Can somebody help me

The evaluation of the paths of the ellipse and hyperbola are as follows;

Part A: The vertices are; (0, 36), (0, -4)

Part B: Comet H comes closest to the sun

Part C: The location of the Sun is the location of the x-coordinate of the path of both ellipse

An ellipse is the locus of a point that moves such that the sum of the distances from two points, known as the focal points, is a constant

Part A: The standard form of the equation of a hyperbola is presented as follows;

\(\dfrac{(x - h)^2}{a^2} -\dfrac{(y-k)^2}{b^2} =1\)

Where;

(h, ,k) = The center of the ellipse

a = Vertex to center distance

c = The distance from center to foci

The equation of an ellipse is presented as follows  

\(\dfrac{(x - h)^2}{a^2} +\dfrac{(y-k)^2}{b^2} =1\)

The vertices of the ellipse are; a + h and k + b

The specified equation is presented as follows;

Comet E = \(\dfrac{(y+16)^2}{400} +\dfrac{x^2}{144} =1\)

The vertices for the comet E are;

(0, 20 + 16) = (0, 36) and (0, 16 - 20) = (0, -4)

Part B: Comet H = \(\dfrac{(y+13)^2}{144} +\dfrac{x^2}{25} =1\)

The vertex of the comet H = (0, -13 + 12) = (0, -1), and (0, -13 - 12) = (0, -25)

Based on the location of the comet H close to the origin, the comet that comes closest to the Sun is comet H

Part C; The location of the Sun at the origin is the location of the x-coordinate of the center of both comets

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Answer:

2.6 kilometers

Step-by-step explanation:

To find the circumference of a circle, we can use the formula:

Circumference = π * diameter

Given that the diameter of the volcanic crater is 840 meters, we can substitute this value into the formula:

Circumference = π * 840

Using the approximate value of π as 3.14159, we can calculate the circumference:

Circumference = 3.14159 * 840

Circumference ≈ 2643.1796 meters

To convert the circumference to kilometers, we divide the value by 1000:

Circumference in kilometers = 2643.1796 / 1000

Circumference ≈ 2.6432 kilometers

Therefore, the circumference of the rim of the volcanic crater is approximately 2.6 kilometers (rounded to 1 decimal place).

The amount of soil needed to fill the garden box is given as follows:

1728 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

V = 19 x 12 x 6 + 10 x 3 x 12

V = 1728 ft³.

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the correct answer is 4.05

The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

The equation would be:

C is the total cost and m is the miles driven.

We know that:
Charge of the truck: $35

Charge per mile: $2.50

Then, form the equation as follows:

C = 35 + 2.50m

Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

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a) The experimental units are the Acacia Trees.

b) The treatments carried used are; active beehives, empty beehives and no single beehive.

c) The response variable is the damage that the elephants caused to the trees.

Experimental design is defined as the process of carrying out research in a manner that is objective and controlled such that precision is maximized and then specific conclusions can possibly be drawn regarding a hypothesis statement. Generally, the purpose of this is to establish the effect that a factor or independent variable has on a dependent variable.

From this question, it is very clear that the experimental units are the Acacia Trees. This is because they are the primary interest or objective of the research.

The treatments carried out here are the active beehives, empty beehives and no single beehive.

The response variable is defined as the result of the experiment where the explanatory variable is manipulated. In this case, the response variable is the damage that the elephants caused to the trees.

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The complete statements are

The complete question is added at the end of this solution

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

Garrick's plant:

Zan's plant:

Garrick's plant is shorter than Zan's plant and the difference in heights is

Actual difference = 100 mm - 10 mm = 90 mm

Measured difference = 88 mm - 8 mm = 80 mm

The percentage errors are calculated using

Percentage errors = Difference/Actual measurement * 100%

So, we have

Garrick's actual error = (10 - 8)/10 *100% = 20%

Zan's actual error = (100 - 88)/10 * 100% = 12%

Hence, Garrick's measurement was 20% off and Zan's was 12% off.

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Answer:

3.75, Terminating

Step-by-step explanation:

To answer this, we simply have to find what 3/4 is as a decimal. So, we know that in order to make 4/4, or 1, we need 4 parts. Let's say that 4/4 would equal 100, so we need to divide 100 into 4 parts:

100 / 4 = 25

Now, to find what 3/4 is, all we have to do is multiply 25 by 3:

25 * 3 = 75

And that is our decimal form, we just need to add the 3:

3.75, and since .75 doesn't keep on repeating, it just stops at .75, this is a terminating decimal

Hope this helps! :)

Based on the given informations, the angle between the ladder and the ground is decreasing at a rate of 0.009 radians/second when the ladder is 5.8 feet away from the house.

Let's call the distance between the base of the ladder and the house "x". The length of the ladder is 24 feet, so the height it reaches up the house is given by the Pythagorean theorem:

h² = 24² - x²

Differentiating both sides with respect to time:

2h dh/dt = -2x dx/dt

We want to find dh/dt when x = 5.8 feet and dx/dt = 0.25 feet/second. First, we need to solve for h:

h² = 24² - 5.8² = 557.84

h = 23.63 feet

Substituting x = 5.8 feet, h = 23.63 feet, and dx/dt = 0.25 feet/second:

2(23.63) dh/dt = -2(5.8)(0.25)

dh/dt = -0.06 feet/second

So the tip of the ladder is slipping down the side of the house at a rate of 0.06 feet/second.

To find the rate of change of the angle, we can use the formula:

tan(Θ) = h/x

Differentiating both sides with respect to time:

sec²(Θ) d(Θ)/dt = (1/x) dh/dt - (h/x²) dx/dt

We already know x = 5.8 feet, h = 23.63 feet, and dx/dt = 0.25 feet/second. We just calculated dh/dt to be -0.06 feet/second. To find sec(theta), we can use the fact that cos(Θ) = x/h:

cos(Θ) = x/h = 5.8/23.63 = 0.245

sec(Θ) = 1/cos(theta) = 4.0816

Substituting these values into the formula above:

(4.0816)² d(Θ)/dt = (1/5.8)(-0.06) - (23.63/5.8²)(0.25)

d(Θ)/dt = -0.009 radians/second (rounded to 3 decimal places)

Therefore, the angle between the ladder and the ground is decreasing at a rate of 0.009 radians/second when the ladder is 5.8 feet away from the house.

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Answer:

9

Step-by-step explanation:

f(x) = 4x- 11

f(5) = 4(5) - 11

f(5) = 20- 11

f(5) = 9

Step-by-step explanation:

The answer is scalene triangle

Answer:

scalene

Step-by-step explanation:

all the sides of a scalene triangle have different lengths, as shown in the picture :)

the height of point P after the windmill blade rotates by an angle of a is approximately 1.1908 feet.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

To find the height h of point P, we can use the sine function, which relates the opposite side of a right triangle (in this case, the height h) to the hypotenuse (in this case, the length of the windmill blade, which is 1.5 feet). The angle between the opposite side and the hypotenuse is the complement of the angle of rotation a, which is π/4 radians minus the angle between the ground and the windmill blade, which is arctan(6/1.5) or approximately 1.3258 radians.

So, the equation for the height h of point P after the windmill blade rotates by an angle of a is: h = 1.5 sin(π/4 - arctan(6/1.5))

Therefore, the height of point P after the windmill blade rotates by an angle of a is approximately 1.1908 feet.

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Answer:

{-3, -∞)

Step-by-step explanation:

The range of a function is how far the y goes up or down of a function goes.

We see the function start at -3 and go forever. So, the range of the functions is {-3, -∞)

Answer: 2 to 7

Step-by-step explanation:

divide both by three, it's the greatest common factor

I think

h(t)=480t–16t^2

Max height is the vertex of the parabola at t = -b/2a

t = -480/-32 = 15 seconds

--> h(15)

B. Matrices a and b can be found, but the proof is too complex to provide here.

What is matrix?

A matrix is a rectangular arrangement of numbers, symbols, or expressions arranged in rows and columns. It is a fundamental concept in linear algebra and is used to represent and manipulate linear equations, vectors, and transformations.

The correct answer is B. Matrices a and b can be found, but the proof is too complex to provide here.

To prove the statement, we need to find specific matrices a and b such that det(a) = 0 and det(ab) ≠ 0. However, providing the explicit examples and proof for this scenario can be complex and may involve various matrix operations and calculations. Therefore, it is not feasible to provide a straightforward explanation in this text-based format.

Suffice it to say that the converse to the statement in part A is indeed false, and it is possible to find matrices a and b that satisfy the given conditions. However, providing a detailed proof or examples would require a more in-depth explanation involving matrix algebra and calculations.

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Answer:

(n+3)^2=81

Step-by-step explanation:

(n+3)^2-17=64

ADD 17 to both sides

(n+3)^2-17+17=64+17

simplify

(n+3)^2=81

To prove that 3x ≤ y, assume the opposite, that is, 3x > y, rearrange the inequality substitute x < 2y and simplify, contradict the given condition that x < 2y, therefore, concluding that 3x ≤ y.

Start by assuming the opposite, that is, 3x > y.

From the given inequality,\(7xy \leq 3x^2 + 2y^2,\), we can rearrange to get:
\(7xy - 3x^2 \leq 2y^2\)

We can substitute \(x < 2y\) into this inequality:
\(7(2y)x - 3(2y)^2 \leq 2y^2\)

Simplifying, we get:
\(y(14x - 12y) \leq 0\)

Since y is a real number, this means that either y ≤ 0 or 14x - 12y ≤ 0.

If y ≤ 0, then 3x ≤ y is trivially true.

If 14x - 12y ≤ 0, then we can rearrange to get:
3x ≤ (12/14)y
3x ≤ (6/7)y
3x < y (since we assumed 3x > y)

But this contradicts the given condition that x < 2y, so our assumption that 3x > y must be false.

Therefore, we can conclude that 3x ≤ y.

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For the answer of factors of expression (12 + 54), in the form of a(b + c), where a is the GCF of 12 and 54 is equals to 6( 2 + 9).

In math, to factor a number means to express it as a product of (other) whole numbers, called its factors. For example, if 7x5 = 35, 7 and 5 are both factors. The divisors that give the remainder to be 0 are the factors of the number. We have an expression of numbers, 12 + 54. We have to write this expression in form of a( b + c), where a is GCF of 12 and 54. Now, we can write the factors of 12 and 54 are 12 = 2×2×3

54 = 2×3 ×3×3

The greatest common factor, GCF of 12 and 54 is 2×3 = 6. So, 12 + 54 = 6× 2 + 6×9

Taking out the common factor 6 from above expression, 6( 2 + 9) which is required form a( b + c). Hence, required expression is 6( 2 + 9).

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Answer:25

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

To solve this, we need to use the geometric mean(altitude theorem).

this is:

\(\frac{segment 1}{altitude} =\frac{altitude}{segment2}\)

We can input the values into this equation:

\(\frac{x}{3} =\frac{12}{x}\)

Now, we can cross multiply x by x and 3 by 12 to get:

\(x^2 = 3(12)\)

Simplifying this, we get:

\(x^2 = 36\)

The square root of 36 is 6, and therefore, x is six.

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The possibility are 1,716 possible ways to cast the roles of Larry, Curly, and Moe from a group of 13 actors.

There are 13 actors auditioning for the roles of Larry, Curly, and Moe, there are 13 choices for who can be cast in the first role, 12 choices left for who can be cast in the second role, and 11 choices left for who can be cast in the third role (assuming that no actor can play more than one role).

To determine the number of ways the roles of Larry, Curly, and Moe could be cast with 13 different actors auditioning, we can use the concept of permutations.

In this case, we have 13 actors and 3 roles to fill, so we calculate it as follows:

Permutations = 13 * 12 * 11 Permutations

= 1,716

So, there are 1,716 different ways the roles of Larry, Curly, and Moe could be cast from the 13 actors auditioning.

Therefore, the number of ways the roles can be cast is:

13 x 12 x 11 = 1,716

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Answer:

$2,436

Step-by-step explanation:

I added the percentage together 30+7+7=42 and I multiplied 0.42 by $4,200 and then I got $1,764 which is the amount I spend on expenses each month. Last, I did 4,200-1,764 and got the answer

Answer:

25

Step-by-step explanation:

let x = the amount of money that shelly has.

let y = the amount of money that john has.

if shelly give john 5 dollars, then they both have the same amount of money.

this leads to the equation:

x-5 = y+5

if john give shelly 5 dollars, then shelly has twice as much money as john has.

this leads to the equation:

x+5 = 2(y-5)

solve for x in each equation to get:

x-5 = y+5 leads to:

x = y+10

x+5 = 2(y-5) leads to:

x+5 = 2y-10 which becomes:

x = 2y-15

you have 2 expressions that are equal to x.

they are:

x = y+10

x = 2y-15

you can set these expressions equal to each other to get:

y+10 = 2y-15

subtract y from both sides of this equation and add 15 to both sides of this equation to get:

y = 25

since x = 2y-15, this leads to:

x = 2(25)-15 which becomes:

x = 35

the equation x = y + 10 leads to the same answer of:

y =35

you have:

x = 25

y = 35

Answer:

10

Step-by-step explanation:

I hope you remember this. 5+5=10

We know that the expression can be combined into log4(200).

To combine the expression log4(8) + 2 log4(5), we can use the Laws of Logarithms. Specifically, we can use the product rule, which states that log*a(x) + log*a(y) = log*a(x y). Applying this rule, we get:

log4(8) + 2 log4(5) = log4(8) + log4(5^2)
= log4(8 * 5^2)
= log4(200)

Therefore, the expression can be combined into log4(200).

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A. CDs are more popular among middle school students than high school students.

B. Of the students surveyed, more students use streaming than CDs.

C. Streaming is more popular among high school students than middle school students.

The statements that are true about results in the two-way frequency table is determined as follows;

Statement A:

"CDs are more popular among middle school students than high school students".

Percent of high school = 14/31 = 0.452 = 45.2%

Percent of middle school = 26/57 = 0.456 = 45.6%

This statement is true.

Statement B:

"Of the students surveyed, more students use streaming than CDs".

total number of CD users = 40

total number streaming = 48

This statement is true

Statement C:

"Streaming is more popular among high school students than middle school students."

Percent high school streaming = 17/31 = 0.548 = 54.8%

Percent middle school streaming = 31/57 = 0.544 = 54.4%

This statement is true.

Statement D:

"Of the students surveyed, there are more than twice as many middle school students who use streaming than high school students."

number of middle school streaming = 31

number of high school streaming = 17

17 x 2 = 34

This statement is false, the middle school student using streaming are not up to twice the number of high school students using streaming.

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As we already found, the probability of winning for any selection is 1/3 = 0.333.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of samples

a) Let's suppose that player 1 chooses rock, and the selection of player 2 can be thought of as random.

If player 2 randomly selects rock, the result of the game is a draw.

if player 2 randomly selects papers, player 1 loses.

if player 2 randomly selects scissors, player 1 win.

Then we have 3 options with the same probability, that will be:

1/3

This is, the probability of winning is equal to the quotient between the number of outcomes that make player one win (1, in this case, scissors) and the total number of outcomes (3) = 1/3

the probability of a draw is equal to the quotient between the number of outcomes that make a draw (1, in this case, rock) and the total number of outcomes (3) = 1/3

The probability of losing is equal to the quotient between the number of outcomes that make player one lose (1, in this case, paper) and the total number of outcomes (3) = 1/3

The complete question is given below.

2. Almost everyone has played the rock-paper-scissors game at some point. Two players face each

other and, at the count of 3, make a fist (rock), an extended hand, palm side down (paper), or a

"V" with the index finger and middle fingers (scissors). The winner is determined by these rules:

rock smashes scissors, paper covers rock, and scissors cut paper. If both players choose the

same object, then the game is a tie. Suppose that Player 1 and Player 2 are both equally likely to

Choose rock, paper, or scissors.

a) Give a probability model for this change process.

b) Find the probability that Player 1 wins the game on the first throw.

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Answer:

√145

Step-by-step explanation:

Its already in its simplest radical form thus it staying in the form of √145.