I am almost bankrupt asking the same question but....

1)If (a^2+1)/a=12,find the value of a^3 +(1)/a^3
2)If y-(1)/y=7 find the value for (y^6-1)/y^3

This is a horizonal line going through y = 4.

Horizontal lines are of the form

Where

a is a number

Slope is rise over run, or, the change in y divided by change in x.

No matter what the change in x is, the change in y is always zero (horizontal line). Thus, the slope is always 0 as well.

1.

The slope of the line is 0

2.

The slope intercept form is:

Since the slope is zero, m = 0 and y intercept (b) is 4, we have:

Answer:

0.1 in per year ; 142 in

Step-by-step explanation:

Giveb that :

Diameter of tree in 1965 = 135 inches

Diameter of tree in 2005 = 139 inches

Average rate of change:

Change in diameter / change in time

(139 - 135) / (2005 - 1965)

4 / 40

= 0.1 in per year

Predict diameter in 2035;

Initial diameter + (average rate of change * (Number of years from initial)).

135 in + (0. 1 * (2035 - 1965))

135 in + (0.1 * 70)

135 in + 7 in

= 142 in

Answer:

60

Step-by-step explanation:

Answer:

I don't know what z I don't know I don't know

Answer:

Maybe 78 and 76

Step-by-step explanation:

Thats what I got, Idrk how to explain it though-

Answer:2,2

Step-by-step explanation:

Answer:

Answered

Step-by-step explanation:

Answer:

well you did the law of inverse on 6x you proved it by putting the one above it and switched the minus with a plus and divided 24 by 6

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

8 people

3 slices per person

8 × 3 = 24

They need 24 slices.

1 pizza has 10 slices.

24/10 = 2.4

They need 2.4 pizzas. Since they need to order a whole number of pizzas, they need to order 3 pizzas.

Answer: 3

Answer:

Use a model to find the sum of two fractions with the same denominator

Add fractions with a common denominator without a model

Add fractions with a common denominator that contain a variable h

Step-by-step explanation:

h

The surface area of the cuboid is 10cm².

By adding up the areas of all of a cuboid's faces, one may determine its surface area. A cuboid's total surface area, measured in square units, is

2 (lw + wh + lh), where l is the cuboid's length, w is its width, and h is its height.

Here in the given question,

There are 2 cubes.

Edge of each cube = 1cm.

Now the cubes are joined and formed a cuboid with:

Length, l = 1 + 1 = 2cm.

Breadth, b = 1cm.

height, h = 1cm

Surface area of the cuboid = 2 (lb + bh + lh)

= 2 (2 × 1 + 1 × 1 + 2× 1)

= 2 (2+1+2)

= 2 × 5

= 10cm².

Therefore, the surface area of the cuboid = 10cm².

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Answer:

Step-by-step explanation:

-g - 12 = 5g - 60

-6g - 12 = -60

-6g = -48

g = 8

Answer:

Step-by-step explanation:

The area of the wall is the sum of the areas of the different sections of the wall. The cost to paint it will be the product of the cost of a tin of paint and the number of tins required.

__

Here, the shape of the wall can be divided into two trapezoids and a rectangle. Each shape has a corresponding area formula. Left-to-right, their areas are ...

Left Trapezoid

  A = 1/2(b1 +b2)h

  A = 1/2(10 m +11 m)(4 m) = 42 m²

Middle Rectangle

  A = LW

  A = (13 m)(11 m) = 143 m²

Right Trapezoid

  A = 1/2(b1 +b2)h

  A = 1/2(11 m +8 m)(10 m) = 95 m²

Wall Area

The total area to be painted is the sum of the above areas:

  total area = 42 m² +143 m² +95 m² = 280 m²

The area that needs to be painted is 280 m².

__

A tin of paint covers 15 m², so the number of tins needed is ...

  (15 m²)t = 280 m²

  t = 280/15 = 18 2/3 . . . . . . divide by the coefficient of t

We can only buy whole tins, so we need to buy 19 tins. Their cost will be ...

  (£7 /tin)(19 tins) = £133

It will cost £133 to paint the wall.

The range at which Dan's car can go is 3.33 miles

A car's range is the distance it can travel with the current amount of fuel in the tank.

The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.

The range of a car can be measured in the unit of distance.

Therefore the range of a car can be calculated as;

R = distance per gallon/ number of gallon.

Dan's car is 40mpg and has 12 gallons in it's tank.

Therefore it's range = 40/12

= 3.33miles.

therefore the range of Dan's car is 3.33miles

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The Laplace transforms of the given functions are:(a) L[2.1u(t)] = 2.1/s  (b) L[2u(t - 1)] = 2e^(-s)/s  (c) L[5u(t - 2) - 2u(t)] = (5e^(-2s) - 2) / s   (d) L[3u(t - b)] = 3e^(-sb)/s

To calculate the Laplace transform of the given functions using the assistance of equation [10], we'll apply the properties of the Laplace transform. Equation [10] states:

L[a * f(t - b)] = e^(-bs) * F(s)

where L represents the Laplace transform, a is a constant, f(t) is the function, b is a positive constant, s is the complex frequency variable, and F(s) is the Laplace transform of f(t).

(a) To find the Laplace transform of 2.1u(t), where u(t) is the unit step function:

L[2.1u(t)] = 2.1 * L[u(t)]

Since the Laplace transform of the unit step function is 1/s, we have:

L[2.1u(t)] = 2.1 * (1/s) = 2.1/s

(b) To find the Laplace transform of 2u(t - 1):

L[2u(t - 1)] = 2 * L[u(t - 1)]

Using equation [10], we have:

L[2u(t - 1)] = 2 * e^(-s * 1) * L[u(t)]

            = 2 * e^(-s) * L[u(t)]

Since the Laplace transform of the unit step function is 1/s, we have:

L[2u(t - 1)] = 2 * e^(-s) * (1/s) = 2e^(-s)/s

(c) To find the Laplace transform of 5u(t - 2) - 2u(t):

L[5u(t - 2) - 2u(t)] = 5 * L[u(t - 2)] - 2 * L[u(t)]

Using equation [10], we have:

L[5u(t - 2) - 2u(t)] = 5 * e^(-s * 2) * L[u(t)] - 2 * L[u(t)]

                    = 5 * e^(-2s) * L[u(t)] - 2 * L[u(t)]

                    = 5 * e^(-2s) * (1/s) - 2 * (1/s)

                    = (5 * e^(-2s) - 2) / s

(d) To find the Laplace transform of 3u(t - b), where b > 0:

L[3u(t - b)] = 3 * L[u(t - b)]

Using equation [10], we have:

L[3u(t - b)] = 3 * e^(-s * b) * L[u(t)]

            = 3 * e^(-sb) * (1/s)

            = 3e^(-sb)/s

So, the Laplace transform of 3u(t - b) is 3e^(-sb)/s.

In summary, the Laplace transforms of the given functions are:

(a) L[2.1u(t)] = 2.1/s

(b) L[2u(t - 1)] = 2e^(-s)/s

(c) L[5u(t - 2) - 2u(t)] = (5e^(-2s) - 2) / s

(d) L[3u(t - b)] = 3e^(-sb)/s

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Required area of the composite figure is 69 cm²

What is area of a composite shape?

the area covered by any composite shape. A composite shape is a shape in which some polygons are put together to form the required shape is called the area of composite shapes . These figures can consist of combinations of triangles, rectangles, squares etc. To determine the area of composite shapes, divide the composite shape into basic shapes such as square, rectangle,triangle, hexagon, etc.

Basically, a compound shape consists of basic shapes put together. This is also called a "composite" or "complex" shape. This mini-lesson explains the area of compound figures with solved examples and practice questions.

Here in this figure, we have two figures.

First one is rectangle and second one is triangle.

Length and breadth of the rectangle are 12 cm and 4 cm respectively.

So, area = Length × Breadth = 12 × 4 = 48 cm²

Again height of the triangle is (11-4) = 7 cm and base of the triangle is (12-6) = 6 cm.

So, area of the triangle = 1/2 × 7 × 6 = 3×7 = 21 cm²

Now if we add both area of rectangle and triangle then we will get area of the composite figure.

So, required area of the composite figure is ( 48+21) = 69 cm²

Therefore, option A is the correct option.

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Answer:

a 17, b 10, c 15, d 20

Step-by-step explanation:

a^2+b^2=c^2

64+225 = 289

a = 17

36+64 = 100

b = 10

81+144 = 225

c = 15

256+144 = 20

Hope that helps

Polynomials are expressions. The solution of the division can be written as \(4x^2-27x+167-\dfrac{996}{x+6}\).

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

The division of the polynomial  (4x³-3x²+5x+6) when divided by (x+6), can be done in the following manner,

\(\dfrac{4x^3-3x^2+5x+6}{x+6}\)

\(=4x^2+\dfrac{-27x^2+5x+6}{x+6}\)

\(=4x^2-27x+\dfrac{167x+6}{x+6}\)

\(=4x^2-27x+167+\dfrac{-996}{x+6}\\\\\\=4x^2-27x+167-\dfrac{996}{x+6}\)

Hence, the solution of the division can be written as \(4x^2-27x+167-\dfrac{996}{x+6}\).

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Answer:

Step-by-step explanation:

OPT D ON EDG 2023

Answer:

Triangle A

Right

Triangle B

Acute

Triangle C

Obtuse

Triangle D

Acute

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

Let's call the original two digit number xy, where x is the tens digit and y is the ones digit. An algebraic representation of this number is 10x + y.

The sum of the two digit number is 8: x+y=8

When the digits are reversed, the number increases by 36: (10y + x) - (10x + y) = 36

Now we have two equations and two unknown parameters, so we have enough information to find those parameters.

Solve for x:

X=8-y

plug in x:

(10y + 8-y) - (10(8-y)+ y) = 36

simplify:

(9y + 8) - (80-9y) = 36

18y - 72 = 36

y = 108/18 = 6

so if y=6, then x=8-y=8-6=2

so our number is 26. 62 is 36 greater than 26.

Greetings from Brasil...

As we have a line, the function will be given by the expression:

F(X) = AX + B

where

A = ΔY/ΔX

B = where the line intersects the Y axis

Looking at the graph we have already concluded that

B = - 3

A = ΔY/ΔX

A = (5 - 3)/(4 - 3)     see attached picture

A = 2

So,

F(X) = AX + B

Answer:

X < 3

Step-by-step explanation:

2x-1<x+2

2x - x < 2 + 1

X < 3

a= 1* 9/1 =9

The answer is 9

Answer:

-9a=-1

a=-1/-9

a=1/9

hope this helps!

Q1) The ball experiences a pressure of 392,000 Pa at the bottom of the lake.

Q2) The ball is made of a dense material like lead or depleted uranium.

Q1) To calculate the pressure experienced by the ball at the bottom of the lake, we can use the formula

P = ρgh

Where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the depth of the ball in the water.

We know that the ball sinks 40 m in 3.6 s, so we can calculate its velocity using the formula

v = gt

Where v is the velocity, g is the acceleration due to gravity (9.8 m/s^2), and t is the time (3.6 s).

v = gt = 9.8 m/s² × 3.6 s = 35.28 m/s

Using the formula for the depth of an object in water

h = (ρ_ball/ρ_water) × r

Where ρ_ball is the density of the ball, ρ_water is the density of water (1000 kg/m³), and r is the radius of the ball.

We can rearrange this formula to solve for the density of the ball:

ρ_ball = (h/ r) × ρ_water

ρ_ball = (40 m / 0.12 m) × 1000 kg/m³ = 333,333.33 kg/m³

This is much higher than the density of any common metal, so it's possible that the ball is made of a dense material like lead or depleted uranium.

Q2) Plugging the values into the pressure formula

P = ρgh = 1000 kg/m³ × 9.8 m/s² × 40 m = 392,000 Pa

So, the ball experiences a pressure of 392,000 Pa at the bottom of the lake.  The density of the ball is calculated to be 333,333.33 kg/m³, which is much higher than the density of any common metal. It's possible that the ball is made of a dense material like lead or depleted uranium.

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The mode of a dataset is the value that appears most frequently. In this case, we need to find the interval of rainfall that occurs most frequently.

From the given data, we can see that the interval "less than 0.01 inch" has the highest frequency with 165 days. Therefore, the mode of this dataset is "less than 0.01 inch"

Effective communication is crucial in all aspects of life, including personal relationships, business, education, and social interactions. Good communication skills allow individuals to express their thoughts and feelings clearly, listen actively, and respond appropriately. In personal relationships, effective communication fosters mutual understanding, trust, and respect.

In the business world, it is essential for building strong relationships with clients, customers, and colleagues, and for achieving goals and objectives. Good communication also plays a vital role in education, where it facilitates the transfer of knowledge and information from teachers to students.

Moreover, effective communication skills enable individuals to engage in social interactions and build meaningful connections with others. Therefore, it is essential to develop good communication skills to succeed in all aspects of life.

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The given case of Gallup asking the same 50 people how many hours had they worked at a job in the past 7 days. is an example of dependent sample.

The measured values in relation in a dependent sample (also called a paired sample).

Some characteristics of dependent sample are-

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Therefore, the equation of the line that is parallel to line g and passes through point P(-2,0) is y = 2x + 4.

An equation is a mathematical statement that asserts that two expressions have the same value. It contains an equals sign (=) and can include variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used in various fields of mathematics, science, engineering, and economics, among others, to model and solve problems.

Here,

Part A: Since line f has a constant y-value of 2, any line parallel to it will also have a constant y-value of 2. Therefore, the equation of the line that is parallel to line f and passes through point P(-2,0) is simply y = 0.

Part B: To find the equation of a line that is parallel to line g and passes through point P(-2,0), we can use the fact that parallel lines have the same slope. The slope of line g is 2, so the slope of any line parallel to it will also be 2. Using the point-slope form of a linear equation, we have:

y - 0 = 2(x - (-2))

y = 2x + 4

Part C: To find the equation of a line that is perpendicular to line f and passes through point Q(3,-2), we can use the fact that the product of the slopes of two perpendicular lines is -1. The slope of line f is 0, so the slope of any line perpendicular to it will be undefined (since division by zero is undefined). Therefore, the equation of the line that is perpendicular to line f and passes through point Q(3,-2) is simply x = 3.

Part D: To find the equation of a line that is perpendicular to line g and passes through point Q(3,-2), we can use the fact that the product of the slopes of two perpendicular lines is -1. The slope of line g is 2, so the slope of any line perpendicular to it will be -1/2. Using the point-slope form of a linear equation, we have:

y - (-2) = (-1/2)(x - 3)

y + 2 = (-1/2)x + 3/2

y = (-1/2)x - 5/2

Therefore, the equation of the line that is perpendicular to line g and passes through point Q(3,-2) is y = (-1/2)x - 5/2.

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