A plane intersects one cone of a double-napped cone such that the plane is neither parallel to the generating line nor perpendicular to the axis. what conic section is formed?

The explicit rule for the nth term of the sequence is an = (an-1)*3 +2.

According to the given statement

we have to find the explicit rule for the nth term of the given sequence,.

So, For this purpose

The given sequence is :

2, 8, 26, 80, 242.

And according to the ap series formula

[tex]a_{n} = (a_{n-1} -1)*3 +2[/tex]

If we put the terms in it then we get the exact value as the value in the sequence.

So,

[tex]a_{n} = (a_{n-1} -1)*3 +2[/tex]

For [tex]a_{2}[/tex]

[tex]a_{2}[/tex] [tex]= a_{1} *3 +2[/tex]

[tex]a_{2}[/tex] [tex]= 2*3 + 2[/tex]

[tex]a_{2}[/tex] [tex]= 8[/tex]

and by this way we get all the values as same as the sequence.

So, The explicit rule for the nth term of the sequence is an = (an-1)*3 +2.

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Answer: 87,654,321

Step-by-step explanation: All the digits of the number A are different so the max length of the number A is 10 digits. But, then you realise that 9 can't be used because 9+1 = 10. So, A is only 9 digits long. If we arrange them from largest to least it would be 87,654,321.

From the attached speed versus time graph, it can be seen that the orange or first or car is speeding up. The third or green car is slowing down, and the blue or second car is maintaining a constant speed.

Speed Analysis from the Graph

The graph in the attachment shows the linear increase in speed of the first car over time. Therefore, we can say that it is accelerating at a certain rate.

The graph shows how the speed of the third car is decreasing with time. This demonstrates that the green vehicle is de-accelerating.

The graph shows a straight line for the second car. It displays that the speed does not alter as seconds or minutes pass. We might infer that the blue car is continuing to travel at its current pace as a result.

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Answer:

A C B

Step-by-step explanation:

Which of the cars is speeding up?  

A

Which of the cars is slowing down?  

C

Which of the cars is maintaining a constant speed?  

B

This number in expanded form 200 + 5 + 5/10 + 9/100  .

What is expanded form in math example?

Given  : 205.95 centimeters.

the number in a expanded form.

200 + 5 + 9/10 + 5/100

we have given 205.95 centimeters.

We can see 2 is at hundred place = 200.

0 is at tens place = 00.

5 is at ones place  = 5.

9 after decimal is at tenth place =  [tex]\frac{9}{10}[/tex].

5 is at hundredth place  = [tex]\frac{5}{100}[/tex] .

Therefore , Expanded form : 200 + 5 + 5/10 + 9/100 .

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Answer:

Step-by-step explanation:

The radius of the sector is 10.27 miles

The area of a sector can be represented as follows;

area of a sector = ∅ / 360 × πr²

where

Therefore,

∅= 25 degrees

area of the sector  = 23 miles²

area of a sector = ∅ / 360 × πr²

23 = 25 / 360 × πr²

cross multiply

23 × 360  = 25πr²

8280 = 25πr²

divide both sides by 25

πr² =  8280 / 25

πr² =  331.2

r² =  331.2 / 3.14

r² = 105.477707006

r = √105.477707006

r = 10.2702336877 miles

Therefore, the radius of the sector is 10.27 miles

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The correct representation of the inequality is -6x + 15 < 10 - 5x and an open circle is at 5 and a bold line starts at 5 and is pointing to the right.

In mathematical concept, an inequality is a representation of an order linking two numbers or algebraic expressions together. These orders are called inequality signs such as greater than (>), less than (<), greater than or equal to(≥), or less than or equal to(≤). Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations.

From the given information, we are given the inequality:

= -3(2x - 5) < 5(2 -x)

Open brackets, we get:

= -6x + 15 < 10 - 5x

Subtract 15 from both sides, we have:

= -6x + 15 - 15 < 10 - 5x - 15

= -6x < -5x - 5

Add 5 to both sides

= -6x + 5 < -5x - 5 + 5

= -6x + 5 < -5x

= -x < - 5

= x < 5

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Stephen read about 9 pages more each week.

What is a linear equation in math?

If stephen reeds 278 pages in 7 week ,

To find number of pages read in 1 week, divide 278 by 7

                    = [tex]\frac{278}{7}[/tex]  ⇒ 39.71

Another person reads 31 pages each week.

So stephen reads allmost 40  per week and alice 31.

Then, we need to find the difference between them

Difference = 40 - 31 = 9

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The inequality is represented by the polynomial y ≥ 3.6 · (x - 11.5) · (x + 3.5).

Herein we must derive the quadratic expression within an inequality of the y ≥ f(x) based on its two roots and a known point on the curve. We can find the coefficients of the quadratic equation by solving this system of linear equations:

(x₁, y₁) = (- 3.5, 0)

12.25 · a - 3.5 · b + c = 0       (1)

(x₂, y₂) = (11.5, 0)

132.25 · a + 11.5 · b + c = 0       (2)

(x₃, y₃) = (8.5, - 54)

72.25 · a + 8.5 · b + c = - 54     (3)

The solution of the system is a = 3.6, b = - 54, c = 144.9. Thus, the inequality is represented by the polynomial y ≥ 3.6 · x² - 54 · x + 144.9, whose factored form is determined by the quadratic formula:

y ≥ 3.6 · (x² - 15 · x + 40.25)

y ≥ 3.6 · (x - 11.5) · (x + 3.5)

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Answer:

S(1,2)

Step-by-step explanation:

The value that is being altered is the y value if you go from Q to T and then T to S. The x value = 1 and remains the same for point S.

To go from Q to T, you go from 8 to 5 on the y value. Remember x remains the same. That's three units (8 - 5 = 3)

To go from T to S must be 3 units as well, since the small diagonal is bisected. 5 - 3 = 2 is the answer.

So point S is noted as S(1,2)

The given expression is a (A) linear expression.

Therefore, the given expression is a (A) linear expression.

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The correct question is given below:

Classify the expression: 5x 2.

(A) linear expression

(B) quadratic expression

(C) cubic expression

(D0 quartic expression

From the given information, we get the value of ABC = 120°.

Given: In the figure, O exists the center of the circle and OABC exists as a parallelogram.

Now, the radius of the circle exists

OA = OB = OC

Opposite sides of a parallelogram are equal

AB = OC and OA = BC

In ∆OAB,

OA = OB = AB and,

In ∆OCB,

OC = OB = BC

Therefore, ∆OAB and ∆OCB exist in equilateral triangles.

All angles of an equilateral triangle are equivalent to 60°.

Hence, ∠ABC = ∠OBA + ∠OBC

∠ABC = 60° + 60°

∠ABC = 120°

Therefore, the value of ∠ABC = 120°.

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Based on these data, it is better to describe the centers of distribution in terms of: B. median for both coffee shops because the data distribution is not symmetric.

A median can be defined as the middle number (center) of a sorted data set, which is typically when the data set is arranged in from the least to greatest or the greatest to least.

In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.

Next, we would calculate the mean and median for the two coffee shops as follows.

For coffee shop A, we have:

Mean = [F(x)]/n

Mean = [12+15+33+45+46+51+52+57]/8

Mean = [311]/8

Mean = 38.875.

Median = (45+46)/2

Median = 91/2

Median = 45.5.

For coffee shop B, we have:

Mean = [F(x)]/n

Mean = [17+16+36+35+12+9+34+15]/8

Mean = [174]/8

Mean = 21.75.

Median = (16+17)/2

Median = 33/2

Median = 16.5.

Since both the mean and median are not close, we can infer and logically deduce that the data distribution isn't symmetric for both coffee shops A and B.

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Step-by-step explanation:

solution

here

15×5

=75inches

The end behavior of the power function is as x tends to infinity, f(x) tends to zero.

In this question,

The power function is [tex]f(x)=3^{-x}2[/tex]

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

The graph below shows the behavior of the function f(x).

The above equation has the degree of 1, which is odd and the leading coefficient has the positive coefficient.

Then the end behavior is

As x -> ∞,

⇒ [tex]\lim_{x \to \infty} f(x)[/tex]

⇒ [tex]\lim_{x \to \infty} 3^{-x}2[/tex]

⇒ [tex]2\lim_{x \to \infty} 3^{-x}[/tex]

⇒ [tex]2\lim_{x \to \infty} 3^{-\infty}[/tex]

⇒ 2(0)

⇒ 0

Thus as x → ∞, f(x) → 0.

Hence we can conclude that the end behavior of the power function is as x tends to infinity, f(x) tends to zero.

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The difference of the x-coordinate of point A and the x-coordinate of point B is 0

The coordinate of a point on an xy-plane is written in the form (x, y). The given figures are circles A and B where the circle A is greater than circle B.

The position of the dots in both sides are positioned at the centre and as such the coordinate point at the centre of both circle will be the origin (0, 0)

According to the question, we are to find the difference of the x-coordinate of point A and the x-coordinate of point B

x-coordinate of pint A = 0

x-coordinate of point B = 0

Take the difference

Difference = 0 - 0

Difference = 0

Hence the difference of the x-coordinate of point A and the x-coordinate of point B is 0

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The equation be x/100 [tex]*[/tex] 28,600 = 33,500, then we get 17%.

Trevor's total employee benefits exists 17.1% of his gross pay.

Therefore, the correct answer is option d. 17.1.

If you would like to know Trevor's total employee advantages, you can estimate this utilizing the subsequent steps:

To find the percentage of the total employee benefits x% of $28,600 exists $33,500.

To estimate the value of x, bring the variable to the left side and bring all the remaining variables to the right side. Simplify the values to estimate the result.

x/100 [tex]*[/tex] 28,600 = 33,500

x = 33,500 [tex]*[/tex] 100 / 28,600

x = 117.13% = 117%

117% - 100% = 17%

x = 17%

The correct result would be 17%.

Trevor's total employee benefits exists 17.1% of his gross pay.

Therefore, the correct answer is option d. 17.1.

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Answer:

It is D

Step-by-step explanation:

The factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.

In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.

In the given expression, a = 1, b = -4, and c = -21.

Thus, ac = -21.

The numbers having a product 21 are:

1*21 = 21,

3*7 = 21.

Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.

Thus, the expression can now be shown as:

x² - 4x - 21

= x² + (3 - 7)x - 21

= x² + 3x - 7x - 21

= x(x + 3) - 7(x + 3) {By taking common}

= (x - 7)(x + 3) {By taking common}.

Thus, the factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

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Answer:

there are 54 buffalos in 150 acres

Step-by-step explanation:

1. determine the rate of buffalos per acres

45 buffalos per 125 acres =

45 / 125 =

0.36 buffalos per 1 acre

now we know the rate of buffalos per 1 acre, we can multiply it by the required amount of acres (in this case 150)

buffalos per 1 acre x total acres = total buffalos per total acres

0.36 x 150 = 54 buffalos

therefore, there are 54 buffalos per 150 acres.

hope this helps :)

Answer:

I think the answer is 12 because 8/6 is 1.3333.... Continously so the smaller traingel is 1.33333 times smaller then the bigger one. So you jus do 9 x 1.3333... To get the bigger angels side

Answer: Statistical

Step-by-step explanation:

I think its statistical because its quantitative data, meaning you can count it.

Answer:

2

Step-by-step explanation:

The trick here is to reduce each of the bases to lowest form first

[tex]12 = 3.4 = 3 .2.2 = 3.2^{2}\\12^{3} = (3.2^{2} )^{3} = 3^{3}2^{6} \\6 = 3.2\\6^{5} = (3.2)^{5} = 3^{5} .2^{5} \\\\Numerator = 3^32^63^52^5 = 3^82^{11}\\Denominator computation\\9 = 3^2\\9^{4} = (3^{2} )^4 = 3^{8} \\Denominator = 3^82^{10} \\\\\frac{Numerator}{Denominator } =\frac{{3^8}{2^{11} }}{3^82^{10}} = \frac{2^{11}} {2^{10}} = 2^1 = 2[/tex]  

Answer:

1.5×2.5/2=1.875.

Step-by-step explanation:

We all know that area of triangle is base into hight upon 2.

Tthe inequality that describes this graph is y ≤ 1/3x - 4/3

The graph that completes the question is added as an attachment

From the attached graph, we have the following points

(0, -1.3) and (3, -0.3)

The slope is calculated as:

m = (y2 - y1)/(x2 - x1)

Substitute the known values in the above equation

m = (-0.3 + 1.3)/(3 - 0)

Evaluate

m = 1/3

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 1/3(x - 0) - 1.3

Evaluate

y = 1/3x - 4/3

From the graph, we have the following highlights:

The first highlight above implies, the inequality can be any of ≥ and ≤

While the second highlight above implies, the inequality is ≤

Hence, the inequality that describes this graph is y ≤ 1/3x - 4/3

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A  comparative design is a type of group design in which the species of animals within the study constitutes one of the independent variables.

A group of animals, plants, or other living things that all have similar traits and are categorized as one species are considered to be living organisms. All humans are one species, for instance.

It is essential for both biologists and the general public to comprehend what species are and how to recognize them. As species disappear, biological variety is lost, and the only way to influence the social, political, and economic factors that influence conservation efforts is to understand the nature of species.

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The equivalent expression of the expression is 128x^5y^6/2x^7y^5

The expression is given as:

128x^5y^6/2x^7y^5

Divide 128 by 2

64x^5y^6/x^7y^5

Apply the law of indices

64y^(6-5)/x^(7-5)

Evaluate the differences

64y/x^2

Hence, the equivalent expression of the expression is 128x^5y^6/2x^7y^5

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Step-by-step explanation:

In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.

The number of combinations of n objects taken r at a time is determined by the following formula:.

nCr = n! / (n-r)! r!

n = total number of objects in the set

r = number of choosing objects from the set

so here , Jane has 8 toys and first she wants to take 2 toys ....

so , 8C2 = 8! / 6! 2! = 28 ways

so , she selected 2 toys ,,, After she wants to take 2 toys among 6 toys ....

so , 6C2 = 6! / 4! 2! = 15

next , picking 2 toys out of 4

So , 4C2 = 4! / 2! 2! = 6

next , 2C2 = 2! / 0! 2! = 1

total ways to pick toys = 28 × 15 × 6 × 1

= 2520 different ways ..

request :- Sorry if there are some mistakes in my English.

Answer:

D. 2

Step-by-step explanation:

soh cah toa rule

sine equals opposite over hypotenuse,

cosine equals adjacent over hypotenuse, and

tangent equals opposite over adjacent

csc is 1/sin which is hypotenuse over opposite

if csc is -√5/2 then

hypotenuse is -√5

opposite is 2

3rd quadrant on a graph is bottom left

both x and y values are negative

hypotenuse means its a triangle

pythagorean theorem

a^2 + b^2 = c^2

a^2 + 2^2 = (-√5)^2

a^2 + 4 = 5

a = 1 = adjacent

tangent equals opposite over adjacent

tan is 2 / 1 which is 2

third quadrant means it's still positive

because tan is positive in quadrant 3

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Answer:

4x +6

Step-by-step explanation:

No explanation

Straight answer