The graph of f(x) is shown in black.Write an equation in terms of f(x) to match the redgraph.For example, try something like this:f(x)+3, f (x - 2), or 4f(x).

x > -8

Let the number be represented by x:

Three times the number = 3x

Six minus three times the number = 6 - 3x

Six minus three times the number is less than 30:

That can be interpreted mathematically as:

6 - 3x < 30

To find the value of x:

Step 1: Collect like terms

- 3x < 30 - 6

-3x < 24

Step 2: Divide both sides by 3:

-x < 8

Multiply both sides by (-1) and change the < sign to >

(-1) (-x) > 8 x(-1)

x > -8

Answer:

0.116

Step-by-step explanation:

[tex]\frac{0.232}{2}[/tex] = 0.116

There were 52 billiard balls in the set.

Assume that billiard balls are arranged in rows to form an equilateral triangle, then the first row consists of 1 ball, second row consists of 2 balls, and third row consists of 3 balls,  and so on. So there must be n balls in the nth row.

So, the total number of billiard balls that forms the equilateral triangle with n rows is:  

1 + 2 + 3 + ... + n = n(n + 1)/2

Let x1 and x2 be the total number of balls in the first and second arrangements respectively.  

Then,

x1 = n(n + 1)/2 + 7

It has been said that there were 3 lesser balls in the second arrangement:  

x2 = (1 + (n + 1))/2 × (n + 1) - 3

x2 = (n + 1) × (n + 2)/2 - 3

Since x1 = x2,

n(n + 1)/2 + 7 =  (n + 1) × (n + 2)/2 - 3

We solve above equation to find the value of n,

multiplying both the sides by 2

n(n + 1) + 14 = (n + 1)(n + 2) - 6

n² + n + 14 = n² + 3n + 2 - 6

n - 3n = -4 - 14

-2n = -18

n = 9

So, x1 = 9(9 + 1)/2 + 7

          = 9(5) + 7

          = 45 + 7

          = 52

Therefore, there were 52 billiard balls in the set.

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The answer of the given inequality is x < 16

Difference between equality and inequality equations

Both mathematical phrases, equations and inequalities, are created by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.

The inequality expression is ,

(1 * x) /4  < 4  or x/4 < 4

=> x < 4 * 4

=> x < 16

Therefore, the answer is x < 16.

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we have

C -----> total charge

b -----> number of buckets of balls

Remmeber that

the equation of the line in slope intercept form is equal to

y=mx+b

where

m is the slope and b is the initial value or y-intercept

In this problem

m=$1.50 per buckey

b=$5

therefore

y=1.50x+5

or

C=1.50b+5

Given:

Using a graphing calculator, we have the graph shown below:

The point of intersection of the equations represents the solution to the system.

Hence, the solution to the system is:

x = 0.216

y = 0.646

The volume of the cone is 45.28 cubic inches.

The amount of sand inside the cone is measured by its volume.

Based on the numbers for the radius and height, the cone's volume is 45.28 cubic inches.

The volume of a cone is the measure of how much space a cone takes up. Cone height and base radius both affect how much space the cone takes up.

The volume of the cone is given by V = [tex]\frac{1}{3}\pi r^{2} h[/tex]

The value of the radius is r = [tex]3\frac{1}{23} = \frac{70}{23}[/tex]

The value of Height is h = [tex]3\frac{5}{3} = \frac{14}{3}[/tex]

So, the Volume of the cone =[tex]V =\frac{1}{3}\pi r^{2} h[/tex]

[tex]V =\frac{1}{3}\pi r^{2} h\\\\V = \frac{1}{3}\pi (\frac{70}{23}) ^{2} \frac{14}{3} \\\\V = 45.28[/tex]

The volume of the cone is 45.28 cubic. inches

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According to the given graph, we have the following:

1) The graph represents a plane descending.

2) The line is slanting downwards and therefore has a negative slope.

3) It takes the plane 15 seconds to touch the ground.

4) The plane starts at 3 kilometers in the sky.

5) Graph does not touch the origin (0,0).

The given graph shows a decreasing line, starting at y = 3, and reaching y = 0 when x = 15.

To determine the width of the statue:

A local park has a length (L), width (W), and height (H) (all in feet)

Solve equation 1 and 2 simultaneously,

Solve equation 3 & 4 simultaneously, make W the subject of formular

Therefore the value of width of the statue = 12 feet

The English Alphabet consist of 26 letters. The number of outcome of the experiment therefore is 26 which consist of the sample space.

S = {A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}

If we have:

To solve for l we can start by inverting the sides and substracting 2w from both sides so that the term with l becomes alone in the left side:

Now, we can divide both sides by 2 so thay the 2 in 2l gets canceled:

So, the answer we would get is

8k + 3 +4k

________________

First, add the k

8k + 4k = (8+4) k = 12 k

________________

you add if there are other variables or numbers

3

________________

12k + 3

Do you have any questions regarding the solution?

Then x=36.

We can count the number of zeros and ones to see how many bits are used to represent 255 in binary i.e. 11111111. Therefore, we have used 8 bits to represent 255 in binary.

Convert 255 to base 2?

       255  =  8 bits

      255 in Binary: 255₁₀ = 11111111₂

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Aye itz just me, this is the solution:

Initial balance = $ 37.99

Purchase 1 = ($ 26.29)

Purchase 2 = ($ 22.98)

Overdraft fee = ($ 25.00)

Deposit = $ 55.07

______________________

New balance = 37.99 - 26.29 - 22.98 - 25 + 55.07

New balance = $ 18.82

Part A

The dimensions of the shape shown are given as

length, l = 12 in

breadth (b) = width, w = 4 in

The area of the shape is given as;

Therefore, the area of the shape is 48 square inches.

Part B

The perimeter of a shape is the sum of all the outer sides enclosing the shape

From the above shape, we add all four sides together

Consequently, we can get the perimeter using formula method as well

Therefore, the perimeter of the shape is 32 inches.

Part C

From the dimension given in the question, since the shape has a length and width, and the length and width are not equal, then the shape is a rectangle.

The shape, therefore, is a rectangle.

Given:

Given the function

and a point x = 3.

Required: Equation of the line tangent to y at x = 3.

Explanation:

The derivative of a function is he slope of the tangent line of the function at a given point. So, finding the derivative gives the slope of the tangent line.

Substitute 3 for x into the derivative.

Therefore, the slope of the tangent line is -31/27.

Substitute 3 for x into y.

(3, 38/9) is the only point on the tangent line where it intersects the original graph.

Plug these coordinates along with slope into the general point-slope form to find the equation.

Solving for y will give the equation in slope-intercept form.

Final Answer: The equation of the tangent line is

The derivative of the function y = -1/x-2 is 1/(x-2)².

Given, the function is y = -1/x-2

Differentiate the function with respect to x.

dy/dx = d/dx (-1/x-2)

the function is in the form of :

d/dx [f(x)g(x)] = f(x)d/dx((x)) + g(x)d/dx(f(x))

here d/dx [f(x)g(x)]  = d/dx [(-1)(1/x-2)]

therefore, d/dx [(-1)(1/x-2)] = (-1)d/dx(1/x-2) +(1/x-2)d/dx(-1)

⇒ d/dx [(-1)(1/x-2)] = (-1)(-1)(x-2)⁻¹⁻¹ + (1/x-2)d/dx(0)

⇒ d/dx [(-1)(1/x-2)] = 1(x-2)⁻² + 0

⇒  d/dx [(-1)(1/x-2)] = 1/(x-2)²

Hence the derivative of the function is 1/(x-2)²

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Answer:

[tex]y-6=-\dfrac{1}{8}(x-10)[/tex]

Step-by-step explanation:

To find the equation of a line that passes through two points, first find its slope by substituting the given points into the slope formula.

Define the points:

Substitute the points into the slope formula:

[tex]\implies m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-6}{2-10}=\dfrac{1}{-8}=-\dfrac{1}{8}[/tex]

Therefore, the slope of the line is -¹/₈.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:

[tex]\implies y-6=-\dfrac{1}{8}(x-10)[/tex]

The given equation is

The first step is to add 4x to both sides of the equation. We have

3 - 2x = 16x^2

Adding 2x to both sides of the equation, we have

3 - 2x + 2x = 16x^2 + 2x

3 = 16x^2 + 2x

Subtracting 3 from both sides of the equation, we have

3 - 3 = 16x^2 + 2x - 3

0 = 16x^2 + 2x - 3

16x^2 + 2x - 3 = 0

This is a quadratic equation. We would solve for x by applying the method of factorisation. The first step is to multiply the first and last terms. We have 16x^2 * - 3 = - 48x^2. We would find two terms such that their sum or difference is 2x and their product is - 48x^2. The terms are 8x and - 6x. By replacing 2x with with 8x - 6x in the equation, we have

16x^2 + 8x - 6x - 3 = 0

By factorising, we have

8x(2x + 1) - 3(2x + 1) = 0

Since 2x + 1 is common, we have

(2x + 1)(8x - 3) = 0

2x + 1 = 0 or 8x - 3 = 0

2x = - 1 or 8x = 3

x = - 1/2 or x = 3/8

We would substitute these values in the original equation to check. We have

The solution is x = 3/8

The problem is;

-2(x-1) - 2 > 8 - 5x +4+ x

open the parenthesis

-2x + 2 -2 > 8- 5x + 4+ x

collect the like-term

-2x+5x-x > 8+4

2x > 12

divide both-side of the inequality by 2

x>6

The first mistake that was made is adding of the x-variables

It is 2x and not -6x

Find the inverse of:

The variable x can take any real value and the function f(x) exists. This means

the domain of f(x) is (-∞, +∞).

Now find the inverse function.

Swapping letters, we get the inverse function:

For each value of x, we get two values of y, thus this is not a function.

The domain of the inverse is restricted to values of x that make the square root exist, thus the domain is x ≥ 0, or [0, +∞)

The range of the inverse is the domain of the original function, that is, (-∞, +∞)

Function: No

Domain: [0, +∞)

Range: (-∞, +∞)

The choice to select is shown below.

Solution

A probability distribution in which all of the values of the random variable occur with equal probability is called a uniform probability distribution. Describe an example of an experiment that would produce a uniform distribution. Then find the theoretical probabilities that would result from this experiment. Include a table and graph of the distribution.

Answer:

The theoretical probability experiment of rolling a die would result in a uniform distribution because the probabilities of rolling a 1,2,3,4,5,6 are all equally likely to occur.

Therefore the sum of rolling two dice is an option

Hence the correct answer is

Option 1

Answer:

Step-by-step explanation:

To determine in how many pices of 2/3ft can a 9ft long ribbon be cut, you have to divide 9 by 2/3:

To divide both fractions, first turn the 9 into a fraction by adding 1 as a denominator

Now you have to invert the fraction that is the denominator of the division

And multiply it by the first fraction

She can divide the ribbon in 13 pieces of 2/3ft each

Given:

Each of these halves is to be cut into fourths.

So:.

A pizza is to be cut into halves

since half is represented by 1/2.

So each piece is now

If each of these halves is to be cut into fourths, then the fraction of final pieces is:

Answer:

1/8

Step-by-step explanation:

Fractions

We have 1/2

!/2 is to be cut in 1/4

1/2 * 1/4 = 1/8

In general, an inverse variation relation has the form shown below

It is given that x=16, then y=5/4; thus,

Therefore, the equation is y=20/x

2) Set x=4 in the equation above; then

When x=4, y=5.

Answer:

6/7

Step-by-step explanation:

24/28 they both are commonly divisible by 4,

making them 6/7

Considering the given table, it is found that:

a. The exponential regression equation is: P(t) = 2408.80(1.059)^t.

b. The yearly percent increase is of 5.9%.

c. P(13) = 5075.

d. The population of the town after 13 years is of 5075.

The exponential regression equation is found inserting the points into a calculator.

The points are given as follows:

(0, 2400), (3, 2801.27), (7, 3608.71), (12, 4974.15), (14, 5426.17), (19, 6898.37).

Using a calculator, the function is:

2408.80(1.059)^t.

The yearly percent increase rate is calculated as follows:

1 + r = 1.059

r = 1.059 - 1

r = 0.059

r = 5.9%.

Then in 13 years, the population will be given as follows:

P(13) = 2408.80(1.059)^13 = 5075.

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