 4/5 = 28/5

use keep, change, flip

Answer:

28/5

Step-by-step explanation:

just did it on khan academy.

Answer:

T=x(T*2) where X=660

Step-by-step explanation:

If it has been 2 hours than t=2

plug in 2 for t and you get x*4

Answer:

28 = x

Step-by-step explanation:

We have two similar triangles.  The ratio of the sides must be in the same proportion

12           8

------- = -------

x-7         14

Using cross products

12 * 14 = 8(x-7)

168 = 8(x-7)

Divide each side by 8

168/8 = 8(x-7)/8

21 = x-7

Add 7 to each side

21+7 = x-7+7

28 = x

(a) The expression to represent the difference between the elevations is 5764 - ( - 9).

(b) The answer will be a positive integer.

(c) The difference between the highest and lowest point is 5773 feet.

The elevation of a county is 5764 feet above sea level.

The elevation of the county is 9 feet below sea level at the lowest point.

(a) The highest point = 5764 feet

The lowest point = 9 feet

Then the difference between the highest and the lowest point will be:

difference = Highest - lowest

difference = 5764 - ( - 9)

(b) The answer will be written as a positive integer.

(c) The difference between the highest and lowest points of the county will be:

difference = Highest - lowest

difference = 5764 - ( - 9)

difference = 5764 + 9

difference = 5773 feet

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The complete question is mentioned below:

At its highest point, the elevation of a county is 5764 feet above sea level. At its lowest point, the elevation of the county is 9 feet below sea level. Answer parts (a) through (c).

a. Write an expression using integers to represent the difference between the elevations.

b. Will the answer be written as a positive or negative integer?

c. What is the difference between the highest and lowest points of the county?

The equation for red graph is y= f(x-1)

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

Given:

y = f(x)

Here if look at the graph with black with function f(x) = x

Now, if we look at the graph closely to shift the black graph to red.

There is shifting the graph in the right hand side which which gives the function y= f(x-1)

Hence, the equation for red graph is y= f(x-1)

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The histogram based on the data distribution where sample mean is less than sample median, the histogram would be skewed to the left.

Histogram is a type of visual (graphical) representation a set of data arranged in a user specific range. It is used summarize data – both discrete and continuous, measured on a interval scale.

When a data whose mean value or average value is less than the median or middle term in an ordered set is represented by a histogram, the shape of the histogram would be skewed to the left. Most of the data in such a histogram will be on the right side of the graph.

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Denote by x the number of cones sold or produced.

Denote by C(x) the total cost.

Denote by R(x) the revenue made.

Denote by P(x) the net profit accumulated.

[tex]C_{T}(x)=C_{fixed}+C_{variable} \: \\ C_{T}(x)=36+0.52x[/tex]

[tex]R_{T}(x)=selling \: price \: x \\ R_{T}(x)=1.4x[/tex]

[tex]P(x)=R_{T}(x)-C_{T}(x) \\ P(x)=1.4x-(36 + 0.52x) \\ P(x)=1.4x - 36 - 0.52x \\ P(x)=0.88x - 36[/tex]

If there exists profit, then P(x) has to be positive.

[tex]P(x) > 0 \\ 0.88x - 36 > 0 \\ 0.88x > 36 \\ x > \frac{36}{0.88} \\ x > 40.90909 \\ x = 41[/tex]

Answer:

3/8 cup

Step-by-step explanation:

You simply divide 3/4 by 2 and get a 0.375

We turn the decimal into a fraction and get 375/1000 then simplify the fraction to 3/8

The number of hours the fifteen people took to clean the cars is 4 hours.

Given that, on Monday, 12 people took 5 hours to clean a number of cars. On Tuesday, 15 people cleaned the same number of cars.

The rate of doing work is equal to the rate of using energy since the force transfers one unit of energy when it does one unit of work.

Assuming that all the people worked at the same rate, work out how many hours the 15 people took to clean the cars.

Now, based on the given conditions, formulate 12 × 5 ÷ 15

= (12 × 5) ÷ 15

= 60 ÷ 15

= 4 hours

Therefore, the number of hours the fifteen people took to clean the cars is 4 hours.

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The percent increase or decrease of the starting and ending quantities below are:

The percent increase can be found by the formula:

= (End - Start) / Start x 100%

The percent increase of these quantities are:

= (10 - 3) / 3 x 100%

= 7 / 3 x 100%

= 2.3333 x 100%

= 233%

= (20 - 9) / 9 X 100%

= 11/9 x 100%

= 1.222 x 100%

= 122%

= (85 - 100) / 100 x 100%

= -15 / 100 x 100%

= -15%

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Answer: Not the solution

Step-by-step explanation:

Based on the given parameters, the explicit rule of the sequence is b(n)= 2^n

The given parameters are

b(1) = 2

b(n) = 2 * b(n - 1) for n >= 2

Calculate b(2) and b(3) using the above equation

When n = 2, we have

b(2) = 2 * b(2 - 1)

This gives

b(2) = 2 * b(1)

So, we have

b(2) = 2 * 2

Evaluate

b(2) = 4

When n = 3, we have

b(3) = 2 * b(3 - 1)

This gives

b(3) = 2 * b(2)

So, we have

b(3) = 2 * 4

Evaluate

b(3) = 8

So, the sequence is

2, 4, 8.....

The above sequence is a geometric progression

The common ratio (r) is calculated as

r = b(2)/b(1)

So, we have

r = 4/2

Evaluate

r = 2

The explicit rule of the sequence is calculated as

b(n)= b(1) * r^n-1

So, we have

b(n)= 2 * 2^n-1

Evaluate

b(n)= 2^n

Hence, the explicit rule of the sequence is b(n)= 2^n

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Possible question

Calculate the explicit rule of the sequence

b(1)=2, b(n)=2⋅b(n−1)−1 for n≥2.

Answer:

7/2z +4

Step-by-step explanation:

z(4-1/2)+4

=7/2z +4

Answer:

7.5

Step-by-step explanation:

Remove parentheses; z=4-1/2+4

Add the 4s: -1/2+8

convert to fraction: 8*2/2-1/2

combine fractions:8*2-1/2

8*2-1=15

15/2

now convert 15/2 to a decimal, boom, 7.5