621126.4862 divided by 126.48 ​

6x^5 - 30x^4 - 84x^3

we can factor out 6x^3

6x^3(x^2 - 5x - 14)

Also, we can factor x - 7 and x + 2 out of x^2 - 5x - 14

The final answer = 6x^3(x - 7)(x  + 2)

a) The circle crosses the y-axis at the points (0, 6) and (0, -2). b) the radius of the circle is 5. c) (i) The length of CP is √34. (ii) The length of PQ is 10.

(a) To find the y-coordinates of the points where the circle crosses the y-axis, we substitute x = 0 into the equation of the circle:

0² + y² + 6(0) - 4y = 12

y² - 4y = 12

y² - 4y - 12 = 0

To solve this quadratic equation, we can factor it:

(y - 6)(y + 2) = 0

Setting each factor to zero, we find two possible values for y:

y - 6 = 0 => y = 6

y + 2 = 0 => y = -2

Therefore, the circle crosses the y-axis at the points (0, 6) and (0, -2).

(b) To find the radius of the circle, we can complete the square to rewrite the equation of the circle in standard form:

x² + y² + 6x - 4y = 12

(x² + 6x) + (y² - 4y) = 12

(x² + 6x + 9) + (y² - 4y + 4) = 12 + 9 + 4

(x + 3)² + (y - 2)² = 25

Comparing this equation with the standard form of a circle, (x - h)² + (y - k)² = r², we can see that the center of the circle is at (-3, 2) and the radius is √25 = 5.

Therefore, the radius of the circle is 5.

(c) (i) To find the length of CP, we can use the distance formula between two points. The coordinates of C are (-3, 2), and the coordinates of P are (2, 5).

The distance formula is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the coordinates into the formula, we have:

CP = √((2 - (-3))² + (5 - 2)²)

= √(5² + 3²)

= √(25 + 9)

= √34

Therefore, the length of CP is √34.

(ii) To find the length of PQ, we can use the fact that PQ is a tangent to the circle. The radius of the circle is 5, and the line segment CP is perpendicular to PQ.

Since CP is perpendicular to PQ, CP is the radius of the circle. Therefore, CP = 5.

Therefore, the length of PQ is equal to 2 times the length of CP:

PQ = 2 * CP

= 2 * 5

= 10

Therefore, the length of PQ is 10.

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The probability of point being in between B and C is 0.167

Probability is a statistic used to indicate the likelihood or potential that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.

The likelihood is based on the range of potential outcomes. the total number of possible outcomes. As an illustration, since there is only one way to get a head and a total of two possible results, the likelihood of flipping a coin and getting heads is one in two. a tail or a head.

Distance between B and C= 4 units

Total distance=24

Probability that point lie between B and C = 4/24 =1/6

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The type of influence on wellness that this represents is given as follows:

A. Social.

An influence on wellness is an activity that improves the morale of certain aspect of our lives.

The aspect improved in this problem is the social aspect, along with the physical aspect, as follows:

Since this is an example of social bonding, option A gives the correct option regarding which type of influence on wellness this is an example of.

For example, reading a book would be intellectual influence, while recycling would be environmental influence.

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The correct answer is "Bus 18, with merely an IQR of 16." The range is also smaller for Bus 18, but range is a less robust measure of variability and can be influenced by outliers.

What is IQR?

The IQR (interquartile range) provides a measure of the spread of the central 50% of the data, and is often used to identify outliers or to compare the variability of different datasets.

What is range?

Finding the variable's highest observed number (maximum) and deducting its minimum observed value yields the variable's range (minimum). Variational limits or a potential range: various steel prices; numerous styles; The scope or size of a method or action: understanding. the utmost or anticipated range of the a weapon's projectile. The number between both the lowest and maximum is known as the range of the a list or set. Align all of the numbers before determining the area. Next, subtract (subtract) the lowest number first from greatest number. The answer includes the list's range. The range of the list is given in the answer.

To compare the consistency of the travel times for Bus 18 and Bus 47, we need to use a measure of variability. Two common measures of variability are range and interquartile range (IQR) (interquartile range)

The range represents the discrepancy between the dataset's maximum and minimum values. The IQR  (interquartile range) is a measure of the spread of the middle 50% of the data, and is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1).

Looking at the graphs, we can see that Bus 18 has a smaller range than Bus 47 (16 vs. 24), but we cannot compare the IQRs just by looking at the graphs.

To calculate the IQR (interquartile range)  for each bus, we need to find the values of Q1 and Q3 for each dataset. We can do this by ordering the data and finding the median of the lower and upper halves. Using the values in the problem as a guide:

For Bus 18:

Q1 = median of {6, 6, 8, 9, 10, 10, 12, 14} = 9

Q3 = median of {16, 18, 18, 20, 22} = 18

So the IQR for Bus 18 is 18 - 9 = 9.

For Bus 47:

Q1 = median of {6, 10, 12, 12, 14, 14, 16, 16, 18} = 14

Q3 = median of {22, 22, 28, 28} = 25

So the IQR for Bus 47 is 25 - 14 = 11.

Based on these calculations, we can see that Bus 18 has a larger IQR (interquartile range)  than Bus 47, indicating that its travel times are more consistent. As a result, "Bus 18, with just an IQR of 16" is the right response. The range is likewise narrower for Bus 18, although range is a less reliable indicator of variability and is susceptible to outlier effect. The IQR  (interquartile range) is a better measure of spread for this comparison because it is less sensitive to outliers.

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Answer:

240

Step-by-step explanation:

Answer:

16 m^3

Step-by-step explanation:

Question:

"a regular square pyramid is 3m height and the perimeter of its base is 16m find the volume of the pyramid"

volume of pyramid = (1/3) * (area of base) * height

The perimeter of the base is 16 m, and the base is a square.

perimeter of square = 4 * side

4 * side = 16 m

side = 4 m

area of square = (side)^2

area of base = (4 m)^2 = 16 m^2

volume of pyramid = (1/3) * (area of base) * height

volume = (1/3) * (16 m^2) * 3 m

volume = 16 m^2

Answer:

He only added Sundays run

Step-by-step explanation:

The sequence an = \(1 + 4n^2\) is increasing.

In the given sequence, each term (an) is obtained by substituting the value of 'n' into the expression 1 + 4n^2. To determine whether the sequence is increasing, decreasing, or not monotonic, we need to examine the pattern of the terms as 'n' increases.

Let's consider the difference between consecutive terms:

\(a(n+1) - an = [1 + 4(n+1)^2] - [1 + 4n^2]\)

\(= 1 + 4n^2 + 8n + 4 - 1 - 4n^2\)

= 8n + 4

The difference, 8n + 4, is always positive for positive values of 'n'. Since the difference between consecutive terms is positive, it implies that each term is greater than the previous term. Hence, the sequence is increasing.

To illustrate this, let's consider a few terms of the sequence:

\(a1 = 1 + 4(1)^2 = 1 + 4 = 5\)

\(a2 = 1 + 4(2)^2 = 1 + 16 = 17\)

\(a3 = 1 + 4(3)^2 = 1 + 36 = 37\)

From these examples, we can observe that as 'n' increases, the terms of the sequence also increase. Therefore, we can conclude that the sequence an =\(1 + 4n^2\)is increasing.

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Answer:

Coupon second discount = 200 off

Step-by-step explanation:

Given:

Price of laptop = $1,313

Coupon first discount = 15% off

Coupon second discount = 200 off

Find:

Choose coupon get the bigger discount

Computation:

Coupon first discount = 15% off

Coupon first discount = 1,313 x 15%

Coupon first discount = $196.95

So,

Coupon second, for get the bigger discount

Answer:

x + 5, angle G is 16 degrees and angle F is

Step-by-step explanation:

3x + 11 = 5x - 9

3x + 10 = 5x

10 = 2x

x = 5

5(5) - 9 = 16

3(5) + 11 = 26

The value of the given sine function is √3/2, so the correct option is 2nd.

Given that an function Sin (-5π/3) we need to evaluate the expression,

To evaluate the trigonometric function sine of the angle (-5π/3), we can use the periodicity of the sine function.

Since the sine function has a period of 2, the sine of any given angle is equal to the sine of that angle plus or minus any multiple of 2.

To find an equal angle inside the main range (between -π and π), we can add 2 to the angle (-5/3).

Once adding 2:

(-5π/3) + 2π = (-5π/3) + (6π/3) = π/3

Now we can evaluate the sine of π/3, which is a commonly known angle. The sine of π/3 is √3/2.

Therefore, sin(-5π/3) = sin(π/3) = √3/2.

Hence the correct option is √3/2

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Answer:

Solve for  

x

by simplifying both sides of the equation, then isolating the variable.

Step-by-step explanation:

is this solve for x? you can just tell me what you are doing with this ex: adding, etc

\(5^2(5^3 \cdot 5^2)\\\\=5^{2+3+2}\\\\=5^7\\\\=78125\)

Answer:

5^7 or 78125

Step-by-step explanation:

5^2 (5^3 x 5^2)

This is the 5^2 is the same thing as 5x5 while 5^3 is the same as saying 5x5x5, when we evaluate these equations we get a new formula:

= 25 ( 125 x 25)

now we simplify.

= 25 (3125)

= 78125

Answer: 4 units, 3 units

Step-by-step explanation:

The side length of the square is measured to be 4 units on the graph

The height can be seen to be 3 units on the graph

4 units on each side

Height is 3 units

Step-by-step explanation:

Perpendicular height is 3 squares up, from the base of the square, to the top of the triangles.

The square measures 4 by 4 on each side.

Hope this helps!

Your answer: B) Statistically significant and quite small MPG prediction errors
This statement best describes the regression, as it indicates that the relationship between the variables is statistically significant.

Without specific data or statistical analysis, it is impossible to accurately determine which statement best describes the regression for y = highway miles per gallon in 91 cars. However, in general, a statistically significant regression means that there is a relationship between the variables being analyzed. The error in predictions refers to the difference between the predicted value and the actual value.

Therefore, A) statistically significant but large error in the MPG predictions and B) statistically significant and quite small MPG prediction errors could both be possible outcomes depending on the specific data and analysis. C) Not quite significant, but predictions should be very good is unlikely to be a valid statement if the regression is not statistically significant.
Additionally, the small MPG prediction errors suggest that the regression model is reliable and accurate in making predictions for highway miles per gallon in the 91 cars.

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x=1

Step-by-step explanation:

f(x)=0 is basically the x-axis. the line passes through 3 points on the x-axis, the only correct pint listed is x=1. :)

Answer:

18 degrees heres youre answer!

Step-by-step explanation:

If Angle 1 is x, and Angle 2 is 9x (because one angle is 9 times as large as the other), then x + 9x = 180. Add like terms: 10x = 180. solve for x by dividing both sides by 10. Therefore, x = 18 degrees = smaller angle.

Answer:

Step-by-step explanation:

Answer:

5.375 in. to the nearest thousandth.

Step-by-step explanation:

Area of a regular heptagon

= 7/4 * cot(pi/7) * s^2    where s is the length of one side.

105 = 7/4 * cot(pi/7) * s^2

s^2  = 105 / (7/4 cot (pi/7)

       = 28.8945

s = sqrt 28.8945

  = 5.375 in.

Answer:

yes 1.57 is a rational number you could write it as 1 & 57/100 or 157/1000

Answer:

P = 61

Q = 79

R = 40

Step-by-step explanation:

(2x - 19) + (x + 39) + x = 180

2x + x + x = 180 + 19 - 39

4x = 160

x = 40

P = 2x - 19 = 2(40) - 19 = 61

Q = x + 39 = 40 + 39 = 79

R = x = 40

Answer:

12

Step-by-step explanation:

1.  3/6 = 6/x

2.  Cross multiply:  3x=36

3.  x=12

The series converges for x in the interval [-1, 1), with the left end included and the right end not included.

To find all the values of x for which the given series converges, we will use the Ratio Test. The series is given by:

\(\sum_{n=1}^\infty \frac{(4 x)^n}{n^{8}}\)

Let's apply the Ratio Test:

\(\lim_{n \to \infty} \frac{\frac{(4 x)^{n+1}}{(n+1)^{8}}}{\frac{(4 x)^n}{n^{8}}} = \lim_{n \to \infty} \frac{n^8 (4x)^{n+1}}{(n+1)^8 (4x)^n}\)

Simplify the expression:

\(\lim_{n \to \infty} \frac{4x n^8}{(n+1)^8}\)

Now, we need to find the values of x for which this limit is less than 1, as the Ratio Test states that the series converges if this limit is less than 1.

\(\frac{4x}{(1+\frac{1}{n})^8} < 1\)

Divide both sides by 4:

\(x < \frac{1}{(1+\frac{1}{n})^8}\)

As n approaches infinity, the term \(\frac{1}{n}\) approaches 0:

\(x < \frac{1}{(1+0)^8} = \frac{1}{1}\)

So, for the series to converge, x must be less than 1.

The series is convergent from x = -1, left end included (Y) to x = 1, right end not included (N).

Your answer: The series converges for x in the interval [-1, 1), with the left end included and the right end not included.

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The length of RT from the figure is 8 units

In order to find the measure of RT, we will use the pythagoras theorem. According to the theorem;

hypotenuse² = adjacent² + opposite²

From the given figure;

ST = hyp = 10

RS = adj = 6

Find RT

RT = √10² - 6²

RT = √100 - 36

RT = √64

RT = 8 units

Hence the length of RT from the figure is 8 units

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Answer:

Step-by-step explanation:

w/18=7/3

w=126/3

w=42

Answer:

9 to the forth power * 7 to the 2nd power*

Answer:

9^4*7^2 is the answer espero que te sirva mucho

Answer:

The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.

The surface area of the pyramid is 112 square inches if the perimeter of the base of a square pyramid is 32 inches. Thus, option A is correct.

The perimeter of a square pyramid = 32 inches

The height of a square pyramid = 3 inches

If the perimeter is 32 inches, then the sum of the lengths of all four sides is 32 inches.

Length of side= 4s = 32

Length of side = 8 inches

Area of square = \(a^{2}\) = \(8^{2}\) = \(64 inch^{2}\)

Area of triangle =  (1/2) x base x height

Area of triangle = (1/2) x (8) x (3)

Area of triangle  = \(12 in^2\)

The total area of four triangles is calculated by:

Total area of triangle = 4 x (12) = \(48 in^2\)

The total surface area of the pyramid =  area of square + Area of triangle The total surface area of the pyramid  = 64 + 48 = 112 in^2

Therefore, we can conclude that the surface area of the pyramid is 112 square inches.

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The complete question is:

The perimeter of the base of a square pyramid is 32 inches. The height of the pyramid is 3 inches. What is the surface area of the pyramid?

Responses

a. 112 in°

b. 96 in²

c. 144 in²

d. 72 in²