What number completes the sequence below? Enter your answer in the input
box at the bottom.
8——-4
16——8
24——12
32——?

Answer:

This is an equation of a parabola.

[tex](y+6)^2=4(x+1)[/tex]

Step-by-step explanation:

A conic section is a curve obtained by the intersection of a plane and a cone. The three major conic sections are parabola, hyperbola and ellipse (the circle is a special type of ellipse).

The standard equations for hyperbolas and ellipses all include x² and y² terms. The standard equation for a parabola includes the square of only one of the two variables.

Therefore, the equation y² - 4x + 12y + 32 = 0 represents a parabola, as there is no x² term.

As the y-variable is squared, the parabola is horizontal (sideways), and has an axis of symmetry parallel to the x-axis.

The conic form of a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

To write the given equation in conic form, we need to complete the square for the y-variable.

Rearrange the equation so that the y-terms are on the left side:

[tex]y^2 + 12y = 4x - 32[/tex]

Add the square of half the coefficient of the y-term to both sides of the equation:

[tex]y^2 + 12y+\left(\dfrac{-12}{2}\right)^2 = 4x - 32+\left(\dfrac{-12}{2}\right)^2[/tex]

    [tex]y^2 + 12y+\left(-6\right)^2 = 4x - 32+\left(-6\right)^2[/tex]

         [tex]y^2 + 12y+36 = 4x - 32+36[/tex]

         [tex]y^2 + 12y+36 = 4x +4[/tex]

Factor the perfect square trinomial on the left side of the equation:

[tex](y+6)^2=4x+4[/tex]

Factor out the coefficient of the x-term from the right side of the equation:

[tex](y+6)^2=4(x+1)[/tex]

Therefore, the equation of the given conic section in conic form is:

[tex]\boxed{(y+6)^2=4(x+1)}[/tex]

where:

The conic section of the equation y² - 9x + 12y + 32 = 0 is a parabola

The given equation is

y² - 9x + 12y + 32 = 0

The above equation is an illustration of a parabola equation

The standard form of a parabola is

(x - h)² = 4a(y - k)²

Where

(h, k) is the center

While the general form of the equation is

Ax² + Dx + Ey + F = 0

In this case, the equation y² - 9x + 12y + 32 = 0 takes the general form

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Answer:

Step-by-step explanation:

(x^3 - 10x + K)/(X+3) = 6 GIVEN

for different values of x there are many possible values of k some i will show

when we substitute x=1

we get k=33

at x=2

weget k=42

so many values are possible for k

because there is no intervel in question which restrics us from taking different values of x or k so you take any value of x you will get different values of k

The graph of the function and its inverse is added as an attachment

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

f(x) = 3 + 2ln(x)

Express as an equation

So, we have

y = 3 + 2ln(x)

Swap x and  y in the above equation

x = 3 + 2ln(y)

Next, we have

2ln(y) = x - 3

Divide by 2

ln(y) = (x - 3)/2

Take the exponent of both sides

[tex]y = e^{\frac{x - 3}{2}}[/tex]

Next, we plot the graphs

The graph of the functions is added as an attachment

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The angular velocity of the object is 31.25 radians/second.

Angular velocity is defined as the change in angular displacement per unit of time. In this case, the object rotates a total of 25 radians in 0.8 seconds. Therefore, the angular velocity can be calculated by dividing the total angular displacement by the time taken.

Angular velocity (ω) = Total angular displacement / Time taken

Given that the object rotates 25 radians and the time taken is 0.8 seconds, we can substitute these values into the formula:

ω = 25 radians / 0.8 seconds

Simplifying the equation gives:

ω = 31.25 radians/second

So, the angular velocity of the object is 31.25 radians/second.

Angular velocity measures how fast an object is rotating and is typically expressed in radians per second. It represents the rate at which the object's angular position changes with respect to time.

In this case, the object completes a rotation of 25 radians in 0.8 seconds, resulting in an angular velocity of 31.25 radians per second. This means that the object rotates at a rate of 31.25 radians for every second of time.

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Note the translated question is:

An object that is rotated moves 25 radians in 0.8 seconds. what is the angular velocity of said object?

Answer:

No

Step-by-step explanation:

To determine if the average number of miles flown per passenger increased by one-third between 1966 and 1976, we need to compare the increase in miles flown during that period.

According to the given table:

To find the increase in miles flown, subtract the 1966 value from the 1976 value:

[tex]\begin{aligned}\sf Increase\; in\; miles\; flown &= \sf 831 \;miles - 711\; miles\\&= \sf 120\; miles\end{aligned}[/tex]

Therefore, the average number of miles flown per passenger between 1966 and 1976 increased by 120 miles.

To check if the increase is one-third of the initial value, we need to calculate one-third of the 1966 value:

[tex]\begin{aligned}\sf One\;third \;of \;711 \;miles &= \sf \dfrac{1}{3} \times 711\; miles\\\\ &= \sf \dfrac{711}{3} \; miles\\\\&=\sf 237\;miles\end{aligned}[/tex]

Since the increase in miles flown (120 miles) is not equal to one-third of the initial 1966 value (237 miles), the statement that the average number of miles flown per passenger increased by one-third between 1966 and 1976 is not true.

Answer:

The volume of the cylinder is 628.318530718

Step-by-step explanation:

The formula used to find the volume of a cylinder (v) is [tex]v = \pi r^2h[/tex], where r = radius and h = height. As the question says to keep the answer exact, we will be using pi as opposed to 3.14.

The radius is 5, and the height is 8. Plug these values into the equation and solve:

[tex]v =\pi *5^2*8[/tex]

[tex]v = 628.318530718[/tex]

So, the exact volume of the cylinder is 628.318530718. Rounded is 628.32

Answer:

200π or 628

Step-by-step explanation:

Note: your picture is not clear so I am assuming the height to be 8.

r = 5

h = 8

Volume = πr²h

= π * 5² * 8

= (25*8) π

= 200π

= 200*3.14

= 628

Answer:

Step-by-step explanation:

Let's denote the length of the rectangle as 3x and the width as 2x, based on the given ratio.

The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, we have:

P = 2(3x + 2x)

40 = 2(5x)

Now, let's solve for x:

40 = 10x

x = 40/10

x = 4

Now that we have the value of x, we can find the length of the rectangle:

Length = 3x = 3(4) = 12

Therefore, the length of the rectangle is 12.

Approximately 76.5% of the student body at Walton High School loves math.

To determine the percentage of the student body that loves math, we need to consider the proportions of males and females in the Walton High School student body and their respective percentages of loving math.

Given that 45% of the student body are males, we can deduce that 55% are females (since the total percentage must add up to 100%). Now let's calculate the percentage of the student body that loves math:

For the females:

55% of the student body are females.

90% of the females love math.

So, the percentage of females who love math is 55% * 90% = 49.5% of the student body.

For the males:

45% of the student body are males.

60% of the males love math.

So, the percentage of males who love math is 45% * 60% = 27% of the student body.

To find the total percentage of the student body that loves math, we add the percentages of females who love math and males who love math:

49.5% + 27% = 76.5%

As a result, 76.5% of Walton High School's student body enjoys maths.

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Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C).

The given functions are f(x) = 3x² and g(x) = -2².

To understand the difference between their graphs, let's examine the characteristics of each function individually:

Function f(x) = 3x²:

The coefficient of x² is positive (3), indicating an upward-opening parabola.

The graph of f(x) will be symmetric with respect to the y-axis, as any change in x will result in the same y-value due to the squaring of x.

The vertex of the parabola will be at the origin (0, 0) since there are no additional terms affecting the position of the graph.

Function g(x) = -2²:

The coefficient of x² is negative (-2), indicating a downward-opening parabola.

The negative sign will reflect the graph of f(x) across the x-axis, resulting in a vertical flip.

The vertex of the parabola will also be at the origin (0, 0) due to the absence of additional terms.

Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C). This means that g(x) is obtained by taking the graph of f(x) and flipping it vertically. The reflection occurs over the x-axis, causing the parabola to open downward instead of upward.

Therefore, the correct answer is option C: g(x) is a reflection of f(x) over the x-axis.

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Answer:

the first 2

Step-by-step explanation:

let me know if it is wrong

Answer:

5.9

Step-by-step explanation:

sin Θ = opp/hyp

sin 36° = x/10

x = 10 × sin 36°

x = 5.88

Answer: 5.9

The triangles DEF and SRQ are not similar triangles

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

The triangles in this figure are

DEF and SRQ

These triangles are not similar

This is because:

The corresponding angles in the triangles are not equal

For DEF, the angles are

50, 90 and 40

For SRQ, the angles are

51, 90 and 39

This means that they are not similar by any similarity statement

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The estimated population of the state in the year 2022 is 19,280,700 people.

The given equation represents the population of a certain state as a function of time, where p is the population in thousands of people and t is the number of years since 2010.

The equation is given as p = 80.7t + 18,312.3.

To estimate the population of the state, we substitute the value of t into the equation. For example, if we want to estimate the population in the year 2022 (12 years since 2010), we substitute t = 12 into the equation:

p = 80.7(12) + 18,312.3

= 968.4 + 18,312.3

= 19,280.7.

The estimated population of the state in the year 2022 is 19,280,700 people.

We can estimate the population for any given year by substituting the corresponding value of t into the equation.

It's important to note that the population is given in thousands of people, so we multiply the final result by 1,000 to obtain the population in actual numbers.

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The equivalent ratio of the corresponding sides and the triangle proportionality theorem indicates that the similar triangles are;

1. ΔAJK ~ ΔSWY according to the SAS similarity postulate

2. ΔLMN ~ ΔLPQ according to the AA similarity postulate

3. ΔPQN ~ ΔLMN

LM = 12, QP = 8

4. ΔLMK~ΔLNJ

NL = 21, ML = 14

Similar triangles are triangles that have the same shape but may have different sizes.

1. The ratio of corresponding sides between the two triangles circumscribing the congruent included angle are;

24/16 = 3/2

18/12 = 3/2

The ratio of each of the two sides in the triangle ΔAJK to the corresponding sides in the triangle ΔSWY are equivalent and the included angle, therefore, the triangles ΔAJK and ΔSWY are similar according to the SAS similarity rule.

2. The ratio of the corresponding sides in each of the triangles are;

MN/LN = 8/10 = 4/5

PQ/LQ = 12/(10 + 5) = 12/15 = 4/5

The triangle proportionality theorem indicates that the side MN and PQ are parallel, therefore, the angles ∠LMN ≅ ∠LPQ and ∠LNM ≅ ∠LQP, which indicates that the triangles ΔLMN and ΔLPQ are similar according to the Angle-Angle AA similarity rule

3. The alternate interior angles theorem indicates;

Angles ∠PQN ≅ ∠LMN and ∠MLN ≅ ∠NPQ, therefore;

ΔPQN ~ ΔLMN by the AA similarity postulate

LM/QP = (x + 3)/(x - 1) = 18/12

12·x + 36 = 18·x - 18

18·x - 12·x = 36 + 18 = 54

6·x = 54

x = 54/6 = 9

LM = 9 + 3 = 12

QP = x - 1

QP = 9 - 1 = 8

4. The similar triangles are; ΔLMK and ΔLNJ

ΔLMK ~ ΔLNJ by AA similarity postulate

ML/NL = (6·x + 2)/(6·x + 2 + (x + 5)) = (6·x + 2)/((7·x + 7)

ML/NL = LK/LJ = (24 - 8)/24

(24 - 8)/24 = (6·x + 2)/((7·x + 7)

16/24 = (6·x + 2)/(7·x + 7)

16 × (7·x + 7) = 24 × (6·x + 2)

112·x + 112 = 144·x + 48

144·x - 112·x = 32·x = 112 - 48 = 64

x = 64/32 = 2

ML = 6 × 2 + 2 = 14

NL = 7 × 2 + 7 = 21

MN = 2 + 5 = 7

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What is needed to be congruent to show that ABC=AXYZ is AC ≅ XZ. option D

Given that in ΔABC and ΔXYZ, ∠X ≅ ∠A and ∠Z ≅ ∠C.

We are to select the correct condition that we will need to show that the triangles ABC and XYZ are congruent to each other by ASA rule..

ASA Congruence Theorem: Two triangles are said to be congruent if two angles and the side lying between them of one triangle are congruent to the corresponding two angles and the side between them of the second triangle.

In ΔABC, side between ∠A and ∠C is AC,

in ΔXYZ, side between ∠X and ∠Z is XZ.

Therefore, for the triangles to be congruent by ASA rule, we must have AC ≅ XZ.

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The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.

To find the net area of the curve represented by the function f(x) = ex - e on the interval [0, 2], we need to calculate the definite integral of the function over that interval. The net area can be determined by taking the absolute value of the integral.

The integral of f(x) = ex - e with respect to x can be computed as follows:

∫[0, 2] (ex - e) dx

Using the power rule of integration, the antiderivative of ex is ex, and the antiderivative of e is ex. Thus, the integral becomes:

∫[0, 2] (ex - e) dx = ∫[0, 2] ex dx - ∫[0, 2] e dx

Integrating each term separately:

= [ex] evaluated from 0 to 2 - [ex] evaluated from 0 to 2

= (e2 - e0) - (e0 - e0)

= e2 - 1

The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.

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There are 70 ways a person can order a two-course meal from the given restaurant.

To determine the number of ways a person can order a two-course meal from a restaurant that offers 10 appetizers and 7 main courses, we can use the concept of combinations.

First, we need to select one appetizer from the 10 available options.

This can be done in 10 different ways.

Next, we need to select one main course from the 7 available options. This can be done in 7 different ways.

Since the two courses are independent choices, we can multiply the number of options for each course to find the total number of combinations.

Therefore, the number of ways a person can order a two-course meal is 10 [tex]\times[/tex] 7 = 70.

So, there are 70 ways a person can order a two-course meal from the given restaurant.

It's important to note that this calculation assumes that a person can choose any combination of appetizer and main course.

If there are any restrictions or limitations on the choices, the number of combinations may vary.

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Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

Answer:

D The base is 7 units and the height is 3 units.

Step-by-step explanation:

The answer is d I counted the width/base then the height/length and found answer.

Answer:

When p, the probability of success, is zero in a binomial distribution, the probability of getting exactly k successes in n trials is also zero for all values of k except when k is zero (i.e., when there are no successes).

So, in the case of (0.3)^0, the result would be 1, because any number raised to the power of 0 is equal to 1. Therefore, the probability of getting zero successes in a binomial distribution when the probability of success is 0.3 is 1.

The measure of the interior angle at vertex F is 72 degrees.

A hexagon is a polygon with six sides. The sum of the interior angles of a hexagon is equal to 720 degrees.

The angle of the hexagon is given in terms of x,

The sum of the angle is equal to 720 degrees

[tex]4\text{x}+4\text{x}+4\text{x}+4\text{x}+2\text{x}+2\text{x} = 720[/tex]

[tex]20\text{x} = 720[/tex]

[tex]\text{x} = 36[/tex]

[tex]\bold{2x = 72^\circ}[/tex]

Therefore, the measure of interior angle at vertex F is equal to 72 degrees.

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Answer:

180 meters

Step-by-step explanation:

To find the perimeter of the actual swimming pool, you need to first find the length and width of the actual swimming pool by multiplying the length and width of the pictured swimming pool by the scale factor of 1200 cm.

Now that we know that the perimeter of the actual pool is 18000 centimeters, we need to convert that to meters! Keep in mind that:

Now we can divide 18000 by 100:

18000 cm ÷ 100 = 180 m

Therefore, the perimeter of the actual swimming pool is 180 m.

i.  The position vector of X is 2b - a.

ii.  The position vector of Y is (3b + c)/4.

iii.  The ratio XY : Y Z is [tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex]. Simplifying this expression will give us the final ratio.

i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.

ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.

iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =[tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex].

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Answer:

If you are in Acellus trust me the answer is 394

Step-by-step explanation:

SA = 2 ( 2 x 12 ) + 2 ( 2 x 10 ) + ( 8 x 6 ) + 2 ( 3 x 8 ) + ( 3 x 6 ) + ( 12 x 16 )

SA = 48 + 40 + 48 + 48 + 18 + 192

SA = 394 square cm.

The limit of the trigonometric expression is equal to 0.

In this problem we find the case of a trigonometric expression, whose limit must be found. This can be done by means of algebra properties, trigonometric formula and known limits. First, write the entire expression below:

[tex]\lim_{\Delta x \to 0} \frac{\cos (\pi + \Delta x) + 1}{\Delta x}[/tex]

Second, use the trigonometric formula cos (π + Δx) = - cos Δx to simplify the resulting formula:

[tex]\lim_{\Delta x \to 0} \frac{1 - \cos \Delta x}{\Delta x}[/tex]

Third, use known limits to determine the result:

0

The limit of the trigonometric function [cos (π + Δx) + 1] / Δx evaluated at Δx → 0 is equal to 0.

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