Determine the inverse of the function f(x) = log3(4x + 5) − 6.

f inverse of x is equal to 3 to the power of the quantity x minus 6 end quantity plus 5 all over 4
f inverse of x is equal to 3 to the power of the quantity x plus 6 end quantity minus 5 all over 4
f inverse of x is equal to 3 to the power of x plus 4 all over 4
f inverse of x is equal to the quantity x plus 6 end quantity cubed minus 5 all over 3

Answer:

120°

Step-by-step explanation:

The equilateral triangle is the triangle that has three sides equal also they are congruent to each other and each side has an angle of 60 degrees

Now for rotation it would be a map to itself at 120 degrees counterclockwise

So the same is to be considered

Hence, the last option is correct

And, the other options are incorrect

Answer:

1 year

Step-by-step explanation:

Hello,

Continuously compounding with an annual interest rate of 4.5% means multiplying the initial investment by (for t tears).

\(\displaystyle e^{(1+4.5\%)t}=e^{\left( 1.045\cdot t \right) }\)

So we need to find t so that:

\(\displaystyle e^{\left( 1.045\cdot t \right) }=3\\\\1.0.45t=ln(3)\\\\t=\dfrac{ln(3)}{1.045}=1.051304...\)

Rounding to the nearest whole number gives 1 year.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

25

Step-by-step explanation:

Trust me

The least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

The equation in this problem is given as follows:

1/x + 2/(x - 3) = 5.

The denominators of each expression are given as follows:

x and x - 3 are not factors of each other, hence we multiply them and the least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

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Answer:

(x+3)(2x+1)

Step-by-step explanation:

2x^2 + 7x + 3

1st step) Multiply the 2 from 2x^2 with the 3

2nd step) Then when you get x^2 + 7x + 6, find the factors of 6 that add up to the 7 from 7x.

3rd step) The factors that add up to the 7 from 7x are 6 and 1. - these factors can be represented as (x+6)(x+1).

4th step) After this, since you multiplied the 2 from 2x^2 with the 3(shown in the first step), you must divide each each factor by the 2 from 2x^2.

5th step) Finally, you should get (x+3)(2x+1). - when dividing 1 and 2, the denominator(2) should be next to/multiply with x, and when dividing the numerator(6) and the 2 from 2x^2 together, you should get x+3 since 6 divided by 2 is 3.

Answer:

I would go with c

Step-by-step explanation:

if it is incorrect sorry

The equation that represents the condition is m° + 66° + m° = 120°. Then the value of m is 27°.

When two lines intersect, then their opposite angles are equal. Then the equation is given as,

m° + 66° + m° = 120°

Simplify the equation for m, then the value of 'm' is calculated as,

m° + 66° + m° = 120°

2m° = 120° - 66°

2m° = 54°

m° = 27°

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Answer:

angles and congruent

Step-by-step explanation:

Let us define place value

Place value is the value of each digit in a number. For example, the 5 in 350 represents 5 tens, or 50; however, the 5 in 5,006 represents 5 thousands, or 5,000. It is important that we understand that whilst a digit can be the same, its value depends on where it is in the number.

Given the number 1,664,963, the place values of each of the numbers are

1= 1 Million

the first 6 from the left= 6 hundred thousands

the second 6 from the left = 6 ten thousands

4= 4 thousands

9= 9 hundreds

the last 6 from the left = 6 tens, and

3= 3 units

Hence, the place occupied by 9 in the number 1,666,963 is 9 hundreds

Answer:

D. \( 2*10^{27} kg \)

Step-by-step explanation:

Mass of Jupiter is given as 1,898,000,000,000,000,000,000,000,000 kg

Estimating this to the nearest whole number would be = 2,000,000,000,000,000,000,000,000,000 kg (rounding up the the "1,898")

To express this in scientific notation form, simply count how many zeros we have to the nearest whole number, 2.

We have 27 zeros there.

Therefore, we would multiply the whole number, 2, by 10 raise to the power of 27.

An estimate of the mass of Jupiter = \( 2*10^{27} kg \)

The ladder will reach a Height of approximately 43.46 meters on the building.

To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.

Using the Pythagorean theorem, we can set up the equation:

(Height of the building)^2 + 7^2 = 44^2

Simplifying the equation, we have:

(Height of the building)^2 + 49 = 1936

Subtracting 49 from both sides, we get:

(Height of the building)^2 = 1887

To find the height of the building, we take the square root of both sides:

Height of the building = √1887

Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.

Therefore, the ladder will reach a height of approximately 43.46 meters on the building.

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Since a sample is a subset of the population the sample mean varies around the mean of the population.

An average of a group of data is called a sample mean. A data set's central tendency, standard deviation, and variance can all be determined using the sample mean. A population average can be determined using the sample mean, among other things.

The statistic known as the sample mean is created by arithmetically averaging the values of a variable in a sample. The sample mean is an estimator of the expected value if the sample is taken from probability distributions with a common expected value.

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The unknown angle measures are d = 76, c = 53, a = 51 and b = 76

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

The lines

The sum of angles on a line is 180

So, we have

b = 180 - 51 - 53

b = 76

By vertical angle theorems, we have

d = 76

c = 53

a = 51

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Answer:

A?

Step-by-step explanation:

Answer:

D. 60.3

Step-by-step explanation:

Finding the mean,

M = (sum of values of data)/(number of data)

now, number of data = 9,

calculating the mean,

M = (54 + 68 + 68 + 54 + 59 + 58 + 68 + 57 + 57)/9

M = 543/9

M = 60.333

M = 60.3

Answer:

(32,92) and (−1,2)

Step-by-step explanation:

You have to equal the two Ys, meaning their values as well or you can find the value of the first x and then plug it in the second equation. There are many ways to solve this to.

X = 31, Y = 63 satisfy the case of 0 ≤ Y < 100 as an expression.

An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.

Assume Kaimi was supposed to be paid X dollars Y cents (0 ≤ Y ≤ 100)

But the teller gave him Y dollars X cents.

Thus kaimi has 100Y + X cents.

A nickel is worth 5 cents.

Hence, after buying the piece of candy for a nickel, Kaimi would be left with 100Y + X - 5 cents.

This is twice his paycheck:

⇒ 100Y + X - 5 = 2(100X + Y)

⇒ 100Y + X - 5 = 200X + 2Y

⇒ 98Y - 199X = 5

199 = 98 × 2 + 3 ⇒ 3 = 199 - 98 × 2

98 = 3 × 32 + 2 ⇒ 2 = 98 - 3 × 32

3 = 2 × 1 + 1 ⇒ 1 = 3 - 2 × 1

2 = 1 × 2 + 0 ⇒ ged(199, 98) = 1

1 = 3 - 2 × 1

= 3 - (98 - 3 × 32) × 1                [∵ 2 = 98 - 3 × 32]

= 3 - 98 × 1 + 3 × 32

= 3 × 33 - 98 × 1

= (199 - 98 × 2) × 33 - 98 × 1    [∵ 3 = 199 - 98 × 2]

= 199 × 33 - 98 × 67

⇒ 1 = 199 × 33 - 98 × 67

⇒ 5(1) = 5 (199 × 33 - 98 × 67)

⇒ 5 = 199(165) - 98(335)         [∵ 5 ×33 = 165, 5 × 67 = 335]

⇒ 199(165) - 98(335) = 5

⇒ 98(-335) - 199(-165) = 5

Hence, (X,Y) = (-165, -335) is a solution to 98Y - 199X = 5

But it is required that 0 ≤ Y < 100

Now since it is the difference of two quantities, 98Y and 199X, that is a constant, 5, either both of these quantities will increase simultaneously or both will decrease simultaneously.

Hence, either both X, Y will increase or both, X, Y will decrease.

To bring Y = -335 in the range of 0 ≤ Y < 100, it needs to be increased.

Hence, both X, Y will increase.

X will increase by the absolute value of the coefficient of Y and vice-versa. Hence, X will increase by 98 and Y will increased by 199 to give

(X, Y) = (-165 + 98, -335 +199) = (-67, -136)

Still, it is not the case that 0 ≤ Y < 100

Hence, again X will increase by 98 and Y will increase by 199 to give

(X, Y) = (-67 +98, -136 +199) = (31, 63)

Now, it is the case that 0 ≤ Y = 63 < 100

∴ X = 31, Y = 63

Note that the increasing X again by 98 and Y by 199 will violate

0 ≤ Y < 100. Hence, this is the unique solution.

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He would need to add 20 cups of flour.

According to the problem Marcus puts in twelve cups of sugar, and the original amount of sugar was 3 cups. If you divide 12 by 3 you get 4. This means that you multiply 5 by 4 to get the total amount of flour required (originally there were 5 cups of flour).

Hope this helps and have a nice day.

-R3TR0 Z3R0

Ha:mu<10  is the appropriate alternative hypothesis that the consumer group wishes to test .

How would you define hypothesis?

An assumption or notion is called a hypothesis when it is put forth with the purpose of debating whether it might be true.

                               In the scientific process, the hypothesis is developed prior to the completion of any relevant study, other than a brief background review.

Ha:mu<10

Because A consumer group is suspicious of this claim, believing that the weight lose is, on average, much less.

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Answer:

48 miles

Step-by-step explanation:

i think thats it.

Answer: 4.

Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.

                                Hope this helps!

If m = -5 or m = 3, the system of linear equations has no solution.

To determine the values of m for which the system of linear equations has no solution, we need to check the determinant of the coefficient matrix, which is:

| 3 m |

| m+2 5 |

The determinant is

=  (3 x 5) - (m x (m+2))

= 15 - m^2 - 2m

= -(m^2 + 2m - 15)

= -(m+5)(m-3)

So, for the system to have no solution, the determinant must be zero, so we have:

-(m+5)(m-3) = 0

This gives us two values of m: m = -5 and m = 3.

Thus, if m = -5 or m = 3, the system of linear equations has no solution.

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Answer:

24

Step-by-step explanation:

Multiply 6 by 2 because Briana put 6 photographs in each card and there are 2 cards. You would get 12.

Since Briana has 2 grandmothers, multiply 12 by 2 and you would get 24.

hope that helps:)

The correct pairings are:

a) Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3

b) Five times the difference of a number squared and six: 5(n² - 6)

c) Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4

d) O twice the difference of nine and a number squared: 2(9 - n²)

The correct pairings of descriptions and expressions are as follows:

Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3

This expression represents taking a number, cubing it, dividing the result by seven, subtracting four, and then adding three.

Five times the difference of a number squared and six: 5(n² - 6)

This expression represents taking a number, squaring it, subtracting six, and then multiplying the result by five.

Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4

This expression represents taking the cube of a number, dividing six by the cube, adding nine, and then subtracting four.

O twice the difference of nine and a number squared: 2(9 - n²)

This expression represents taking a number, squaring it, subtracting it from nine, and then multiplying the result by two.

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Answer:

Step-by-step explanation:

Let the midpoint of the two points A (x₁, y₁) and B(-5, 5) be M(2, 0)

Using the formula for calculating the midpoints of two coordinates

(X₁, Y₁) = \((\frac{{x_1}+x_2}{2}, \frac{{y_1}+y_2}{2} )\)

\(X_1 = \frac{{x_1}+x_2}{2}\\Y_1 =\frac{{y_1}+y_2}{2}\)

Given if (X₁, Y₁) is the midpoint, then X₁ = 2, Y₁ = 0

x₂ = -5 and y₂ = 5

Substituting this given values into the equation above to get the unknown coordinate;

\(X_1 = \frac{{x_1}+x_2}{2}\\-2 = \frac{{x_1}-5\\}{2}\\-4 = x_1-5\\x_1=-4+5\\x_1 =1\)

Similarly;

\(Y_1 = \frac{{y_1}+y_2}{2}\\0 = \frac{{y_1}+5\\}{2}\\0 = y_1+5\\y_1=0-5\\y_1 =-5\)

The coordinate of A = (1,-5)

To find the total time it takes for the airplane to travel from Mumbai to Tokyo via Seoul, we need to add the time taken for the Mumbai-Seoul leg and the Seoul-Tokyo leg.

The airplane takes 3.2 hours to fly from Mumbai to Seoul.

The airplane takes 1 1/3 hours to fly from Seoul to Tokyo, which is equivalent to 1.33 hours.

To find the total time, we add the two durations:

3.2 hours + 1.33 hours = 4.53 hours

Therefore, it takes approximately 4.53 hours for the airplane to travel from Mumbai to Tokyo if it flies through Seoul.

Answer:

12 and -10

Step-by-step explanation:

a coefficient is a number multiplied by a variable

Answer:

The slope of the points is (3,3)

Step-by-step explanation:

If you plot both points on a graph and start at the one furthest down on the graph, then go up three and to the right three you get to your second point and you have your slope. Remember going down or to the left makes the slope negative and it is always rise over run.

Answer: y=4

Explanation:

The expression we have is:

to solve for y we do the following steps.

Step 1: Add 3 on both sides of the equation

Solving the operations we get:

Step 2: Divide both sides of the equation by 5

Doing the divisions we get:

9514 1404 393

Answer:

Step-by-step explanation:

Count the number of times each digit is shown in the product.

 3 is a factor 2 times

  4 is a factor 5 times

_____

Additional comment

An exponent can be used to show repeated multiplication, so the product could be written ...

  3^2·4^5

Step-by-step explanation:

In the expression 3·3·4·4·4·4·4

3 = 2 times

4 = 5 times

As they are factors, they can also be written as:-