f(x)=b x and g(x)=logbx are inverse functions. Explain why each of the following is true.
c. The inverse of f₁(x)=b x-h is not equivalent to a vertical stretch or compression of g .

The greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex] is [tex]10x^{4} y[/tex] .

The greatest common factor of a set of numbers is defined as the largest number that divides all the numbers in that given set and leaves 0 as remainder in each case.

In the given expression

[tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex]

Applying Prime Factorization and Writing all the terms in the above expression as

[tex]20x^{6} y=10x^{4}y *2x^{2}[/tex]

[tex]40x^{4} y^{2} =10x^{4} y*4y[/tex]

[tex]10x^{5} y^{5} =10x^{4}y*xy^{4}[/tex]

As we can see that [tex]10x^{4} y[/tex] is common and greatest in all the terms .

Hence [tex]10x^{4} y[/tex] is the Greatest common factor.

Therefore , the greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex] is [tex]10x^{4} y[/tex] , the correct option is (a)[tex]10x^{4} y[/tex].

The given question is incomplete , the complete question is

What is the greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex]

(a)[tex]10x^{4} y[/tex]

(b)[tex]5x^{2} y^{5}[/tex]

(c)[tex]5x^{4} y[/tex]

(d)[tex]20x^{6} y[/tex]

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The coordinates of endpoint B are (-7, 11)

From the question, we are to determine the coordinates of the endpoint B

If the coordinates of the endpoints of a line, AB, are A(x₁, y₁) and B(x₂, y₂), then the coordinates of the midpoint is given by

((x₁+x₂)/2, (y₁+y₂)/2)

From the given information,

The coordinates of A are (3, 7) and the coordinates of the midpoint are (-2, 9)

Let the coordinates of endpoint B be (x, y)

Then,

(3+x)/2 = -2

3 +x =-4

x = -4 -3

x =  -7

and

(7 + y)/2 = 9

7 + y = 18

y = 18 - 7

y = 11

Hence, the coordinates are (-7, 11)

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The function's formula is given by c=150-8s .

It is given in the question that

number of candies taken by tyrone in each snack  = 8

number of times tyrone snacks = 18

Total candies= (number of times tyrone snacks)x(number of candies taken in each snack )

Total candies=18x8=144.

There are 6 candies left in the bag .

So total candies = 144+6=150.

It is also given that "s" is the number of snacks tyrone eats .

and "c" is the number of candies remaining.

number of candies tyrone eats in each snack = 8

number of candies tyrone eats in s each snack =8s

the number of candies remaining = (total candies) - (number of candies tyrone eats in s each snack ).

Substituting the values we get

c=150-8s.

Therefore , the function's formula is given by c=150-8s .

The given question is incomplete , the complete question is

Tyrone likes to snack on his big bag of candy. he takes 8 pieces of candy from the bag each time he snacks. after he has snacked 18 times, there are only 6 pieces of candy remaining in the bag. the number "c" of pieces of candy remaining in the bag is a function of s, the number of snacks Tyrone eats. Write the function's formula.

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Answer:

3000 = 2*2*2*2*3*5*5*5

Step-by-step explanation:

6000/2 = 3000

3000/3 = 1000

1000/2 = 500

500/2 = 250

250/2 = 125

125/5 = 25

25/5 = 5

5/5 = 1

3000 = 2*2*2*2*3*5*5*5

The trench will require 9168 cubic feet of dirt to be removed.

Here, we are given that a homeowner is digging a 3 -ft-deep trench around the perimeter of his property.

Length of the property = 210 feet

Breadth of the property = 180 feet

Let us now consider one side of the 180-foot-long trench.

There are two such trenches, each with a width of 4 feet and a height of 3 feet.

Thus the volume of the trench = 2(length × breadth × height)

Volume = 180 × 4 × 3 × 2

= 4320 cubic feet

Now we are left with two other sides of the trench with the following dimensions-

Height = 3ft

Breadth = 4ft

Length = 210 - 8 = 202ft

Thus, volume = 202 × 4 × 3 × 2

= 4848 cubic feet

Thus, the total volume of the trench = 4848 + 4320 = 9168 cubic feet.

Hence, The removal of 9168 cubic feet of earth is necessary.

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Your question was incomplete. Check for the missing figure below.

Prime factorization of 10 x 4  is 2 x 5 x 2 x 2.

Finding the prime numbers that are multiplied together to produce the original number is the process of prime factorization. The prime factors of 16, for instance, are 2 x 2 x 2 x 2.

Any number can be represented as a sum of prime numbers by prime factorization. A number with exactly two factors, 1 and the number itself, is said to be a prime number. As an illustration, the prime factorization of 18 is 2 x 3 x 3. Here, the two main factors of 18 are 2 and 3. For instance, 72 = 2 x 3 x 3  x 2 can be written as a product of prime factors. The prime factorization of 72 is said to be the expression 2 x 3 x 3  x 2.

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Answer:4
7
82
83

Step-by-step explanation:

REALLY EASY

Answer:

[tex]19\%[/tex]

Percentages are evaluated values that say how much of a whole is occupied by that value. For example, if we were to say 75% of a strawberry pie remained, we could also see this as 3/4, or three-fourths.

To solve this particular problem, we will need to divide two values and convert a decimal to a percentage.

First, set up the fraction of economics majors that are freshman students to the total number of freshman students.

[tex]\displaystyle \frac{1634}{8600}[/tex]

Then, divide the two using a calculator or long division.

[tex]\displaystyle \frac{19}{100}[/tex]

Finally, to convert this to a decimal, use a calculator.

[tex]0.19[/tex]

To convert a decimal to a percentage, multiply the decimal by 100.

[tex]0.19 \times 100 = 19\%[/tex]

The final answer is [tex]19\%[/tex].

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Answer:

19%

Key Points:

In order to find the percentage of freshman majoring in economics, we must divide the econ major students by the overall size of the freshman class.

[tex]\frac{1634}{8600}[/tex]

Our next step is to grab a calculator and input 1634 ÷ 8600. You can alternatively use the long division method but a calculator would work best. After calculating, your answer should come out to be 0.19

Now, you need to multiply it by 100 so that you can create a percentage.

0.19 × 100 = 19%

Therefore, 19% of the freshman class are economics majors.

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Answer:

Okay? whats the question

Step-by-step explanation:

Answer:

the answer to that question is 3

[tex]y = \begin{cases}- 2x + 1& x > 1 \\- x + 2&x\leqslant1\end{cases}[/tex]

from the figure

[tex](x_1,y_1) \: (x_2,y_2) = >y = \frac{y_2 - y_1}{x_2 - x_1} \: x + a \\ a = y_1 - \frac{y_2 - y_1}{x_2 - x_1} \: x_1[/tex]

ln(e²) = 2, by properties of logarithm.

Now, as we know by properties of logarithm, [tex]log_b(a)^m = m(log_b(a))[/tex],

ln (e²) = 2 ( ln(e))

Also, as ln (e) = 1, ln (e²)  = 2 (1) = 2.

Hence, ln(e²) = 2, by properties of logarithm.

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Using scientific notation, the number of significant digits that the product should have is:

B. 3.

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

When two numbers in scientific notation are multiplied, we have that:

For this problem, the product is given by:

[tex]5.2187 \times 10^{-3} \times 2.05 \times 10^7 \times 3.4 \times 10^3[/tex]

Multiplying the bases and adding the exponents, we have that:

[tex]5.2187 \times 2.05 \times 3.4 \times 10^{-3 + 7 + 3} = 42.8 \times 10^{7}[/tex]

42.8 has to be divided by 10 to assume for the base have only one digit, hence:

[tex]42.8 \times 10^{7} = 4.28 \times 10^6[/tex]

Hence, considering the rounding, the number has 3 significant digits(4, 2 and 8), and option B is correct.

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An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . The simplified expression of  (6 x 10⁻⁴)(6 x10⁻⁶) is 36 x10⁻¹⁰.

An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.

(6 x 10⁻⁴)(6 x10⁻⁶) is the given expression

Now multiply 6 with 6 and   10⁻⁴ with 10⁻⁶

36 x 10⁻⁴x  10⁻⁶

We need to add the powers of same base.

36 x10⁻⁴⁻⁶

36 x10⁻¹⁰

Therefore the simplified expression of (6 x 10⁻⁴)(6 x 10⁻⁶) is 36 x10⁻¹⁰.

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Answer:

Number 1 is 4

Number 2 is 10

Step-by-step explanation:

Number 1 is x

Number 2 is 3x - 2

so x + (3x - 2) = 14

x + 3x - 2 = 14

4x = 14 + 2

4x = 16

x  = 4

so

Number 1 is 4

Number 2 is 3(4) - 2 = 10

Answer:

25

Step-by-step explanation:

If youre going by 5's youd get 30 but then you gotta take away -5 so it comes out to 25

Answer:

25

Step-by-step explanation:

There are 10000 different possible codes to guess the correct code on the first try..

A percentage, or a figure between 0 and 100 percent, can also be used to express probability. The likelihood of an event occurring increases with its probability value or percentage. How many potential outcomes an event has will determine how likely it is to occur.

1)There are 5040 possible codes if the digits are not repeated.

2)Probability of guessing correct code on first try p = 1/5040.

3)There are 10000 different codes, if the digits are repeated.

Given,

Total digits = 10.

{0,1,2,3,4,5,6,7,8,9}

4 digit code must be formed.

1. Code without repeating digits

 → 4 digit code

Therefore possible ways = 10×9×8×7

= 5040

2. Probability of guessing correct code on first try.

n(A)→ event which has correct code=1

n(S)→total possible ways=5040.

P(A) = n(A)/n(S) = 1/5040

3. If the digits are repeated

→ 4 digit repeated

Therefore possible ways = 10×10×10×10

= 104

= 10000 ways

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Answer: (Looking back, I may have gotten this question wrong, but if I haven't then nice.)

a) 13 degrees

b) acute angle

Step-by-step explanation:

Given that we know a triangle is 180 degrees. Lets recall what an obtuse, acute, right and reflex angle are.

Obtuse: An angle greater than 90 degrees

Acute: An angle less than 90 degrees

Right: An angle that is 90 degrees

Reflex: An angle in between 180-360 degrees

Since we know that two of the three angles are 54 and 113 degrees, we can say that 54+113+x=180. That means that the missing angle, x, is 13 degrees.

Knowing that 13 is less than 90, we can also say that the third angle is an acute angle.

Answer:

y=x+6

Step-by-step explanation:

The gradient of the line is change in y/ change in x

Thus meaning the gradient is 1. (defined as x)

The line crosses through the y-axis on the point (0,6)

So your euqation will be y = (1 - the gradient) x + (interception of y-axis) 6

Answer:

y = x + 6

Step-by-step explanation:

The general form of an equation of a line is

y= mx+b

y = slope ·x + y-intercept

Find the slope of the line, m:

-Pick any 2 points on the line, for example lets pick the points (0, 6) and (3, 10)

-Start at any of the points and go towards the other while note the path

start at (0, 6) and to go to (4, 10) we have to

go up (rise) 4 units  from 6 to 10 and

go to the right (run) 4 from 0 to 4.

Slope = m = rise/run = 4/4 = 1

m = 1

Find the y-intercept, b:

The y-intercept is where the line intersects the y-axis. By looking at the given graph we can see y-intercept is 6.

b = 6

The equation of our line is

y = x + 6

Six hundred residents of a city are polled to obtain information on voting intentions in an upcoming city election. The 600 residents in this study is an example of a sample.

Those people who make up a sample are taken from a broader population. Sampling is the process of deciding which group you will use to gather data for your study.

In order for a sample to be representative of the population we are interested in investigating, each participant must have an equal chance of being randomly chosen for the study.

For example, you could interview a sample of 100 students if you were examining the attitudes of students at your university.

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Based on the information provided,  neither Brandi nor Sharana jogged at a slower rate.

Rate can be defined as the speed at which an event happens or an object moves over a particular period of time.

It is also known as the ratio at which two or more term, quantities or objects with different units are compared.

The formula for rate is expressed as;

Rate = distance/ time

From the information given, we have that;

Substitute the values

Brandi's rate = 1/ 30 = 0. 03

Sharana's rate = 1. 5/ 45 = 0. 33

From the values gotten, we can see that neither Brandi nor Sharana jogged at a slower rate.

Thus, neither Brandi nor Sharana jogged at a slower rate.

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The decay factor for the annual rate of change of -0.1 % is 0.999.

A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.

With the function displayed to the right, you may represent exponential growth or decay.

A(x) = a( 1 + r)ˣ

Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.

Now, we have the annual rate of change as:

r = - 0.1 % = - 0.1 / 100 = - 0.001

From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.

So, let B = 1 + r

B = 1 + r

B = 1 + (- 0.001)

B = 1 - 0.001

B = 0.999

Now, the value of B is less than 1 therefore, the corresponding decay factor is 0.999.

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Answer:

A

Step-by-step explanation:

The opposite of cubing is cube root

cube rooting both sides would leave you with h = Sqr^3 of 343

The factoring of the expression 2 x²+x=3 is (x-1) (2x+3)

By ordering the values, we get:

2x² + x - 3 = 0

To solve this exercise, we have to follow the rules of factoring:

1. Factor 1 from 1x:

2x² + x - 3 = 0

2x²  + (-2 + 3) x -3 = 0

2. Apply the distributive property:

2x² - 2x + 3x - 3 = 0

3. Groups the first two terms and the last two terms:

(2x² - 2x) + 3x - 3 = 0

4. Factorize the greatest common denominator (GCM) of each group:

2x(x - 1) + 3(x - 1) = 0

5. Simplify the common term (x - 1) with the distributive property:

(x-1) (2x+3)

Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.

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Answer: 5/12

Step-by-step explanation:

6x6=36

36 is all possible values.

1+2+3+4+5=15

The higher the number betty rolls there will be one less possible value that will be bigger than hers.

15/36=5/12

Answer: the answer is: 500,000

The coordinates of K' are (-2, 3) and the coordinates of M' are (-4, 1)

What are the coordinates of K'?

The graph represents the given parameter

On the graph, we have the following coordinates for point K

K = (4, 1)

The transformation vector is given as

[-6]

[2]

The transformation vector implies that

(x, y) = (x - 6, y + 2)

So, we have

K' = (4 - 6, 1 + 2)

Evaluate

K' = (-2, 3)

Hence, the coordinates of K' are (-2, 3)

What are the coordinates of M'?

The graph represents the given parameter

On the graph, we have the following coordinates for point M

M = (2, -1)

The transformation vector is given as

[-6]

[2]

The transformation vector implies that

(x, y) = (x - 6, y + 2)

So, we have

M' = (2 - 6, -1 + 2)

Evaluate

M' = (-4, 1)

Hence, the coordinates of M' are (-4, 1)

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No, all functions do not have an inverse functions. Those that do exists named invertible.

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

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.

No, all functions do not have an inverse functions. Those that do are called invertible.

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