Use synthetic division and the factor theorem to determine if x−c is a factor of f(x). f(x)=6x3+9x2−12x−2;x+21​ Is x+21​ a factor of f(x)=6x3+9x2−12x−2?

\(\longrightarrow{\green{- 9 {x}^{2} + 14x + 16}}\) 

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\( \sqrt{49} + [ \sqrt{81} - x \: (9x - 14) ] \\ \\ = \sqrt{7 \times 7} + [ \sqrt{9 \times 9} - 9 {x}^{2} + 14x] \\ \\ = \sqrt{( {7})^{2} } + [ \sqrt{ ({9})^{2} } - 9 {x}^{2} + 14x ] \\ \\ (∵ \sqrt{ ({x})^{2} } = x ) \\ \\ = 7 + (9 - 9 {x}^{2} + 14x) \\ \\ = 7 + 9 - 9 {x}^{2} + 14x \\ \\ = - 9 {x}^{2} + 14x + 16\)

\(\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}\)

Answer:

Step-by-step explanation:

Formula Development

Let the width = w

Let the Length = 5*w

P = 72

P =2w + 2L

Area = 5w * w

Solution

Start with the Perimeter. Solve for w.

P = 2w + 2L                  Substitute the givens

72 = 2w + 2*5w            Combine

72 = 2w + 10w              Combine   Combine again

72 = 12 w                       Divide by 12

72/12 = 12w/12

w = 6

Now for the area

Area = 5w * w

w = 6

Area = 5*6*6

Answer: Area = 180 cm^2

Answer:

f(x)=x-2

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: (−∞,∞),x|x ∈R}(-∞,∞),{x|x ∈R}

Range: (−∞,∞),{y|y∈R}

g(x)=x^2-3x+2

Domain: (−∞,∞),{x|x ∈R}(-∞,∞),{x|x ∈R}

Range: [−1/4,∞),{y∣y≥−1/4}

The given equation is a recursive formula where a subscript i equals the product of a subscript i-1 and 2, with the initial value of a subscript 1 being -4a.

The equation represents a recursive relationship between the terms of the sequence. Starting with the initial term, a subscript 1, the subsequent terms are determined by multiplying the previous term, a subscript i-1, by 2. This recursive formula can be written as a subscript i = a subscript i-1 * 2.

Given that a subscript 1 = -4a, we can use this initial value to find the subsequent terms of the sequence. To calculate a subscript 2, we substitute i = 2 into the formula:

a subscript 2 = a subscript 2-1 * 2 = a subscript 1 * 2 = -4a * 2 = -8a.

Similarly, for a subscript 3:

a subscript 3 = a subscript 3-1 * 2 = a subscript 2 * 2 = -8a * 2 = -16a.

By applying the recursive formula repeatedly, we can generate the terms of the sequence. Each term is obtained by multiplying the previous term by 2.

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Answer:

C

Step-by-step explanation:

\(\frac{3-\sqrt{3} }{3+\sqrt{3} } *\frac{3-\sqrt{3} }{3-\sqrt{3} } \\\\=\frac{(3-\sqrt{3})^{2} }{(3+\sqrt{3} )(3-\sqrt{3} )} \\\\=\frac{9-2*3\sqrt{3}+3 }{9-3}\\\\=\frac{12-6\sqrt{3} }{6} \\\\=2-\sqrt{3}\)

Following the 5-step FDR (Function Design Recipe), here is the implementation of the area_cylinder function in MATLAB:

% Step 1: Problem Analysis

% The problem is to calculate the of a cylinder given its radius and height.

% Step 2: Specification

function area = area_cylinder(radius, height)

% area_cylinder calculates the area of a cylinder

%   Inputs:

%       - radius: the radius of the cylinder base

%       - height: the height of the cylinder

%   Output:

%       - area: the area of the cylinder

% Step 3: Examples

% Example 1: area_cylinder(6, 7) should return 376.9911

% Example 2: area_cylinder(3, 4) should return 131.9469

% Step 4: Algorithm

% The formula to calculate the area of a cylinder is: A = 2*pi*r^2 + 2*pi*r*h,

% where r is the radius of the base and h is the height of the cylinder.

% We can use this formula to calculate the area.

% Step 5: Implementation

% Calculate the area using the formula

area = 2 * pi * radius^2 + 2 * pi * radius * height;

end

You can now call the area_cylinder function with the radius and height values to calculate the area of the cylinder. For example:

area = area_cylinder(6, 7);

disp(['The area of the cylinder is: ', num2str(area)]);

This will output: "The area of the cylinder is: 376.9911" for the given radius of 6 and height of 7.

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Answer:

1.) Kindly check attached picture for possibility diagram

(2)

1) 0.125 2)0.963 3.)0.234 4.)0.625 5.)0.656

Step-by-step explanation:

Probability = required outcome / Total possible outcomes

1) P(product is a prime number)

Appearance of prime numbers = 8 times

P(product is a prime number) = 8/64 = 0.125

2.) P(not a perfect square) = 1 - p(perfect square)

1 - (12/64) = 52/54 = 0.963

3.) P(a multiple of 5) = 15/64 = 0.234

4.)P(less than or equal to 21) = 40/64 = 0.625

5.)P(divisible by 4 or 6) = 42/64 = 0.656

Answer:

In a 45°−45°−90° triangle, the length of the hypotenuse is 2√‾ times the length of a leg.  Note that an isosceles right triangle must be a 45°−45°−90° triangle. x2+x2=2x2=(x2‾√)2

i know this isn't an easy explanation but hopefully it might clear something up for you? ill keep looking for things just in case..

Answer:

x = 7

Step-by-step explanation:

use pythagoras theorem

x² + ײ = (7.sqrt(2))²

2x² = 49x2

x² = 49

× = 7

To find the center of mass of the planar lamina, introduce an appropriate coordinate system and follow the steps mentioned below. Round your answers to three decimal places.

To introduce an appropriate coordinate system and find the center of mass of a planar lamina, follow these steps:
1. Choose a coordinate system: Select a coordinate system that best suits the problem and simplifies the calculations. Common choices are Cartesian (x, y), polar (r, θ), or any other suitable coordinate system.
2. Assign coordinates to each point: Label each point on the lamina with its respective coordinates according to the chosen coordinate system.
3. Determine the mass of each point: Assign a mass to each point on the lamina. This can be done by considering the density of the material and the area element at each point. If the mass is not explicitly given, assume it to be 1 for simplicity.
4. Find the total mass of the lamina: Sum up the masses of all the points on the lamina to obtain the total mass.
5. Calculate the x-coordinate of the center of mass: Multiply the x-coordinate of each point by its mass, and then sum up these products. Divide the result by the total mass to get the x-coordinate of the center of mass.
6. Calculate the y-coordinate of the center of mass: Multiply the y-coordinate of each point by its mass, and then sum up these products. Divide the result by the total mass to get the y-coordinate of the center of mass.
7. Round the answers: Round the x-coordinate and y-coordinate of the center of mass to three decimal places, as specified in the question.
Therefore, to find the center of mass of the planar lamina, introduce an appropriate coordinate system and follow the steps mentioned above. Round your answers to three decimal places.

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An unusual event is an occurrence that has a low probability of happening. The cutoff for identifying unusual events not always be​ 0.05, because it is not always a good idea to utilize the same cutoff to spot unexpected occurrences.

An unusual event is an occurrence that has a low probability of happening.

If an event is improbable, its likelihood is zero. If an occurrence is unavoidable, its probability is one.

The probability of an event happening increases as it gets closer to 1. An occurrence that has a probability of 0.375, for instance, is more likely to happen than one with a probability of 0.125.

The less likely an event is to occur, the closer the probability is to 0. An unusual event is what this kind of event falls under. A probability of 5%, or 0.05, is typically regarded as unusual event.

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43.36% of the scores fall between 690 and 900 on the collegiate mathematics readiness assessment.

To determine the percentage of scores between 690 and 900, we need to calculate the area under the normal distribution curve between these two values.

First, we need to standardize the scores using the formula z = (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation.

For the score 690:

z1 = (690 - 680) / 120 = 0.0833

For the score 900:

z2 = (900 - 680) / 120 = 1.8333

Next, we need to find the area between these two standardized scores. We can use a standard normal distribution table or a statistical calculator to find the corresponding probabilities.

From the standard normal distribution table, we find that the area to the left of z1 is approximately 0.5328 and the area to the left of z2 is approximately 0.9664.

To find the area between z1 and z2, we subtract the smaller area from the larger area:

Area = 0.9664 - 0.5328 = 0.4336

Finally, we convert the area to a percentage by multiplying by 100:

Percentage = 0.4336 * 100 ≈ 43.36%

Therefore, approximately 43% of the scores fall between 690 and 900 on the collegiate mathematics readiness assessment.

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Answer:

Step-by-step explanation:

1. Write the question.

17 - 2x = -11

2. Subtract 17 from both sides

-17          -17

    - 2x = -28

3. Negatives cancel

      2x = 28

4. Divide both sides by 2

        /2     /2

        x = 14

5. Check the answer, write the equation.

17 - 2x = -11

6. Substitute x with the value

17 - 2(14) = -11

17 - 28 = -11

-11 = -11

The answer is correct!

Hope this helped,

Kavitha

From the details that we have here we can say that the amount of vinegar that is mixed with 1 milliliter of soy sauce is 0.67

the vinegar is given as 100

the soy sauce is given to be 150

The ratio would be

100 / 150

= 0.67

hence we can say that the amount of vinegar that is mixed with 1 milliliter of soy sauce is 0.67

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Answer:

BC- AB < CA < AB + BC

Step-by-step explanation:

The sides opposite the larger angles are longer than the sides opposite smaller angles.

So, BC (opposite < A) is longer than AB (opposite < C) so,

BC > AB

The other side AC cannot be greater than AB + BC, otherwise the triangle would not exist, so,

AC < AB + BC

Also, CA > BC - AB  

The range for AC is

BC- AB < CA < AB + BC

Answer:

168 miles

Step-by-step explanation:

d = rt

d = 42 × 4

d = 168

Answer:

d = rt

d = 42×4

d = 168

Step-by-step explanation:

That is the distance between the towns.

You have to multiply the amount of miles by the time it took.

Answer:

RY and ST are skew in this rectangular prism.

x= 0.5714

Explanation

Step1

therefore, replace

so, the answeris

x= 0.5714

I hope this helps you

Answer:

-3

Step-by-step explanation:

-1*-1*-3

-*-=+

1*-3=

-3

The measure of an inscribed angle with the center of the circle in the interior of the angle is half the measure of its intercepted arc.

According to Corollary 2 of the Inscribed Angle Theorem, when an angle is inscribed in a circle and the center of the circle lies in the interior of the angle, the measure of the inscribed angle is half the measure of its intercepted arc.

In other words, if we have a circle and an angle formed by two intersecting chords or secants, and the center of the circle is located within the angle, then the measure of the inscribed angle is equal to half the measure of the arc intercepted by the angle.

This corollary is a useful property that helps establish a relationship between inscribed angles and their intercepted arcs in a circle. It allows us to determine the measure of an inscribed angle by considering the corresponding intercepted arc, and vice versa.

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Answer: A is 60 degrees, B is 60 degrees, C is 60 degrees ...

As the triangle shows that all the sides are equal in length. We can say it's an equilateral triangle. Now all the three sides added in a triangle always equals to 180 degrees. So you can either do it in a formula way that if one side is x then all the other two side is x as well because all the side lengths are equal as stated. So we can come to this formula,

3x = 180

x = 180/3

x = 60

Or, we can just remember this that if all the angles are equal in a triangle then each angle will always be 60 degrees...

Brainliest pweaseeeee if the answers are correct!

Answer:

13

Step-by-step explanation:

h^2=5^2+12^2

h^2=25+144

h^2=169

h=sqr169

h=13

Answer:

13

Step-by-step explanation:

by Pythagorean theorem a²+b²=c²

a=5, b=12, c=AC

5²+12²= 25+144

=169

c²=169

c=✓169

=± 13 ( but length could only be positive)

AC=13

Answer:

Step-by-step explanation:

what i do not undersante

The mean in minutes of the length of time given= 9.1

The formula used for the determination of mean when a frequency table is given is

= total/n

Where total = frequency×midpoint

n = 42

To calculate the total, the mid point of each length of time is determined as follows;

1+4/2 = 2.5 × 4 = 10

4+7/2= 5.5 × 8 = 44

7+10/2 = 8.5 × 14= 119

10+13/2 = 11.5× 9 = 103.5

13+16/2= 14.5×5 = 72.5

16+19/2= 17.5× 2= 35

Total= 10+44+119+103.5+72.5+35 = 384

Therefore mean = 384/42= 9.1

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Answer:

8%

Step-by-step explanation:

Hello,

8% of the students take neither History or French

so we have 8*200/100=8*2=16 students  out of French and History

let s say that

a is the number of students taking only History

b is the number of students taking both History and French

c is the number of students taking only French

10% of those who take History also take French

so 0.10(a+b)=b <=> 0.10a+0.10b=b

<=> 0.10a+0.10b-0.10b=b-0.10b=0.9b

<=> 0.10a=0.90b

let's multiply by 10 it comes a = 9b

4 times as many students take History as take French

so a + b = 4 (b + c)

it comes 9b + b = 10b = 4b + 4c

<=> 10b-4b=4b+4c-4b=4c

<=> 6b=4c

<=> 3b=2c

<=> c = 3b/2

and we know that a + b + c = 200 - 16 = 184

so

9b + b + 3b/2 = 184 we can multiply by 2 it comes

20 b + 3b = 184*2

23b = 184*2 = 23 * 8 *2 = 23*16

b = 23*16/23 = 16

so b = 16

c = 3*16/2 = 24

c = 24

a = 9b = 144

a = 144

you can see the Venn diagram below

and then the probability that a student picked at random does History and French is 16/200 = 8%

so the answer is 8%

hope this helps

The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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Answer:

1 and 3 are arithmetic.

Q1:

Common Difference = -3

Next Number = -12

Q2:

Common Difference = No common difference

Next Number = 12

Q3:

Common Difference = 13

Next Number = 179

Step-by-step explanation:

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k. An arithmetic equation will have a common difference.

Answer:

Step-by-step explanation:

x+61=90

x=29 degrees

Answer:

111 meters, break each area into a rectangle, find the areas, then add.