Which of the following is the inverse of y=6*?
O y = logo
y = log,6
O y = logix
Y=log, 6x

Answer:

5/2 13/6 80/21

Step-by-step explanation:

the reciprocal is just flipping the fraction over, if they asked you to simplify its

4 1/2, 2 1/6, and 3 4/5  

Answer:

938 feet

Step-by-step explanation:

264^2+ 900^2= c^2

879696= c^2

938= c

To find the value of (f o g)' at a given value, you first need to understand the concept of composite functions and the chain rule of differentiation. Let's break it down step by step.

To find the value of (f o g)' at a given value, you need to evaluate g(x) and f(x), find their derivatives, and use the chain rule to find the derivative of (f o g) at the given value. It is important to understand the concepts of composite functions and the chain rule to be able to solve problems involving these concepts.

What are composite functions? Composite functions are functions that are formed by composing two or more functions. The notation used to denote composite functions is (f o g)(x), which means that the output of function g is used as the input for function f. In other words, we first evaluate g(x), and then use the result as the input for f(x).

What is the chain rule of differentiation? The chain rule of differentiation is a method used to find the derivative of composite functions. It states that if a function is composed of two or more functions, then its derivative can be found by taking the derivative of the outer function and multiplying it by the derivative of the inner function.

To find the value of (f o g)' at a given value, we need to follow these steps:1. Find g(x) and f(x)2. Find g'(x) and f'(x)3. Evaluate g(x) at the given value4. Use the chain rule to find (f o g)' at the given value

step 1: Find g(x) and f(x)Let's say that we have two functions: g(x) = x^2 + 3x + 1 and f(x) = sqrt(x). To find (f o g)(x), we first need to evaluate g(x) and then use the result as the input for f(x). Therefore, (f o g)(x) = f(g(x)) = sqrt(x^2 + 3x + 1)

Step 2: Find g'(x) and f'(x)To find g'(x), we need to take the derivative of g(x) using the power rule and the sum rule. Therefore, g'(x) = 2x + 3To find f'(x), we need to take the derivative of f(x) using the power rule and the chain rule. Therefore, f'(x) = 1/2(x)^(-1/2)

Step 3: Evaluate g(x) at the given valueSuppose we want to find (f o g)' at x = 2. To do this, we need to first evaluate g(x) at x = 2. Therefore, g(2) = 2^2 + 3(2) + 1 = 11

Step 4: Use the chain rule to find (f o g)' at the given value now we can use the chain rule to find (f o g)' at x = 2. Therefore, (f o g)'(2) = f'(g(2)) * g'(2) = 1/2(11)^(-1/2) * (2)(3) = 3/sqrt(11)

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Mrs. Kenny can complete 5 projects with 1/4 of a pound of clay left over.

We know that,

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

To find out how many projects Mrs. Kenny can complete with 7/8 pound of clay, we need to divide 7/8 by 1/6:

= (7/8) ÷ (1/6)

To divide fractions, we need to invert the second fraction and multiply:

= (7/8) × (6/1)

Simplifying the fractions, we get:

(7 × 6)/(8 × 1) = 42/8 = 5 1/4

Thus, Mrs. Kenny can complete 5 projects with 1/4 of a pound of clay left over.

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\( \mathfrak{V=a³}\)

Where,

In our case,

\( \sf \: V= {5}^{3} \)

\( \sf \: V= {125} \: ft^{3} \)

➪ Thus, The volume of the cube is 125 feet³...~

We know that:

\(Volume = L^{3} = (L)^{3}\)

Substituting the side length into the equation:

\(Volume = (L)^{3}\)

\(Volume = (5)^{3}\)

Evaluating the volume:

\(Volume = (5)(5)(5)\)

\(Volume = 125 \space\ ft^{3}\)

Step-by-step explanation:

B^2+8b+7 is a quadratic expression. It can be factored as (b+7)(b+1).

To factor a quadratic expression, you can use the following steps:

1. Find two numbers that add up to the coefficient of the middle term (8) and multiply to the constant term (7).

2. Write the quadratic expression as a product of two binomials, with the two numbers you found in step 1 as the coefficients of the terms in each binomial.

In this case, the two numbers that add up to 8 and multiply to 7 are 7 and 1. So, we can factor B^2+8b+7 as follows:

(b+7)(b+1)

This means that B^2+8b+7 is equal to the product of (b+7) and (b+1).

Here is a step-by-step explanation of how to factor B^2+8b+7:

1. The coefficient of the middle term is 8.

2. The constant term is 7.

3. The two numbers that add up to 8 and multiply to 7 are 7 and 1.

4. Therefore, B^2+8b+7 can be factored as (b+7)(b+1).

Answer:

132cm^2

Step-by-step explanation:

to solve for the area of this we can split it into smaller shapes and sum the areas afterward-

the top rectangle has an area equal to Length x Width

4x7 = 28cm^2

the centre rectangle is done similarly-

7x8 = 56cm^2

lastly the two triangles which are solved with base x height divided by two

now since we know that the centre piece is 7cm across, and that the two side triangles are equal in size, that means that we know the base to be 19-7 divided by 2 which gives 6 each-

\(\frac{(6)(8)}{2}\) (2) = (6)(8) = 48cm

now summing them we have 28 + 56 + 48 = 132cm^2

Answer: $1346.40

Step-by-step explanation:

Volume of the pool is:

\((6)(8)(8)+\frac{1}{2}(6)(8)(6)=528\)

This has a cost of \((528)(2.55)=\boxed{\$1346.40}\)

The volume of the pool will be 528 cubic feet. Then the cost to fill the pool will be $1,346.4.

Let the prism with A is the base area and a height of H. Then the volume of the prism is given as

V = A × H

Then the volume of the pool will be

V = [(6 × 8) + (1/2 × 6 × 6)] × 8

V = (48 + 18) × 8

V = 66 × 18

V = 528 cubic feet

Then the cost to fill the pool will be

C = $2.55 × 528

C = $1,346.4

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Answer:

2698

Step-by-step explanation:First you take 1000 from 5000 and then distribute it to 395

Answer:

you would subtract 2697 from 5395. you have it in the correct format. the answer would be 2,698.

Step-by-step explanation:

The slope is unchanged and the y intercept shifted up by 9 units

The first equation is given that

f(x) = 6x + 2

Slope intercept form is

y = mx + b

Where m is the slope of the line

b is  the y intercept

Compare both the equation

The slope of the line m = 6

The y intercept of the line = 2

New equation is

g(x) = 6(x + 1.5) + 2

Apply distributive property in the equation

g(x) = 6x + 9 + 2

g(x) = 6x + 11

The slope of the line = 6

y intercept of the line  = 11

Hence, the slope is unchanged and the y intercept shifted up by 9 units

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Answer:

1/2, 11/6

Step-by-step explanation:

y=-4+9y

9y-y=4

8y=4

y=1/2

3x-5=1/2

3x=5+1/2=11/2

x=11/6

Answer:

35 millimeters

Step-by-step explanation:

1.4 inches * 1millimeters / 0.04inches = 35 millimeters

use this equation:

starting units * desired units / starting units = desired units

Answer:

B

Step-by-step explanation:

or the second graph

The solution to the inequality 2(b+2) > 24 is b > 10 and the graph representing this solution is the last graph (figure attached)

To find the graph we solve the equation first

To solve the inequality 2(b + 2) > 24, we will follow these steps:

Distribute the 2 on the left side:

2b + 4 > 24

Subtract 4 from both sides:

2b > 24 - 4

2b > 20

Divide both sides by 2 (since it is a positive number):

b > 20/2

b > 10

Therefore, the solution to the inequality 2(b+2) > 24 is b > 10.

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Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

The equivalent distance of 60,000 centimetres in kilometers as required to be determined is; 0.6 km.

According to the task content and the metric system conversions;

1 m = 100 cm

Therefore, it follows from proportion that; 60,000 cm is equivalent to; 60,000 / 100 = 600 m.

Additionally, it follows that; 1 km = 1000 m, it therefore follows from proportion that; 600 m is equivalent to; 600 / 1000 = 0.6 km.

Ultimately, the equivalent distance of 60,000 centimetres in kilometers is; 0.6 km.

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Answer:

Hey mate.....

Step-by-step explanation:

This is ur answer....

= 180 - (112 + 47)

= 180 - 159

= 21

Hope it helps you,

Mark me as the brainliest.....

Follow me! :)

Answer:

a = 3

Step-by-step explanation:

Collect like-terms:

\( - 16 = a - 19\)

\(a = - 16 + 19\)

\(a = 3\)

Answer: 3

Step-by-step explanation: you take 19 from 3 giving you -16

Answer:

Option B. y – 3 = –1/7(x – 3)

Step-by-step explanation:

From the question given above, the following data were obtained:

Slope (m) = –1/7

Coordinate = (3, 3)

x₁ coordinate = 3

y₁ coordinate = 3

The equation of the line can be written as follow

y – y₁ = m(x – x₁)

y – 3 = –1/7(x – 3)

Answer:

<

Step-by-step explanation:

1) Substitute 5 into the question

2) Work out the sides

3) Put it into an inequality

5 < 7

Hope this helps, have a great day!

Answer:

16x²

Step-by-step explanation:

Answer:

ok

Step-by-step explanation:

Answer:

You just need to substitute the variables. Example, problem 9; N=9 and q=10, 9×10? You got your answer.

Answer:

25

Step-by-step explanation:

From the given information;

Numbers of posters that can be printed in an hour = no of impression/hour × no of plate utilized in each impression.

= 1000x

Thus, the required number of hours it will take can be computed as:

\(\implies \dfrac{100000}{1000x} \\ \\ =\dfrac{100}{x}\)

cost per hour = 125

If each plate costs $20 to make, then the total number of plate will equal to 40x

∴

The total cost can be computed as:

\(C(x) = (\dfrac{100}{x}) \times 125 + 20 x --- (1)\)

\(C'(x) = (-\dfrac{12500}{x^2}) + 20 --- (2)\)

At C'(x) = 0

\(\dfrac{12500}{x^2} = 20\)

\(\dfrac{12500}{20} = x^2\)

\(x^2= 625\)

\(x = \sqrt{625}\)

x = 25

\(C'' (x) = -12500 \times \dfrac{-2}{x^3} +0\)

\(C'' (x) = \dfrac{25000}{x^3}\)

where; x = 25

\(C'' (x) = \dfrac{25000}{25^3}\)

C''(x) = 1.6

Thus, at x = 25, C'' > 0

As such, to minimize the cost, the printer needs to make 25 metal plates.

The point on the ellipsoid where the tangent plane is perpendicular to the line with parametric equations x = 2 - 4t, y = 1 + 8t, and z = 3 - 2t is (-3/2, 1/2, 3/2).

The gradient of the ellipsoid is given by (2x, 8y, 2z). At the point (x₀, y₀, z₀) on the ellipsoid, the gradient is (2x₀, 8y₀, 2z₀).

The line with parametric equations x = 2 - 4t, y = 1 + 8t, and z = 3 - 2t has a direction vector of (-4, 8, -2).

For the tangent plane at the point (x₀, y₀, z₀) to be perpendicular to the line, the normal vector of the plane must be parallel to the direction vector of the line. Thus, we have:

(2x₀, 8y₀, 2z₀) · (-4, 8, -2) = 0

-8x₀ + 64y₀ - 4z₀ = 0.

Also, the point (x₀, y₀, ₀) lies on the ellipsoid, so we have:

x₀² + 4y₀² + z₀² = 9.

We solve the system of equations to find the values of x₀, y₀, and z₀:

x₀ = -3/2, y₀ = 1/2, ₀ = 3/2.

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50miles

Step-by-step explanation:

Answer:

500 miles

Step-by-step explanation:

80% is converted to its decimal form 0.8

Multiply 0.8 times "x" which is the unknown total distance of the trip (80% of the total trip) to get 400 because 80% of the trip is 400 miles. Then find x

0.8x = 400

400/0.8 = x

500 = x

Answer:

d. C. 4; enlargement

Step-by-step explanation:

Scale factor = Ratio of one of the side length of the scale diagram to the corresponding side length of the original diagram

Side length of scale diagram = 8 units

Corresponding side length of original diagram = 2 units

Thus:

Scale factor = 8/2 = 4

Scale factor = 4

Since it's an while number, it implies that it is an enlargement.

Answer:

g(-3x) = -9x - 3

Step-by-step explanation:

Step 1: Define function

g(x) = 3x - 3

g(-3x) = x = -3x

Step 2: Substitute

g(-3x) = 3(-3x) - 3

g(-3x) = -9x - 3

Based on the number of pieces that Ted learned to sing over 7 weeks, the number of voice lessons he can sing over 8 weeks would be 16 pieces  

First, find the number of music pieces that Ted is learning to sing per week:

= Number of pieces / Number of week

= 14 / 7

= 2 pieces per week

The number of pieces in 8 weeks that Ted would have learned is:

= Number of weeks x Pieces learned per week

= 8 x 2

= 16 pieces

In conclusion, Ted would have learned 16 pieces in 8 weeks.

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