Identify the rule for fg when f(x) = –3x – 6 and g(x) = x2 – x – 6.

When a cylinder is sliced in such a way that the plane passes through the cylinder in a slanted direction without going through either base, the resulting cross section is an elliptical shape.

To visualize this, imagine a cylinder with circular bases. When a plane intersects the cylinder in a slanted direction, it cuts through the curved surface of the cylinder, creating an elliptical cross section.

The exact shape and size of the elliptical cross section will depend on the angle at which the plane intersects the cylinder and the specific orientation of the cylinder. The major axis of the resulting ellipse will be parallel to the slanted direction of the plane, while the minor axis will be perpendicular to it.

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Answer:

24x³-62x²+49x-12

Step-by-step explanation:

We can start by multiplying the first two brackets together first.

(3x-4)(2x-1)(4x-3) = (6x²-3x-8x+4)(4x-3)

Evaluate like terms.

(6x²-3x-8x+4)(4x-3) = (6x²-11x+4)(4x-3)

Multiply the two brackets together.

(6x²-11x+4)(4x-3) = 24x³-18x²-44x²+33x+16x-12

Simplify.

24x³-18x²-44x²+33x+16x-12 = 24x³-62x²+49x-12

Tell me if you need it in factorised form.

Answer:

18

Step-by-step explanation:

you need to multiply the base by the height then divide it by 2

Answer:

1st slide:

A. a translation 5 units to the left

B.translation 7 units down

2nd slide

A. Wider than and opens in the opposite direction of

B. Narrower than and opens in the same direction as

3rd slide

1,-5,3

4th slide

A. Right, 8

B. Down,6

5th slide

Sample response:complete the square to get the equation in vertex form with a=-16, h=1, and k=19. The path is a reflection over the x-axis and narrower. It is also translated right 1 unit and up 19 units.

6th slide

The upside down U with the y axis to the right

7th slide

A. 1,-5

B. -3,2

8th slide

A. 1 1

B. 1

C. 2

9th slide

3,1

10th slide

4,-32

2,-15

11th slide

Step-by-step explanation:

The translation of the equation y = x to the graph of y = (x+5) has a translation of 5 units to the left. The correct option is B.

The process of changing the location of the image on the coordinate system will be known as the translation. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

Given equations are y = x and y = x + 5. When the two equations are plotted on the graph it is observed that the line of the equation y = x + 5 lies on the left side of the line y = x of about 5 units.

Therefore, the translation of the equation y = x to the graph of y = (x+5) has a translation of 5 units to the left. The correct option is B.

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Answer:

we cry bc math is hard JKK unless ?

but fr we can write out an equation by doing (1/5 ÷ 3/4) and then switch the sign to multiplication and we can keep the first fraction the same (in this case 1/5) and then we flip the second fraction BUT when we flip the second fraction upside-down we have to change the symbol to multiplication (1/5x4/3)

then after that all we do is multiply the denominators and numerators :)

1 x 4 = 4

_______

5 x 3 = 15

answer would be 4/15

A fraction is a way to describe a part of a whole. The result of the division of the fraction is 4/15.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The division of two fractions is carried out by multiplying the dividend fraction(Numerator) by the reciprocal of the divisor fraction(Denominator).

The divisions of the given fractions are carried out as shown below.

1/5 ÷ 3/4

\(=\dfrac{\dfrac{1}{5}}{\dfrac{3}{4}}\\\\\\= \dfrac{1 \times 4}{5 \times3}\\\\=\dfrac{4}{15}\)

Hence, the result of the division of the fraction is 4/15.

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The domain of the function shown in the graph is the one in option A:

6 ≤ k ≤ 11

The domain of a function y = f(x) is the set of the inputs of the function. To identify the domain in a graph, we need to look at the horizontal axis (also called the x-axis).

On the graph we can see that it starts at x = 6 with a closed dot, and it ends at x = 11 also with a closed dot.

That means that these values belong to the domain, so we can write the domain as follows:

Domain = 6 ≤ k ≤ 11

(notice that the variable in the horizontal axis is k).

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Answer:760$ in a week because they worked 5 out of 7 days and made 152$ a day

Step-by-step explanation:

9.5 x 16 = $152

152 x 5 (only weekdays)

<!> Branliest is appreciated! <!>

The rank of the standard matrix for T is 2, which is determined by the number of linearly independent columns in the matrix.

To find the rank of the standard matrix for the linear transformation T: R^5 → R^3, we need to determine the number of linearly independent columns in the matrix.

The standard matrix for T can be obtained by applying the transformation T to the standard basis vectors of R^5.

The standard basis vectors for R^5 are:

e1 = (1, 0, 0, 0, 0),

e2 = (0, 1, 0, 0, 0),

e3 = (0, 0, 1, 0, 0),

e4 = (0, 0, 0, 1, 0),

e5 = (0, 0, 0, 0, 1).

Applying the transformation T to these vectors, we get:

T(e1) = (1 + 0, 0 + 0 + 0, 0 + 0) = (1, 0, 0),

T(e2) = (0 + 1, 1 + 0 + 0, 0 + 0) = (1, 1, 0),

T(e3) = (0 + 0, 0 + 1 + 0, 0 + 0) = (0, 1, 0),

T(e4) = (0 + 0, 0 + 0 + 1, 1 + 0) = (0, 1, 1),

T(e5) = (0 + 0, 0 + 0 + 0, 0 + 1) = (0, 0, 1).

The standard matrix for T is then:

[1 0 0 0 0]

[1 1 0 1 0]

[0 1 0 1 1]

To find the rank of this matrix, we can perform row reduction or use the concept of linearly independent columns. By observing the columns, we see that the second column is a linear combination of the first and fourth columns. Hence, the rank of the matrix is 2.

Therefore, the rank of the standard matrix for T is 2.

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COMPLETE QUESTION - Let T: R5-+ R3 be the linear transformation defined by the formula T(x1, x2, x3, x4, x5) = (x1 + x2, x2 + x3 + x4, x4 + x5). (a) Find the rank of the standard matrix for T.

The equations of the lines are y = 3x - 5 and y = (1/2)x - 7

An equation is an expression that shows how numbers and variables are related to each other.

A linear function is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Two lines are parallel if they have the same slope

1) y = 3x + 6; (4, 7)

The parallel line would have a slope of 3 and pass through (4, 7), hence:

y - 7 = 3(x - 4)

y = 3x - 5

2) y = (1/2)x + 5; (4, -5)

The parallel line would have a slope of 1/2 and pass through (4, -5), hence:

y - (-5) = (1/2)(x - 4)

y = (1/2)x - 7

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Answer:

\(y=-3x-8\)

Step-by-step explanation:

Given the quadratic function g(x) = -2x^2 + 20x - 46.The formula for finding the range of a quadratic function is range = {y: y ≤ (4ac - b^2) / 4a, when a > 0 and y ≥ (4ac - b^2) / 4a, when a < 0}.

From the given quadratic function, a = -2, b = 20, and c = -46.

Substituting these values in the above formula, we get

Range = {y: y ≤ (4(-2)(-46) - 20^2) / 4(-2)}= {y: y ≤ -23}

Hence, the range of the quadratic function g(x) is (-∞, -23].

Therefore, the answer is:Range of g(x) = (-∞, -23].Since the word limit mentioned in the question is more than 120, thus the answer is given in a detailed manner.

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The given polynomial is

x^2 - 9x^3 - 5x^2 - 4x + 5

By simplifying it, it becomes

- 9x^3 + x^2 - 5x^2 - 4x + 5

- 9x^3 - 4x^2 - 4x + 5

We want to divide it by x + 3. To use the remainder theorem, we would substitute x = - 3 into the polynomial to find the remainder, r. We have

r = p(- 3) = -9(-3)^3 - 4(-3)^2 - 4(-3) + 5

243 - 36 + 12 + 5

r = 224

Thus, the remainder when P(x) = x^2-9x^3-5x^2-4x+5 is divided by x + 3 is 224

P(-3) = 224

-

a)

\(speed \leqslant 110 \: km{h}^{ - 1} \)

b)

\(max \: passengers \leqslant 35\)

c)

\(passing \: mark \geqslant 40\)

d)

\(distance \: between \: school \: and \: house \\ \ < 10km\)

e)

\(score \: for \: award \ > 80\)

f)

\(age < 10\)

Answer: 1320 ways.

Step-by-step explanation:

For this problem you should use the formula for variations in combinatorics. You use this when choosing a few objects from a group in which the order of the objects is of importance:

\(P^{12} _{3}=\frac{12!}{(12-3)!}=\frac{12 \cdot 11\cdot 10\cdot ...\cdot 1}{9 \cdot 8 \cdot ... \cdot 1} = 12 \cdot 11 \cdot 10 = 1320\)

where ! stands for factorial.

The piecewise defined function for fencing the backyard would be 30(300) + 25(x - 300), if x > 300, or 30x, if 0 < x ≤ 300, as seen below.

A piecewise defined function is a function that is defined by different formulas on different intervals or "pieces" of its domain. This means that the formula used to calculate the output (the function value) of the function depends on the value of the input (the independent variable).

For this particular question, let C be the cost of fencing a backyard and let x be the length of the fence in feet. Then, we can write the piecewise defined function as:

C(x) =  30x, if 0 < x ≤ 300 OR

C(x) = 30(300) + 25(x - 300), if x > 300

In other words, if the length of the fence is less than or equal to 300 feet, the cost is simply 30 times the length of the fence. If the length of the fence is greater than 300 feet, the cost is the cost of the first 300 feet (30 times 300), plus 25 times the additional length of the fence beyond 300 feet.

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Answer:

3 + 2n

Step-by-step explanation:

2 + 1 = 3.

2n cannot be added into this because it has a letter in front of it. Therefore, it stays on its own.

2n + 3

1 and 3 are like terms, and because there are no more variables, the 2n will stay alone :)

The correct statement is:

C. that at least one of the events must occur.

Use the concept of probability defined as:

Le 'f' represents the number of favorable outcomes and 't' denotes the total number of outcomes then, the probability of an event is defined as f/t.

Given that,

The experiment has a set of events.

And these events are collectively exhaustive.

When an occurrence that occurs during an experiment that is collectively exhaustive:

It means that at least one of the events must occur.

It guarantees that all potential outcomes are addressed and that there won't be any gaps in the outcomes of the experiment.

Hence,

Option C is correct.

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The complete question is:

What does it mean when an experiment has a set of events that are collectively exhaustive? multiple choice questions.

A. that all of the events will occur.

B. that only one of the events can occur as a result of the experiment.

C. that at least one of the events must occur.

Answer:

2x+3y= -1

Step-by-step explanation:

2x+3y=5

3y= -2x+5

y= -2/3x + 5/3

m= -2/3

put the points( -2,1) in this equation to get b

1= -2(-2/3)+b

b= 1-4/3

=-1/3

so the equation is

y = -2/3x -1/3

3y= - 2x-1

2x+3y= -1

Answer:

The answer is 429 = 3×11×13.

Step-by-step explanation:

You have to divide by prime number :

429 ÷ 3 = 143

143 ÷ 11 = 13

13 ÷ 13 = 1

Answer:

3×11×13

Step-by-step explanation:

The Jacobian of the transformation is: ∂(x, y) / ∂(r, θ) = [ -18e^(-3r)sin(θ)  6e^(-3r)cos(θ) ]   [ 3e^(3r)cos(θ)    -e^(3r)sin(θ) ]

To find the Jacobian of the transformation given by x = 6e^(-3r)sin(θ) and y = e^(3r)cos(θ), we need to compute the partial derivatives of x with respect to r and θ, and the partial derivatives of y with respect to r and θ.

The Jacobian matrix is given by:

J = [ ∂x/∂r  ∂x/∂θ ]

       [ ∂y/∂r  ∂y/∂θ ]

Let's calculate the partial derivatives:

∂x/∂r = -18e^(-3r)sin(θ)

∂x/∂θ = 6e^(-3r)cos(θ)

∂y/∂r = 3e^(3r)cos(θ)

∂y/∂θ = -e^(3r)sin(θ)

Now we can assemble the Jacobian matrix:

J = [ -18e^(-3r)sin(θ)  6e^(-3r)cos(θ) ]

       [ 3e^(3r)cos(θ)    -e^(3r)sin(θ) ]

Therefore, the Jacobian of the transformation is:

∂(x, y) / ∂(r, θ) = [ -18e^(-3r)sin(θ)  6e^(-3r)cos(θ) ]

                                  [ 3e^(3r)cos(θ)    -e^(3r)sin(θ) ]

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Answer:

x = 27.2 or 27 1/5

Step-by-step explanation:

cos 54° = 16/x

x = 27.2 or 27 1/5

Answer:

No

Step-by-step explanation:

i did it on khan

Answer:

It would be 8% .

Good luck ^^

The centroid of the region in the first quadrant bounded by the given curve is (81/170, 81/170).

The centroid of an area is geometric center of that area. The location of the centroid is often denoted with a C with the coordinates being (ˉx, ˉy)  that they are the average x and y coordinate for the area.

In order to calculate the coordinates of the centroid, we'll need to calculate the area of the region first.

Now we solve of given curve are;

y=x^8

y=x^{1/8}

Now putting the value of y. we get

x^8=x^{1/8}

x=x^{64}

x^{64}-x=0

x{x^63 -1}

after equating equal to zero

x=0   x=1

y=\(\int\limits^0_1{x} \,\)x[x^9/8 - x^9]

by putting limit we get

y= 8/17 -1/10

y=63/170

Similarly we find

x  =63/170

After that multiply with mass of center to get 81/170,81/170.

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Answer:

The system of equations y=14-2x and 6x+3y=42.

Step-by-step explanation:

Please see attachment to see the answer as a graph.

Hope this helps!

A NORMAL distribution is a symmetrical probability distribution with a bell-shaped curve. It is also called a Gaussian distribution or a normal curve. This distribution is often used in statistics to represent a large number of natural phenomena, such as the distribution of height, weight, or IQ scores in a population.

The first deviation of a NORMAL distribution includes 68.2% of the data. This means that if we were to take a random sample of data from a normally distributed population, about 68.2% of the data would be within one standard deviation of the mean.

The second deviation includes 95.4% of the data. This means that about 95.4% of the data would be within two standard deviations of the mean.

The third deviation includes 99.7% of the data. This means that about 99.7% of the data would be within three standard deviations of the mean.

It is important to note that while these percentages hold true for a NORMAL distribution, they may not apply to other types of distributions.

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Answer:

the answer is ">"

Answer:

>

Step-by-step explanation:

because -6 is bigger than -22