Which equation represents the hyperbola (y -2)^2/4 - (x-2)^2/9=1
in general form?

Answer:

[tex]6.5\pi\ in[/tex]

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=3\frac{1}{4}\ in[/tex]

Convert to an improper fraction

[tex]r=3\frac{1}{4}=\frac{3*4+1}{4}=\frac{13}{4}\ in[/tex]

substitute

[tex]C=2\pi(\frac{13}{4})[/tex]

[tex]C=\frac{13}{2}\pi=6.5\pi\ in[/tex]

I think the answer is A

The question about the number of cities with more than 2 inches of snow is a statistical question as it involves data collection and analysis. Hence option a is correct.

The question, 'How many cities had more than 2 inches of snow?' is considered a statistical question. This is because it deals with the collection, analysis, interpretation, and presentation of data regarding the amount of snow that fell in various cities. Statistics is an area of mathematics that pertains to data analysis, and this question would likely require the processing and summarization of snowfall data from a number of cities.

Answer:

a. The coordinates of the vertex are (2 , 3)

b. The focal length of the parabola is 8

c. The equation, in standard form, of the parabola is (y - 3)² = -8(x - 2)²

Step-by-step explanation:

* Lets revise the equation of a parabola  

- If the equation is in the standard form (y − k)² = 4p(x − h), then:

# Use the given equation to identify h and k for the vertex, (h , k)

# Use the value of k to determine the axis of symmetry, y = k

# Use h , k and p to find the coordinates of the focus, (h + p , k)

# Use h and p to find the equation of the directrix, x = h − p

# The endpoints of the focal diameter,  (h + p , k ± 2p)

# The focal length is I4pI

* Now lets solve the problem

∵ The parabola has focus at (0 , 3)

∵ The coordinates of its focus, (h + p , k)

∴ h + p = 0 ⇒ (1)

∴ k = 3

∵ Its directrix at x = 4

∵ The equation of the directrix, x = h − p

∴ h - p = 4 ⇒ (2)

- Add (1) and (2) to find h and p

∴ h + p + h - p = 0 + 4 ⇒ add the like terms

∴ 2h = 4 ⇒ divide both sides by 2

∴ h = 2

- Substitute the value of h in (1)

∴ 2 + p = 0 ⇒ subtract 2 from both sides

∴ p = -2

a. ∵ h = 2 and k = 3

∵ The vertex of the parabola is (h , k)

∴ The coordinates of the vertex are (2 , 3)

b. ∵ The focal length is I4pI

∵ p = -2

∴ The focal length = I4 × -2I = I-8I = 8

∴ The focal length of the parabola is 8

c. ∵ The equation in the standard form is (y − k)² = 4p(x − h)

∵ h = 2 , k = 3 , p = -2

∴ The equation is (y - 3)² = 4(-2)(x - 2)²

∴ The equation is (y - 3)² = -8(x - 2)²

∴ The equation, in standard form, of the parabola is (y - 3)² = -8(x - 2)²

Answer:

240 grams

Step-by-step explanation:

Tara uses:

In total, Tara uses

[tex]1250+500+410=2160\ g[/tex] of ingredients.

She is making dinner for 9 people, so the weight of each serving is

[tex]2160:9=240\ g[/tex]

The circumference would be 213.6283 cm and the area would be 3,631.68 cm^2

Answer:

x = 26.7

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan64° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{13}[/tex]

Multiply both sides by 13

13 × tan64° = x, thus

x ≈ 26.7

Answer:

x = 26.7 units

Step-by-step explanation:

1. Find the third side: 180 = 90 + 64 + A, where A is the unknown angle

A = 180 - 154, A = 26°

2. Law of sines: sinA/a = sin B/b, where A and B are angles on a triangle, and a and b are the angles' opposite sides.

Plug in: sin(26°)/13 = sin(64°)/x

Means-extremes + multiply: x = 13sin(64°)/sin(26°)

Simplify: x ≈ 26.7 units (It is better to put one equation straight into the calculator instead of doing it one at a time, since the answer will be more accurate.)

Answer:

226 teams

Step-by-step explanation:

A team can be:

Count all combinations:

1. 5 girls from 5 girls can be chosen in 1 way.

2. 4 girls from 5 girls can be chosen in

[tex]C^5_4=\dfrac{5!}{4!(5-4)!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 4\cdot 1}=5[/tex]

different ways and 1 boy from 5 boys can be chosen in

[tex]C^5_1=\dfrac{5!}{1!(5-1)!}=\dfrac{5!}{1!\cdot 4!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 4\cdot 1}=5[/tex]

different ways, so in total,

[tex]5\cdot 5=25[/tex]

different combinations.

3. 3 girls from 5 girls can be chosen in

[tex]C^5_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!\cdot 2!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 1\cdot 2}=10[/tex]

different ways and 2 boys from 5 boys can be chosen in

[tex]C^5_2=\dfrac{5!}{2!(5-2)!}=\dfrac{5!}{2!\cdot 3!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 1\cdot 2\cdot 3}=10[/tex]

different ways, so in total,

[tex]10\cdot 10=100[/tex]

different combinations.

4. 2 girls from 5 girls can be chosen in

[tex]C^5_2=\dfrac{5!}{2!(5-2)!}=\dfrac{5!}{2!\cdot 3!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 1\cdot 2\cdot 3}=10[/tex]

different ways and 3 boys from 5 boys can be chosen in

[tex]C^5_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!\cdot 2!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 1\cdot 2}=10[/tex]

different ways, so in total,

[tex]10\cdot 10=100[/tex]

different combinations.

In total, there are

[tex]1+25+100+100=226[/tex]

possible teams.

Answer:

2x3 − 11x2 + 16x − 3

Step-by-step explanation:

tynna get points. this is not the answer, sorry

Answer:

8+4i

Step-by-step explanation:

You use the formula a+bi

You add the whole numbers which equal a (11 + -3)

You add the imaginary numbers which equal bi (-2i+6i)

You get 8+4i

The last one❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤

The last one Is correct

Answer:

233.33333 miles in 7 hours

Step-by-step explanation:

233.33333 miles in 7 hours

Answer:

25

Step-by-step explanation:

Expression: (2⁸ ⋅ 5⁻⁵ ⋅ 19⁰)⁻² ⋅ (5⁻²/2³)⁴ ⋅ 2²⁸

Inner-most powers: 2⁻¹⁶ • 5¹⁰ • 1 • 5⁻⁸/2¹² • 2²⁸

Combine like terms: 2¹² • 5²/2¹²

Cancel out: 5²

Solve: 25

The expression (2^8 ⋅ 5^−5 ⋅ 19^0)^−2 ⋅ 5^-2/(2^3)^4 ⋅ 2^28 simplifies to 2^24 * 5^8.

To find the simplified form of the expression (2^8 ⋅ 5^−5 ⋅ 19^0)^−2 ⋅ 5^-2/(2^3)^4 ⋅ 2^28, you use the properties of exponentiation.

First, any number to the power of 0 is always 1, so 19^0 is 1. Also, any number to a negative power is just the inverse of that number to the positive power. Thus, 5^−5 becomes 1/(5^5). So, the part in parentheses simplifies as follows:

2^8 ⋅ 5^−5 ⋅ 19^0 = 2^8 * 1/(5^5) * 1 = 2^8 / 5^5.

To raise this fraction to the negative 2 power, you swap the numerator and the denominator and raise it to the positive 2 power:

[tex](2^8 / 5^5)^-2 = (5^5 / 2^8)^2 = 5^1^0 / 2^1^6.[/tex]

Next, we tackle the second part of the expression: 5^(-2) / (2^3)^4 = 1/(5^2) / 2^12 = 2^12 / 5^2.

Finally, we multiply this by 2^28.

So, the entire expression simplifies to:

[tex]5^1^0 / 2^1^6 * 2^1^2 / 5^2 * 2^2^8 = 5^1^0 * 2^1^2 * 2^2^8 / (2^1^6 * 5^2) = 5^8 * 2^2^4 = 2^2^4 * 5^8[/tex]

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Answer:

Solving One-Step Equations. A one-step equation is as straightforward as it sounds. You will only need to perform one step in order to solve the equation. One goal in solving an equation is to have only variables on one side of the equal sign and numbers on the other side of the equal sign

Step-by-step explanation:

ex: 3x-9=25

Give brainlist plzzz

Answer:

Step-by-step explanation:

A one-step equation is an algebraic equation you can solve in only one step. Once you've solved it, you've found the value of the variable that makes the equation true. To solve one-step equations, we do the inverse (opposite) of whatever operation is being performed on the variable, so we get the variable by itself.

Answer by Khan Academy

The mode is the number repeated most often, so if we arrange these numbers in order, we can see what numbers repeat the most-

1 1 1 2 3 3 5 7 8 8 9

The number that repeats the most is 1

(1 counted 3 times)

(3 counted twice)

(8 counted twice)

The mode for the set of values is 1. It's calculated by counting how many times a number appears in a data collection.

Mode is the number in the data set repeating maximum number of times. It is obtained by calculating how many times the number are repeating in a data set.

The given data set is;

5 9 1 2 7 3 1 8 8 1 3

Numbers      Count (No of times)

1                        3

3                       2

8                       2  

1 is the most repeating number. It repeats three times.

Hence, the mode for the set of values is 1.

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The angles are congruent meaning that you can set them equal to each other:

26 = 5x + 11

Now you can solve for x

26 - 11 = 5x + (11 - 11)

15 = 5x

15/5 = 5x/5

x = 3

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

26 = 5x + 11

5x = 15

x = 3

Answer:

(-√3 , -1)

Step-by-step explanation:

I can confirm this is the correct answer because I just took the Plato test and (2cos210, 2sin210) equals the answer.

Answer:

B. [tex]f(x)=0.2(x-2)^2+1[/tex]

Step-by-step explanation:

The equation of a parabola in the vertex form is given by:

[tex]f(x)=a(x-h)^2+k[/tex], where V(h,k) is the vertex of the parabola

This parabola opens upwards and has its vertex at: V(2,1)

The a-value must therefore be positive.

The function must be

[tex]f(x)=0.2(x-2)^2+1[/tex]

The correct option is B.

Answer:

[tex]8[/tex]

Step-by-step explanation:

[tex]4(2x-5) \\ \\ 4(2x)-4(5) \\ \\ 4*2=8 \\ \\ 8x-20[/tex]

For this case we have the following expression:

[tex]4 (2x-5) =[/tex]

We simplify according to the steps of Ranger.

We apply distributive property to the terms within parentheses.[tex]4 * (2x) -4 * (5) =[/tex]

We find each product:

[tex]8x-20[/tex]

Answer:

The simplified expression is 8x-20

An "8" is placed in the blank space

Answer 2625

Step-by-step explanation: if the population is 210,000 and the rate is 12.5%

then make two fraction lines on your paper and on the second fraction line put 12.5% as the numerator and then 100 as the denominator  then on the first fraction put x as your numerator and 210,000 as the denominator   then cross multiple 120,000 to 12.5 then divide by 100  which your answer should be 2625

Answer:

17.25 km N37.9°E

Step-by-step explanation:

The way to solve this is to determine the vertical and horizontal distances traveled.

The bearing means 45° east of north.

Vertically, the car travels a distance of:

y = 3 + 15 cos 45°

y = 3 + 7.5√2

y ≈ 13.6

Horizontally, the car travels a distance of:

x = 15 sin 45°

x = 7.5√2

x ≈ 10.6

The total distance we find with Pythagorean theorem:

d = √(x² + y²)

d = √(10.6² + 13.6²)

d ≈ 17.25

The bearing from north we find with tangent:

tan θ = x / y

tan θ = 10.6 / 13.6

θ ≈ 37.9°

To eliminate 't' from the parametric equations X=6cos t and Y=3sin t, square both equations and substitute the resulting cos^2 t and sin^2 t values into the trigonometric identity equation sin^2 t + cos^2 t = 1. This results in the equation X^2 / 36 + Y^2 / 9 = 1, effectively eliminating 't' from the equations.

Eliminating the Parameter for X=6cos t and Y=3sin t

Our goal here is to eliminate the parameter 't' from the two given equations, which is a common task in parametric equations.

For such problems involving sin and cos, we can use the trigonometric identity sin^2 t + cos^2 t = 1. However, the provided equations don't directly represent sin t or cos t. To bring them in those forms, we start by squaring both equations.

Squaring X and Y yields: X^2 = 36cos^2 t and Y^2 = 9cos^2 t.

Next, we solve each equation for cos^2 t and sin^2 t separately.

cos^2 t = X^2 / 36 and sin^2 t = Y^2 / 9.

Substituting these values into the trigonometric identity equation, we get: X^2 / 36 + Y^2 / 9 = 1 which is the equation of an ellipse in x and y. Hence, 't' has been eliminated.

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To eliminate the parameter x = 6 cos t and y = 3 sin t, you can express x in terms of y as x = cos(t) and substitute it into the equation y = 3 sin(t), resulting in y = 3 sin(arccos(x)).

To eliminate the parameter in this case, we need to express x in terms of y. We can start by dividing the equation X = 6 cos(t) by 6 to get x = cos(t). Then we can substitute this expression for x in the equation y = 3 sin(t) to get[tex]y = 3 sin(cos^(-1)(x)).[/tex]

Since [tex]cos^(-1)(x)[/tex]is the inverse of cosine, we can rewrite this as y = 3 sin(arccos(x)).

So, when we eliminate the parameter, we have the equation y = 3 sin(arccos(x)).

Answer:

Nonlinear system of inequalities

Step-by-step explanation:

Answer:

Nonlinear system of inequalities

Step-by-step explanation:

The chemical reaction between hydrogen and chlorine to form hydrochloric acid is balanced as H2 + Cl2 -> 2HCI. This denotes one molecule of hydrogen and one molecule of chlorine reacting to produce two molecules of hydrochloric acid.

The equation presented in the question is H2 + Cl2 -> HCI. This is a chemical reaction in which hydrogen (H2) and Chlorine (Cl2) react to form hydrochloric acid (HCI). However, the equation is not balanced as it stands. Balancing a chemical equation involves ensuring that there are equal numbers of each type of atom on each side of the equation.

In this case, the balanced equation is: H2 + Cl2 -> 2HCI This means that one molecule of hydrogen and one molecule of chlorine react to form two molecules of hydrochloric acid.

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Answer:

12

Step-by-step explanation: we will use pathogorean theorem because there is a right triangle. a^2+b^2=c^2

We know BE=9 we need AE to find AB

You can make another triangle on the end. AD=28 - 12 (BC) = 16

16/2 = 8 so AE= 8

8^2+9^2=c^2

145=c^2

Square root of 145=c

C=12.04

Answer:

I believe the answer is 62.

Step-by-step explanation:

Hope my answer has helped you!

the square root of 108 is about 10.4 and since the negative symbol is on the outside of the square root symbol, the answer is -10.4

Answer:

A.

Step-by-step explanation:

The answer is A. B happens between 7 and 9, C happens before 6:30, and D happens between 9:30 and 10.

Answer:

D

Step-by-step explanation:

95 texts is 38% of her total messages.

95 = 0.38 × x

x = 95 / 0.38

x = 250

Answer:

71.49134 feet

Step-by-step explanation:

Side a = 112

Side b = 99

Side c = 71.49134

Angle ∠A = 80.37° = 80°22'11" = 1.40272 rad

Angle ∠B = 60.63° = 60°37'49" = 1.0582 rad

Angle ∠C = 39° = 0.68068 rad

: )

The distance between the kites will be 128.16 feet.

What is Pythagoras theorem?

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

Linda has 99 feet of string out to one kite and 112 feet out to the other kite.

And, The angle formed by the two strings is 39°.

Now,

Find the distance between the kites as;

Since, Linda has 99 feet of string out to one kite and 112 feet out to the other kite.

And, The angle formed by the two strings is 39°.

Let the distance between the kites = x

So, We can formulate as;

x² = (112)² + 99² - 2 × 112 × 99 cos 39°

Solve for x as;

x² = 12,544 + 9,801 - 22,176 × 0.267

x² = 22,345 - 5,921

x² = 16,424

x² = √16,424

x = 128.16

Thus, The distance between the kites will be 128.16 feet.

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