What is the remainder when 2x^3−9x^2+11 is divided by x−6?

Answer:

13

Step-by-step explanation:

8-13=-5

Answer:

13

Step-by-step explanation:

8 - 13 = -5

that is your answer

The derivative \(\( y' \)\) of the implicit function \(\( y^2 - xy = -2 \)\) is 0, indicating a constant slope with no change in relation to \(\( x \)\).

To find \(\( y' \)\)for the implicit function \(\( y^2 - xy = -2 \)\), we can differentiate both sides of the equation with respect to \(\( x \)\) using the chain rule. Let's go step by step:

Differentiating \(\( y^2 \)\) with respect to \(\( x \)\) using the chain rule:

\(\[\frac{d}{dx}(y^2) = 2y \cdot \frac{dy}{dx}\]\)

Differentiating \(\( xy \)\) with respect to \(\( x \)\) using the product rule:

\(\[\frac{d}{dx}(xy) = x \cdot \frac{dy}{dx} + y \cdot \frac{dx}{dx} = x \cdot \frac{dy}{dx} + y\]\)

Differentiating the constant term (-2) with respect to \(\( x \)\) gives us zero since it's a constant.

So, the differentiation of the entire equation is:

\(\[2y \cdot \frac{dy}{dx} - (x \cdot \frac{dy}{dx} + y) = 0\]\)

Now, let's rearrange the terms:

\(\[(2y - y) \cdot \frac{dy}{dx} - x \cdot \frac{dy}{dx} = 0\]\)

Simplifying further:

\(\[y \cdot \frac{dy}{dx}\) \(- x \cdot \frac{dy}{dx} = 0\]\)

Factoring out:

\(\[(\frac{dy}{dx})(y - x) = 0 \]\)

Finally, solving:

\(\[\frac{dy}{dx} = \frac{0}{y - x} = 0\]\)

Therefore, the derivative \(\( y' \)\) of the given implicit function is 0.

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Answer:-1

Step-by-step explanation:

in order to solve this type questions you should "orginize" numbers same variables:

-6x+4x=6-4

-2x=2

x=-1

The present value of the loan, rounded to the nearest cent, is $37,196.88.

To calculate the present value of a loan, we can use the formula for the present value of an ordinary annuity:

PV = PMT * ((1 - (1 + r)^(-n)) / r),

where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is $3,400, the interest rate is 5.19% compounded semi-annually, and the loan term is 7 years, which is equivalent to 14 semi-annual periods.

First, let's convert the interest rate to its semi-annual equivalent by dividing it by 2. So, the interest rate per semi-annual period is 5.19% / 2 = 2.595%.

Now, we can plug these values into the formula:

PV = $3,400 * ((1 - (1 + 0.02595)^(-14)) / 0.02595).

Calculating this equation, we find that the present value of the loan is approximately $37,196.88 when rounded to the nearest cent.

Therefore, the present value of the loan, rounded to the nearest cent, is $37,196.88.

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Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

The range, as x tends to negative infinity, the function will tend to zero. And as x tends to infinity, h(x) also tends to infinity.

So the range exists R: (0, ∞).

A mathematical function with the following formula is an exponential function: f (x) = \($$a^{x}\). where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most frequently encountered exponential-function base.

Let the exponential function be

\($h(x)=125^x\)

The base, 125 , exists larger than 1 , which means that we contain an exponential growth.

So, as x increases, also does h(x).

As x decreases, also does h(x).

Now, the domain of any exponential equation exists the set of all real numbers.

For the range, as x tends to negative infinity, the function will tend to zero. And as x tends to infinity, h(x) also tends to infinity.

So the range exists R: (0, ∞).

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Answer:

34 cents

Step-by-step explanation:

I'm hope this helps!

We can write a ratio:

15/5 = 36/x

Let "x" equal the unknown part of the triangle.

Solution:

15/5 = 36/x

~Cross multiply

15x = 180

~Divide 15 to both sides

x = 12

Best of Luck!

Answer:

(-0.8, 2.2)

Step-by-step explanation:

Where the two lines intersect is the solution to the System of Equations.

Answer:

the answer would be (-0.8, 2.2) since it hasn't hit -3 yet and if it were to be -1 it would be in the bottom left

Answer:

x = 3

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp side / adj side

tan 30 = sqrt(3) / x

x tan 30 = sqrt(3)

x = sqrt(3) / tan 30

x =sqrt(3) / (1 / sqrt(3))

x = sqrt(3) * sqrt(3)

x = 3

Answer:

1. Divide

4 divided by 5.50

3 divided by 3.30

1. About 0.7

2. About 0.9

This means that 4 candy bars for 5.00 is the better buy!

Step-by-step explanation:

Hope this helps!! :))

Answer

Answer = (6.95 × 10⁻¹⁰)

Explanation

We are asked to solve (13.9 × 10⁻⁸) ÷ (2 × 10²)

To solve this, we will have

Hope this Helps!!!

Answer:

On Monday

Step-by-step explanation:

40÷10=4

21÷7=3

So per hr 4 is bigger, so on Monday

As the size of the sample increases, the sampling distribution of sample means becomes more normally distributed.

The Central Limit Theorem (CLT) states that as the sample size increases, the distribution of sample means will become more normally distributed regardless of the shape of the population distribution.

As long as the sample size is sufficiently large (usually greater than 30).

This means that the mean and standard deviation of the sampling distribution of sample means will approach the mean and standard deviation of the population distribution.

In other words, when the sample size is small, the sampling distribution may not follow a normal distribution and may be skewed.

However, as the sample size increases, the effect of the individual observations' randomness on the mean becomes smaller.

Consequently, the distribution of sample means becomes more symmetrical and follows a normal distribution.

Thus, the larger the sample size, the more reliable the estimate of the population mean becomes, and the more likely the distribution of sample means will be normally distributed.

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Answer:

77/32...2 13/32

Step-by-step explanation:

11/12*21/8

Keep Change Change

HOPE THIS HELPS

If the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units

The length of the hypotenuse = 13.5 units

The angle = 41 degrees

Here we have to use the trigonometric function

sin θ = Opposite side / Hypotenuse

cos θ = Adjacent side / Hypotenuse

tan θ = Opposite side / Adjacent side

In this question hypotenuse and angles are given and we have to find the opposite side.

sin θ= opposite side /  Hypotenuse

Substitute the values in the equation

sin 41 = Opposite side / 13.5

Opposite side = sin 41×13.5

= 8.86 units

Hence, if the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units.

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The solution of the nonlinear differential equation is y(t) for 5 seconds with a time resolution of 0.1 seconds.

To solve the given nonlinear differential equation and plot the solution using MATLAB, you can follow the steps below:

Step 1: Define the differential equation

Create a separate script file, let's call it nonlinear_equation.m, and define the differential equation as a function:

function dydt = nonlinear_equation(t, y)

   dydt = zeros(3, 1);

   dydt(1) = y(2);

   dydt(2) = y(3);

   dydt(3) = exp(-1.5 * y(1)) * (1 - 6 * y(1) / y(2)) * y(3) / y(2);

end

Step 2: Solve the differential equation

Create another script file, let's call it solve_equation.m, to solve the differential equation numerically and plot the solution:

% Define the time span and initial conditions

tspan = 0:0.1:5;

y0 = [1; pi/6; 0];

% Solve the differential equation numerically

[t, y] = ode45(atnonlinear_equation, tspan, y0);

% Plot the solution

plot(t, y(:, 1), 'b', t, y(:, 2), 'r', t, y(:, 3), 'g');

xlabel('Time');

ylabel('y(t)');

title('Solution of the Nonlinear Differential Equation');

legend('y', 'y''', 'y'''');

grid on;

Step 3: Run the MATLAB script

Save both the nonlinear_equation.m and solve_equation.m files in the same directory. Then, run the solve_equation.m script in MATLAB.

It will generate a plot with the solution y(t) for 5 seconds with a time resolution of 0.1 seconds.

Make sure you have the Ordinary Differential Equation (ODE) solver (ode45) available in your MATLAB installation. This solver is commonly included in MATLAB's core functionality.

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Therefore , the solution of the given problem of unitary method comes out to be the parking lot has 60 trucks.

It is possible to accomplish the objective by using this widespread convenience, pre-existing variables, or all significant components from the initial Diocesan adaptable survey that adhered to a specific methodology. If it doesn't, both of the essential components of a term confirmation outcome will undoubtedly be lost, but if it is, there is going to be another opportunity to contact the entity.

Here,

Let's begin by giving the unknowns variables:

x = number of vehicles

Van count = 4 times

Since there are 205 cars overall, the number of lorries is equal to (205 - 11x).

The value of x can be determined using the second bit of knowledge:

=> 4x/3 = (205 - 11x)/2

When we simplify this solution, we obtain:

=> 8x = 3(205 - 11x)

=> 8x = 615 - 33x

=> 41x = 615

=> x = 15

We can now determine the quantity of vans:

Van count = 4x = 4(15) = 60

Consequently, the parking lot has 60 trucks.

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y  =  − 1 /8x - 19/4

i think

Let f, g and h be the functions from the set of integers to the set of integers defined by f(x) = 2x +3, g(x) = 3x + 2 and h(x) = x3 +1.

(a) To find (f º g)(x), we substitute g(x) into f(x) as follows:

  (f º g)(x) = f(g(x)) = f(3x + 2) = 2(3x + 2) + 3 = 6x + 4 + 3 = 6x + 9.

(b) To find (g º f)(x), we substitute f(x) into g(x) as follows:

  (g º f)(x) = g(f(x)) = g(2x + 3) = 3(2x + 3) + 2 = 6x + 9 + 2 = 6x + 11.

(c) To find the inverse of f(x), denoted as l'ind (f)(x), we solve for x in terms of f(x):

  x = (f(x) - 3) / 2.

  Rearranging the equation, we get f^(-1)(x) = 1/2x - 3/2.

(d) To find (h + h)(x), we add h(x) to itself:

  (h + h)(x) = h(x) + h(x) = (\(x^3\) + 1) + (x^3 + 1) = 2\(x^3\) + 2.

(e) To find the inverse of h(x), denoted as h^(-1)(x), we solve for x in terms of h(x):

  x = (h(x) - 1)^(1/3).

  Rearranging the equation, we get h^(-1)(x) = (x - 1)^(1/3).

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6=30

12=60

15=80

Step-by-step explanation:

for 6 mini she will use 30 pepperoni slices

if she uses 60 pepperoni slices =12 mini

for 16 mini she will use 80 pepperoni slices.

For confirmation use the graph table.

Answer:

A.

Step-by-step explanation:

Answer:

=The opposite angles of a parallelogram are equal

=(3x+4)

=(5x-2)

=-2x=-6

=x=6+2

=x=3=

1st angle=3x+4=13

3rd angle=5x-2=13

=sum of adjacent side of angle is 180°

=Let the adjacent (2nd angle ) be y=

y+13°=180°

=y=180°-13°

=y=167°=

2nd angle=4th angle

=2nd angle=167° 

=4th angle=167°

Step-by-step explanation:

This might be confusing, but I hope it helps <3

Answer:

A (1,0), B (3,0) Q (2,-1) P(0,3)

Step-by-step explanation:

A(1,0) B (3,0) these are the roots of the current graph so the factors or the x-intercepts.

Q is the minimum so it is halfway between the x-intercepts

halfway = 3+1/2 , x=2

plug x=2 into the equation

y=(2-1)(2-3)

y=  -1

therefore Q = (2,-1)

P is the y-intercpet when x=0, so plug x=0 into the equation

y=(0-1)(0-3) = 3

therefore Q =

(0,3)

The absolute maximum of f(x) is e^(2pi), which occurs at x = 2pi, and the absolute minimum of f(x) is approximately -1.30, which occurs at x = 5*pi/4

a. To find the absolute maximum and minimum values of f(x), we can use the first derivative test and the endpoints of the given interval.

First, we find the first derivative of f(x):

f'(x) = e^xcos(x) - e^xsin(x)

Then, we find the critical points of f(x) by setting f'(x) = 0:

e^xcos(x) - e^xsin(x) = 0

e^x(cos(x) - sin(x)) = 0

cos(x) = sin(x)

x = pi/4 or x = 5*pi/4

Note that these critical points are in the domain [0, 2*pi].

Next, we find the second derivative of f(x):

f''(x) = -2e^xsin(x)

We can see that f''(x) is negative for x in [0, pi/2) and (3pi/2, 2pi], and f''(x) is positive for x in (pi/2, 3*pi/2).

Therefore, x = pi/4 is a relative maximum of f(x), and x = 5*pi/4 is a relative minimum of f(x). To find the absolute maximum and minimum of f(x), we compare the values of f(x) at the critical points and the endpoints of the domain:

f(0) = e^0cos(0) = 1

f(2pi) = e^(2pi)cos(2pi) = e^(2pi)

f(pi/4) = e^(pi/4)cos(pi/4) ≈ 1.30

f(5pi/4) = e^(5*pi/4)cos(5pi/4) ≈ -1.30

Therefore, the absolute maximum of f(x) is e^(2pi), which occurs at x = 2pi, and the absolute minimum of f(x) is approximately -1.30, which occurs at x = 5*pi/4.

b. To find the intervals on which f(x) is increasing, we look at the sign of f'(x) on the domain [0, 2pi]. We know that f'(x) = 0 at x = pi/4 and x = 5pi/4, so we can use a sign chart for f'(x) to determine the intervals of increase:

x 0 pi/4 5*pi/4 2*pi

f'(x) -e^0 0 0 e^(2*pi)

f(x) increasing relative max relative min decreasing

Therefore, f(x) is increasing on the interval [0, pi/4) and decreasing on the interval (pi/4, 2*pi].

c. To find the x-coordinate of each point of inflection of the graph of f, we need to find where the concavity of f changes. We know that the second derivative of f(x) is f''(x) = -2e^xsin(x), which changes sign at x = pi/2 and x = 3*pi/2.

Therefore, the point (pi/2, f(pi/2)) and the point (3pi/2, f(3pi/2)) are the points of inflection of the graph of f.

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Given the previous length of the bedroom and the current scale factor, the length of the bedroom in the current scale drawing is 1008ft.

Scale factor is simply a measure for similar figures, who look the same but have different scales or measures.

To get new dimension;

New dimension = scale factor × current dimension

Given that;

New dimension = scale factor × current dimension

New length of the bedroom = 112 × 9ft

New length of the bedroom = 1008ft

Therefore, given the previous length of the bedroom and the current scale factor, the length of the bedroom in the current scale drawing is 1008ft.

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To find g(-2), we'll substitute -2 for x in the equation g(x) = -4x² - 5x + 9. So,g(-2) = -4(-2)² - 5(-2) + 9g(-2). The value of g(-2) is -6.

To find g(-2), substitute -2 for x in the equation

g(x) = -4x² - 5x + 9 to get

g(-2) = -6 + 9g(-2)

We are given three functions as follows:

f(x) = (1/3)x - 5, g(x)

= -4x² - 5x + 9, and

h(x) = 1/(x - 8) + 3.

We are asked to find g(-2), which is the value of g(x) when x = -2.

Substituting -2 for x in the equation g(x) = -4x² - 5x + 9, we get

g(-2) = -4(-2)² - 5(-2) + 9.

This simplifies to g(-2) = -16 + 10 + 9 = -6.

Hence, g(-2) = -6.

The value of g(-2) is -6.

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