z + mx = yx Solve for x

The center of the hyperbola given as (y + 3)²/9 − (x − 2)²/2 = 1 is (2, -3)

From the question, the equation of the hyperbola is given as

(y + 3)²/9 − (x − 2)²/2 = 1

As a general representation, a hyperbola is represented as

(y - k)²/a² − (x − h)²/b² = 1

From the above general representation, the coordinates of the center of the hyperbola is

Center = (h, k)

By comparing the equations (y - k)²/a² − (x − h)²/b² = 1 and (y + 3)²/9 − (x − 2)²/2 = 1, we  have the following representstion

(h, k) = (2, -3)

This means that

Center = (2, -3)

Hence, the center is (2, -3)

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Answer:

(2,-3) See question 10

Step-by-step explanation:

To solve an inequation for x you have to follow the same procedure you follow when solving equations, with exception that when you multiply/divide by a negative number the direction of the inequality gets inverted.

So to solve the given inequelity for x, you have to pass "+49" to the other side of the expression. To do so, subtract it from both sides of the expression:

The result of the inequality is x > -21

Using the mid point, the coordinates of the end point V is (7, -27)

A midpoint is a point lying between two points and is in the middle of the line joining the two points.

In other words, the midpoint of a line segment is a point that lies halfway between 2 points.

Therefore, the coordinates of the endpoint V can be found as follows:

using the mid point,

(xₙ, yₙ) = (x₁ + x₂ / 2, y₁ + y₂ / 2)

Therefore,

(5, -11) = (3 + x₂ / 2, 5 + y₂ / 2)

Hence,

5 = 3 + x₂ / 2

cross multiply

10 = 3 + x₂

10 - 3 = x₂

x₂ = 7

Hence,

- 11 = 5 + y₂ / 2

-22 = 5 + y₂

-22 - 5 = y₂

y₂ = - 27

Therefore, the coordinates of V is (7, -27)

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ANSWER

R1, R2, R3, R4, G1, G2, G3, G4. Option B.

Answer:

1. 39, 46

2. 180

Step-by-step explanation:

1. count up by 7

2. not sure..

Answer:

x ≥ - [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

4x + 4 ≤ 9x + 8 ( subtract 5x from both sides )

4 ≤ 5x + 8 ( subtract 8 from both sides )

- 4 ≤ 5x ( divide both sides by 5 )

- [tex]\frac{4}{5}[/tex] ≤ x , then

x ≥ - [tex]\frac{4}{5}[/tex]

Answer:

4x + 4 ≤ 9x + 8   Subtract 4x from both sides

       4 ≤ 5x + 8   Subtract 8 from both sides

      -4 ≤ 5x         Divide both sides by 5

        ≤ x  

       x ≥  

Step-by-step explanation:

Answer:

y=[tex]\frac{3}{2}[/tex]x - [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

To get slope intercept form (y=mx+b), simplify and solve for y.

y+1=[tex]\frac{3}{2}[/tex](x-1)

Simplify

y+1=[tex]\frac{3}{2}[/tex]x - [tex]\frac{3}{2}[/tex]

Solve for y

y=[tex]\frac{3}{2}[/tex]x - [tex]\frac{5}{2}[/tex]

Answer: 23 - 19 = 4

Step-by-step explanation:

Answer:

how many does eat cookies left??? what

Step-by-step explanation:

anyway, it should be 4 cookies i guess?

23 - 19 = 4

...unless this is like a trick question with bad grammar

The cost of the total bill for the friends is $154.665.

This implies a levy that's paid to the government by individuals and firms.

From the information, the.group of friends’ dinner bill before tax is $122.75, sales tax rate is 8% and they want to leave an 18% tip after tax.

The total bill will be:

= Cost of food + Tax + Tip

= $122.75 + (8% × $122.75) + (18% × $122.75)

= $122.75 + $9.82 + $22.095

= $154.665

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After subtraction we can see Stephanie has only 1 pizzas left.

What is subtraction?

The definition of subtraction is subtracting one number or amount from another. It is addition's opposite operation. Subtraction subtracts a number from another to find the difference, whereas addition adds or groups numbers to find the sum. The word "subtract" can also mean to compare two values to determine how many factors account for a value's difference from another. That is the most fundamental concept behind the term "difference" for the solution to a subtraction problem.

We are given that,

Stephanie has 5 pizzas, Also she shared 4 of the pizzas with her friends

Hence she is left with 5-4= 1 pizza
Hence Stephanie has left with 1 pizza

Therefore the correct option is option D)
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The proportion of these banks that had an interest rate less than 2.5 percent is 0.724.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 2.5

μ = mean = 2.28

σ = standard deviation = 0.37

z-score = (2.5 - 2.28) / 0.37

z-score = 0.22 / 0.37

z-score = 0.5946

To get the proportion, find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = 0.5946

By interpolating the values,

probability = 0.724

proportion = 0.724

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The rate at which the volume of the cone is changing is -5235.98 inches³/s when the radius of the circular cone is 50 inches and the height is 10 inches.

The formula for the circular cone can be given as;

V = 1/3 πr²h

Now we take the derivative with respect to time as follows;

V = 1/3 πr²h

dV/dt = 1/3π d/dt(r²h)

dV/dt = 1/3π [2r(dr/dt) × h + r²(dh/dt)]

Now we substitute the values in this equation as follows;

dV/dt = 1/3π [2 × 50 × 5 × 10 + (50²) (-4)]

dV/dt = 1/3π [ 5000 - 10000]

dV/dt = 1/3π [-5000]

dV/dt = -5235.98

Hence the negative sign indicates that the volume is decreasing over time and the rate of change is calculated to be -5235.98 inches³/s.

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Answer:

can't answer the first two questions as figure is not mentioned in picture

3. -3

4. 6

5. 3/4

6. -3

7. 5

8. 3

Step-by-step explanation:

We will have the following:

When we solve for x we will have

So, x is equal or grater than -5.

The most appropriate choice for Simultaneous linear equation will be given by -

8 packages of coffee and 4 packages of tea are sold.

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here,

A coffee shop sold 11 packages of coffee and 50 packages of tea, for which customers paid a total of $288

So,

11x + 50y = 288 ...............(1)

The day before, 12 packages of coffee and 38 packages of tea was sold, which brought in a total of $248

So,

12x + 38y = 248

2(6x + 19y) = 248

6x + 19y = [tex]\frac{248}{2}[/tex]

6x + 19y = 124 ....................(2)

Multiplying (1) by 6 and (2) by 11,

66x + 300y = 1728

66x + 209 y = 1364

Subtracting above two equations,

91 y = 364

[tex]y = \frac{364}{91}[/tex]

y = 4

Putting the value of y in (2),

6x + 19[tex]\times[/tex]4 = 124

6x + 76 = 124

6x = 124 - 76

6x = 48

[tex]x = \frac{48}{6}\\x = 8[/tex]

8 packages of coffee and 4 packages of tea are sold.

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The most appropriate choice for Simultaneous linear equation will be given by -

8 packages of coffee and 4 packages of tea are sold.

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here,

A coffee shop sold 11 packages of coffee and 50 packages of tea, for which customers paid a total of $288

So,

11x + 50y = 288 ...............(1)

The day before, 12 packages of coffee and 38 packages of tea was sold, which brought in a total of $248

So,

12x + 38y = 248

2(6x + 19y) = 248

6x + 19y =

6x + 19y = 124 ....................(2)

Multiplying (1) by 6 and (2) by 11,

66x + 300y = 1728

66x + 209 y = 1364

Subtracting above two equations,

91 y = 364

y = 4

Putting the value of y in (2),

6x + 194 = 124

6x + 76 = 124

6x = 124 - 76

6x = 48

8 packages of coffee and 4 packages of tea are sold.

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The probability that the coin lands heads up six times in a row is 0.016

Probability is the term used in mathematics to understand how likely an event is to happen or can also be described as how likely it is that a proposition is true.

It can be determined by dividing the favorable outcomes or events by the total number of outcomes.

As the coin has two sides, the probability that when the coin lands, it lands heads up is determined as follows;

Probability = 1 / 2

Now the probability that the coin lands heads up six times in a row can be calculated as follows;

Probability = (1^6) / (2^6)

Probability = 1 / 64

Probability = 0.015625

Rounding it to three decimal places as follows;

Probability = 0.015625 = 0.016

Therefore, the probability that the coin lands heads up six times in a row is calculated to be 0.016

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The area of the figure given below is 56.6 units² .

In the question ,

a figure is given

where there is one rectangle and two semicircles .

the length of the rectangle is given as 11 units

and the breadth of the rectangle is = 4 units

we know that the area of the rectangle is = length × breadth

on substituting the values ,

we get

area = 11 × 4

area = 44 units²

the radius of the semicircle = 2 units

the are of the semi circle = (1/2)*π*r²

since there are two semicircle , the area of the two semi circle will be

= 2 * (1/2)πr²

= π*r²

On substituting , the value of radius = 2 ,

we get the area is = 3.14*(2)² = 12.56       using π = 3.14

so the area of the complex figure is = 44 + 12.56 = 56.56

≈ 56.6

Therefore , The area of the figure given below is 56.6 units²  .

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The probability that joe and jane end up in the same class is 0.3258 .

In the question ,

it is given that

90 students is to be split into 3 equal size classes , so ,

the three classes  will have 30 students each .

let these classes be Class A , Class B and Class C .

Let Joe and Jane be in Class A .

the total number of ways of selecting 30 students for class A from 90 students is C(90,30) .

Since , we have fixed Joe and Jane in Class A , the remaining 28 spots of class A can be filled by remaining 88 students  in C(88,28) ways ,

So , the probability that Joe and Jane end up in the same class is

= C(88,28)/C(90,30) .

Since there are three  classes ,

the required probability is 3*C(88,28)/C(90,30) .

= 3×[tex]\frac{88!}{28!*60!}[/tex]×[tex]\frac{60!*30!}{90!}[/tex]

= 29/89

= 0.3258

Therefore , the probability that joe and jane end up in the same class is 0.3258   .

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x = 12° and y = 7° are the value of linear angles.

What is linear pair of angles?

8x° = 96°

x = 96/8

x = 12°

8x° = 11y + 19

8 * 12° = 11y + 19

96 = 11y + 19

11y = 96 - 19

11y =    77

y = 77/11

y = 7°

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The number is 234.

Step-by-step explanation:

Let the 3 digits be H , T and U so the number is HTU.

H + T + U = 9

T = 0.5H + 0.5U

U = 2H

So  from the last 2 equations

T = 0.5H + 0.5(2H)

T = 0.5H + H

T = 1.5H

So substituting for T and H is the first equation:

H + 1.5H + 2H = 9

4.5H = 9

H = 2.

So T = 1.5*H = 1.5 *2 = 3.

Explanation

From the given question

We are given the formula to compute the amount that a sum of $8000 compounded quarterly will yield after time t at a rate of 2.8%

The formula is given by

Part A

part B

the amount in the account after 7 years will be

The amount that will be in the account after 7 years will be $9725.57

Part C

APY is given by

In our case we have

Hence, we will have the APY as

Hence, the APY is 2.829%

Mathematics → Solid Figures → Volume

The volume of a cylinder is:

In this question,

r = 2 ft (4/2 =2)

h = 5 ft

Then, the volume of the cylinder is (Vc):

Using π = 3:

The volume of a rectangular prism (Vr) is:

In this question:

l = 9 ft

w = 5 ft

h = 5 ft

Then, the volume of the rectangular prism is:

The volume of the object (V) is the sum of the volumes:

Answer: 285 ft³.

The length of the rectangular pegboard is 80 inches

A rectangle is a polygon with four sides in which two opposite sides are parallel and equal

Since Vince is cutting a rectangular piece of pegboard to use in his garage for organization. The width of the pegboard is 8 inches less than half the length. The perimeter of the pegboard is 224 inches.

Let

Since the width of the pegboard is 8 inches less than half the length, we have that

W = L/2 - 8

Also, since the pegboard is a rectangle, its perimeter, P = 2(L + W)

Now, its perimeter P = 224 inches.

So, 2(L + W) = 224

L + W = 112

Now, substituting the width, W into the equation, we have

L + W = 112

L + L/2 - 8 = 112

L + L/2 = 112 + 8

L + L/2 = 120

3L/2 = 120

L = 120 × 2/3

L = 240/3

L = 80 inches

So, the length of the pegboard is 80 inches

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The equation of the line is found as y = -x/2 + 9/2.

For the given question;

The equation of the perpendicular line is given as;

y = 2x - 7

Compare the equation with the standard form of slope intercept.

y = mx + c

m = slope and c is the y intercept.

m1 = 2

Now, the line is perpendicular, thus the relation between both slopes is;

m1 × m2 = -1

m2 = -1/2

The passing coordinates of the line is (1. 4).

Find the equation using formula.

y - y1 = m2(x - x1)

y - 4 = (-1/2) (x - 1)

Simplifying,

y = -x/2 + 9/2

Thus, the equation of the line is found as y = -x/2 + 9/2.

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Different possibilities for the given case are, 267540

4 railroads chosen from 15 class I railroads

2 railroads chosen from 8 class II railroads

1 railroad chosen from 7 class III railroads

So total combinations    = ¹⁵C₄ ˣ ⁸C₂ ˣ ⁷C₁

   = (15!)/(4!*11!) x (8!)/(2!6!) x (7!)/(1!6!)

   = 15 x 7 x 13 x 4 x 7 x 7 = 267540

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In the Mediterranean, the Mycenaeans rose to prominence by a mix of military prowess, economic connections, and cultural sway.

Thus, Military Might: The Mycenaeans had a strong military force and were expert warriors. They used sophisticated bronze weapons and chariot warfare as a tactic.

They were able to increase their influence and take control of neighbouring territories thanks to their military might.

Control over Trade Routes: The Mycenaeans had complete control over key trade routes in the Mediterranean, particularly those that extended from the Aegean to the eastern Mediterranean and beyond.

Thus, In the Mediterranean, the Mycenaeans rose to prominence by a mix of military prowess, economic connections, and cultural sway.

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The length of the diagonal of the TV is 2500 inches

Calculating your TV size is less complicated than you might think. A TV's size refers to its diagonal length, which comes from measuring from the upper left hand corner of the actual TV screen to the lower right hand corner.

TV that is 30 inches tall and 40 inches wide.

The length of the diagonal of the TV of the equation is

[tex]30^{2} + b^{2} =40^{2}[/tex]

Then

[tex]30^{2} +40^{2} =2500[/tex]

so

The length of the diagonal of the TV is 2500 inches

Calculating your TV size is less complicated than you might think. A TV's size refers to its diagonal length, which comes from measuring from the upper left hand corner of the actual TV screen to the lower right hand corner. Most are expressed in inches.

The screen surface's diagonal length is calculated from one corner to the other corner (bottom left to top right or top left to bottom right)

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