what’s the answer to this question

The factored form of the polynomial P(x) = x³ + 2x² + 4x + 8 is P(x) = (x + 1)(x² + x + 7). The quadratic factor x^2 + x + 7 cannot be further factored into linear factors with real coefficients.

To factor the polynomial P(x) = x³ + 2x² + 4x + 8, we can look for potential roots by applying synthetic division or by using synthetic substitution. In this case, we can start by trying small integer values as possible roots, such as ±1, ±2, ±4, and ±8, using the Rational Root Theorem.

By synthetic substitution, we find that -1 is a root of the polynomial. Dividing P(x) by (x + 1) using long division or synthetic division, we get:

P(x) = (x + 1)(x² + x + 7)

Now, we need to factor the quadratic expression x² + x + 7. However, upon factoring this quadratic expression, we find that it cannot be factored further into linear factors with real coefficients. Therefore, the factored form of P(x) is:

P(x) = (x + 1)(x² + x + 7)

Please note that the quadratic factor x² + x + 7 does not have any real roots. Therefore, the complete factored form of P(x) is as given above.

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Answer:

-13-4=-17

Step-by-step explanation:

When you are subtracting more from a negative number, you can think of it as adding those numbers together. 13+4 would be 17, so if you flip the signs to negatives, it would be -17.

(a) U × V = (22, -37, -60)

(b) V × U = (-22, 37, 60)

(c) V × V = (0, 0, 0)

(a) To find U × V (cross product of U and V), we use the formula:

U × V = (u2v3 - u3v2, u3v1 - u1v3, u1v2 - u2v1)

Plugging in the values, we get:

U × V = (2*(-2) - 3*(-2), 3*(-8) - 8*7, 8*(-2) - 2*(-8))

      = (-4 + 6, -24 - 56, -16 + 16)

      = (2, -80, 0)

      = (22, -37, -60)

(b) To find V × U (cross product of V and U), we use the same formula:

V × U = (v2u3 - v3u2, v3u1 - v1u3, v1u2 - v2u1)

Plugging in the values, we get:

V × U = (-2*3 - 7*2, 7*8 - (-8)*3, (-8)*2 - (-2)*8)

      = (-6 - 14, 56 + 24, -16 - 16)

      = (-20, 80, -32)

      = (-22, 37, 60)

(c) To find V × V (cross product of V with itself), we use the same formula:

V × V = (v2v3 - v3v2, v3v1 - v1v3, v1v2 - v2v1)

Since V is (-8, -2, 7), we substitute the values:

V × V = (-2*7 - 7*(-2), 7*(-8) - (-8)*7, (-8)*(-2) - (-2)*(-8))

      = (-14 + 14, -56 + 56, 16 - 16)

      = (0, 0, 0)

The cross products of the given vectors are:

(a) U × V = (22, -37, -60)

(b) V × U = (-22, 37, 60)

(c) V × V = (0, 0, 0)

The cross product U × V represents a vector that is orthogonal to both U and V. The cross product V × U represents a vector that is orthogonal to both V and U. The cross product V × V results in the zero vector, indicating that V is linearly dependent on itself.

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Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Answer:

Step-by-step explanation:

y= 1/4x + 2.5

Answer: the pattern is that the rectangles width and length get timed 2.

Step-by-step explanation: that pattern will continue until the rectangle will get bigger than the unobservant universe...

Answer:   \(d \ge 1 \ \text{ or } \ d \le -3\\\\\)

Both parts are needed to form the full solution set.

=============================================

Work Shown:

\(3|d+1|-7 \ge -1\\\\3|d+1| \ge 6\\\\|d+1| \ge 2\\\\d+1 \ge 2 \ \text{ or } \ d+1 \le -2\\\\d \ge 1 \ \text{ or } \ d \le -3\\\\\)

In the second step, I added 7 to both sides. In the third step, I divided both sides by 3. Afterward, I used the rule that \(|x| \ge k\) breaks down into \(x \ge k \ \text{ or } \ x \le -k\) for some positive value k. The last thing to do is to subtract 1 from both sides to fully isolate d.

By using Permutation, The number of ways in which 4 distinct prizes be awarded is 5,040.

Number of Contestants = 10

Number of distinct prizes = 4

We will use permutation to evaluate the number of ways in which 4 distinct prizes be awarded,

The first prize can be given in 10 ways

The second prize can be given in 9 ways

The third prize can be given in 8 ways

The fourth prize can be given in 7 ways

Now, Total number of ways 4 prizes can be awarded = 10 * 9 * 8* 7 = 5,040

Thus, the number of ways in which 4 distinct prizes be awarded is 5,040

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The statement if 3x - 4 > 8 , then x > 4 is true

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

If 3x - 4 > 8 , then x > 4

Add 4 to both sides of the inequality

So, we have

3x > 12

Divide both sides by 3

x > 4

The above means that if 3x - 4 > 8 , then x > 4 is true

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Answer:

72-63=9

9/72=13%

13% IS .13 SO TENTH IS .1

I AM NOT SURE ABOUT THE TENTH

Step-by-step explanation:

Answer:

It may be C or D

I think its C.

Sorry if I'm wrong.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

let the number be n then increasing - 7 by n is - 7 + n and

- 7 + n = 12 ( add 7 to both sides )

n = 19

Answer:

Variant c

Step-by-step explanation:

c²=4*9

c=6

You can apply phyphagor

b²=6²+9²=36+81=117

\(3 \sqrt{13} \)

The option that would decrease the margin of error is B. increasing the sample size.

The margin of error is a statistic that expresses the amount of random sampling error in survey results. The greater the margin of error, the less confident one should be that a poll result will accurately reflect the results of a population census.

Because the sample size is in the denominator of the margin of error calculation, increasing the sample size reduces the margin of error. Furthermore, by expressing a value in a range, the margin of error assists researchers in determining its accuracy.

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Complete question

An animal rescue agent wanted to estimate the true proportion of all animals in shelters that are adopted each month. To do so, she selects a random sample of 100 animals that were in shelters last month and determines that the 95% confidence interval for the true proportion of animals adopted each month is between 0.12 and 0.24. Which of the following would decrease the margin of error?

selecting another sample

increasing sample size

decreasing sample size

increasing confidence level

The point that did not lie on the circle was (-2, -3).

The given equation of the circle is (x - 3)² + (y + 2)² = 25. We need to find the point that does not belong to the graph of the circle.The general equation of the circle is (x - a)² + (y - b)² = r²where (a, b) is the center of the circle and r is the radius.By comparing the given equation with the general equation, we get:(x - 3)² + (y + 2)² = 25.

The center of the circle is (3, -2) and the radius is √25 = 5.Now, let's check each point one by one whether it lies on the circle or not:(8, -2)Putting x = 8 and y = -2 in the equation, we get:(8 - 3)² + (-2 + 2)² = 25which is true.

Therefore, (8, -2) lies on the circle.(3, 3)Putting x = 3 and y = 3 in the equation, we get:(3 - 3)² + (3 + 2)² = 25which is true. Therefore, (3, 3) lies on the circle.(3, -7)Putting x = 3 and y = -7 in the equation, we get:(3 - 3)² + (-7 + 2)² = 25which is true.

Therefore, (3, -7) lies on the circle.(0, 2)Putting x = 0 and y = 2 in the equation, we get:(0 - 3)² + (2 + 2)² = 25which is true. Therefore, (0, 2) lies on the circle.(-2, -3).

Putting x = -2 and y = -3 in the equation, we get:(-2 - 3)² + (-3 + 2)² = 50which is false.

Therefore, (-2, -3) does not lie on the circle.Hence, the point that does not belong to the graph of the circle is (E) (-2, -3).

The point that does not belong to the graph of the circle is (E) (-2, -3). To get the answer, we compared the given equation with the general equation of a circle.

Then we found out the center and radius of the circle. Finally, we checked each point one by one to find out whether it lies on the circle or not. The point that did not lie on the circle was (-2, -3)

The circle is one of the most commonly encountered shapes in geometry. The circle is the locus of all points in a plane that are equidistant from a given point, known as the center of the circle. The radius is the distance between the center and any point on the circle.

The equation of a circle with center (a, b) and radius r is given by (x - a)² + (y - b)² = r².

The given equation of the circle is (x - 3)² + (y + 2)² = 25. We compared the given equation with the general equation to find out the center and radius of the circle.

We found out that the center was (3, -2) and the radius was 5. To find the point that did not belong to the graph of the circle, we checked each point one by one. We found that the point (-2, -3) did not lie on the circle.

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Answer:

Step-by-step explanation:

It is asking for the "mode" which is the data element you see the most, therefore it is 2.

Answer:

LOL me neither what grade you in I'm in 11 grade and never learned this

The volume of the cylindrical tank for refrigerant with an inside diameter of 14 inches and a height of 16 inches is 10,736 cubic inches.

The volume of a cylinder can be calculated using the formula:

\(\[ V = \pi r^2 h \]\)

where V represents the volume, \(\(\pi\)\) is a mathematical constant approximately equal to 3.14159, r is the radius of the cylinder (which is half the diameter), and h is the height of the cylinder.

In this case, the inside diameter of the tank is given as 14 inches, so the radius can be calculated as \(\(r = \frac{14}{2} = 7\)\) inches. The height of the tank is given as 16 inches. Substituting these values into the formula, we get:

\(\[ V = 3.14159 \times 7^2 \times 16 \approx 10,736 \text{ cubic inches} \]\)

Therefore, the volume of the cylindrical tank for refrigerant is approximately 10,736 cubic inches.

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The square root of the 15384 by division method is a 124.032.

According to the statement

We have to find that the square root with the division method.

So, For this purpose, we know that the

The long division is the mathematical method for dividing large numbers into smaller groups or parts

And

A generalised version of this method called polynomial long division is also used for dividing polynomials

From the given information:

The number is a 15384.

And then

Firstly in this number by the squaring of the same number and by this method after going down until the remainder is zero.

And after solving the square root of 15384

The answer will become 124.032.

So, The square root of the 15384 by division method is a 124.032.

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14. There are 56 different arrangements of president and vice-president possible in a club consisting of eight members.

16. There are 10 different arrangements possible.

14. Finding the number of different arrangements of president and vice-president in a club with eight members, consider that the positions of president and vice-president are distinct.

For the position of the president, there are eight members who can be chosen. Once the president is chosen, there are seven remaining members who can be selected as the vice-president.

The total number of different arrangements is obtained by multiplying the number of choices for the president (8) by the number of choices for the vice-president (7). This gives us:

8 * 7 = 56

16. To determine the number of different arrangements possible for Tito's essay, we can use the concept of combinations. Tito has to choose three questions out of the five available to write his essay. The number of different arrangements can be calculated using the formula for combinations, which is represented as "nCr" or "C(n,r)." In this case, we have 5 questions (n) and Tito needs to choose 3 questions (r) to write his essay.

Using the combination formula, the number of different arrangements can be calculated as:

\(C(5,3) = 5! / (3! * (5-3)!)= (5 * 4 * 3!) / (3! * 2 * 1)= (5 * 4) / (2 * 1)= 20 / 2= 10\)

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Answer:

Step-by-step explanation:

The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse

Answer:

A. You would trace an argument by seeing if the reasons and evidence are relevant in their support of the claim.

Step-by-step explanation:

The tracing of an argument should be seen when the reasons & evidence should be relevant for supporting the claim.

The following information should not be considered:

Therefore we can conclude that the first option is correct.

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Answer:

A. 4

Step-by-step explanation:

If the length 6 become 3 in the corresponding side of the congruent shape,

then 8 becomes 4 (Ratio 2:1)

Hope this helps

Answer:

0

Step-by-step explanation:

-2-(-4)-2

We can break down the problem first. The beginning of the problem is...

-2-(-4)

Two negatives make a positive. An equivalent way to say this is

-2+4

-2+4=2

Next, we can solve for the last part. At the end of the equation, you have to subtract 2, so that's what we'll do!

2-2=0

The answer to this is 0!

I hope you understood the explanation...have an amazing day!!!! :3

Suppose A is a 4x4 matrix, B is a 4x3 matrix, and C is a 3x4 matrix such that A = BC. To show that A is not invertible, we need to demonstrate that it does not have an inverse.

Since B is a 4x3 matrix, it has 4 rows and 3 columns, which means that its rank can be at most 3. The product of two matrices, in this case, BC, will have a rank that is less than or equal to the minimum rank of the two matrices involved (B and C). Therefore, the rank of A (which is equal to the rank of BC) will be less than or equal to the rank of B, which is at most 3.

For a matrix to be invertible, its rank must be equal to its dimension. However, since A is a 4x4 matrix, its dimension is 4. Given that the rank of A is at most 3, it cannot have a rank equal to its dimension, and thus, A is not invertible.

To show that a is not invertible, we need to prove that a doesn't have an inverse matrix. One way to do this is by contradiction.  Suppose that a is invertible, which means that there exists a matrix a^-1 such that aa^-1 = a^-1a = I, where I is the identity matrix.

Then, we can use the fact that a=bc to substitute for a in the above equation:

(bc)a^-1 = a^-1(bc) = I

Next, we can use the associativity of matrix multiplication to rearrange the above equation:

b(ca^-1) = (a^-1b)c = I

Now, notice that ca^-1 is a 3 by 3 matrix, and b is a 4 by 3 matrix. So, the product b(ca^-1) is a 4 by 3 matrix. On the other hand, (a^-1b)c is a 3 by 4 matrix. This is a contradiction because two matrices with different dimensions cannot be equal. Therefore, our initial assumption that a is invertible must be false, and a is not invertible.

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Answer:

its the first graph from 1/2 - 1 - 1 1/2

Step-by-step explanation:

its all even and its constantly going up

Answer:

Step-by-step explanation:

6--6 = 12

4-1 = 3

12/3 = 4

y=4x

-6-4 = -10

y=4x-10

The formula of slope:

Slope = (d - b) / (c - a)

where (a, b) and (c, d) are the two points.

The equation of the line that passes through (1, -6) and (4, 6) is

y = 4x - 10

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The line passes through (1, -6) and (4, 6).

The formula of slope:

Slope = (d - b) / (c - a)

where (a, b) and (c, d) are the two points.

Now,

(1, -6) = (a, b) and (4, 6) = (c, d)

Slope = (6 + 6) / (4 - 1) = 12 / 3 = 4

m = 4

The equation of a line is given as y = mx + c.

(1, -6) = (x, y)

-6 = 4 x 1 + c

-6 = 4 + c

-6 - 4 = c

c = -10

Now,

The equation of the line that passes through (1, -6) and (4, 6) is

y = 4x - 10

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