Determine all intervals on which the graph of f is decreasing.

The situation represent a non-linear function

A function can be described as an expression,  law or rule that explains the relationship between two variables.

These variables are;

The different types of functions are;

A nonlinear function is defined as a function having a graph that is not a straight line.

This means that the equation of the graph does not that the mathematical form, ax +b  

From the information given, we have that;

Area = 2s²

Hence, it is a non-linear function.

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Answer:

The zeroes of the function are: [tex]\frac{-1}{3}[/tex].

Option b would be the correct answer.

Step-by-step explanation:

The zeros of a function are defined as the point at which the value of the function is zero. We can say the zeros are the x values where the graph intersects the x-axis. We obtain these algebraically by setting the function equal to zero then solving.

Given

[tex]y=3x+1[/tex]

Lets find all real zeros of the function.

Replace [tex]y[/tex] with 0.

[tex]0=3x+1[/tex]

Subtract 1 from both sides of the equation

[tex]-1=3x[/tex]

Divide both sides of the equation by 3.

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

Simplify the right side by cancelling the common factor of 3.

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

The amount of fence needed to enclose a rectangular garden is 90 feet.

To determine the amount of fence needed to enclose a rectangular garden with length 14 feet and width 31 feet, you need to calculate the perimeter of the rectangle. The perimeter is the total length of all four sides of the rectangle.

The formula for the perimeter of a rectangle is given by

2 * (length + width)

In this case, the length is 14 feet and the width is 31 feet, so the perimeter is

2 * (14 + 31) = 2 * 45 = 90 feet

This means that 90 feet of fence is needed to enclose the rectangular garden.

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Answer:

The area of rectangle WXYZ is 175.36 square inches. To find the area, you multiply the length (10.8 inches) by the width (16.2 inches). 10.8 x 16.2 = 175.36.

The number of ways that NC license plates meet the requirement is 78125

There are 7 places to be filled in the number plate

The NC license plate can be represented as below.

Since there are 5 vowels. So, each of the first three places can be filled in 5 ways. and also each of the last four places can be filled in 5 ways.

So, each place looks like the below:

5 ways 5 ways 5 ways 5 ways 5 ways 5 ways 5 ways

So, the number of possible NC license plates that meets the requirement is

5^7 = 78125

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Half a kilogram of mixed nuts costs 36 cents.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Five-sixths of a kilogram costs 60 cents.

That means,

1 kilogram of mixed nuts costs = 60 x 6/5 = 72 cents.

So,

half a kilogram of mixed nuts costs = 72/2 = 36 cents.

Therefore, the required cost is 36 cents.

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The function that best represented by this graph is f(x) = −x² + 1.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

A graph of a function is given in the image.

The parent function of the graph is g(x) = x².

And the graph is negative of the parent function.

And shifted upwards to 1 point.

That means, the function is f(x) = −x² + 1.

Therefore, the function is f(x) = −x² + 1.

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Answer:

24×1 equal 24 and multiply it by 1/6 is 24/6 and simplifying it would make 4.

answer=4

not sure if this is what u want

Step-by-step explanation:

hope it helps

The numbers are classified as rational or irrational as follows:

Rational numbers are the whole numbers plus decimals that can be represented by fractions, involving both positive and negative numbers.

The set of irrational numbers is composed by numbers that cannot be represented by fractions, such as non-exact roots, which are non-terminating and non-repeating decimal numbers.

Hence the numbers are classified as follows:

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Answer:

(d - 4)² - 7

Step-by-step explanation:

Formula for completing the square: x² + ax + b = (x + [tex]\frac{a}{2}[/tex])² - ([tex]\frac{a}{2}[/tex])² + b

d² - 8d + 9 = (d - [tex]\frac{8}{2}[/tex])² - ([tex]\frac{8}{2}[/tex])² + 9

                  = (d - 4)² - 4² + 9

                  = (d - 4)² - 16 + 9

                  = (d - 4)² - 7

The equation for the equilibrium of carbonic acid (H2CO3) and bicarbonate (HCO3-) is: H2CO3 ⇌ H+ + HCO3- and equation for the equilibrium of bicarbonate (HCO3-) and carbon dioxide (CO2) is: HCO3- ⇌ H+ + CO2.

The equation for the equilibrium of carbonic acid (H2CO3) and bicarbonate (HCO3-) is: H2CO3 ⇌ H+ + HCO3-

The equation for the equilibrium of bicarbonate (HCO3-) and carbon dioxide (CO2) is: HCO3- ⇌ H+ + CO2

At 37°C, the pKa for carbonic acid (H2CO3) is 3.83, which means that the concentration of H+ in the first equation will be 10^-3.83 = 0.000195 M. The concentration of HCO3- in the first equation will be 0.000195 M.

The pKa for bicarbonate (HCO3-) is 10.25, which means that the concentration of H+ in the second equation will be 10^-10.25 = 0.00000007 M. The concentration of CO2 in the second equation will be 0.00000007 M.

Therefore, The equation for the equilibrium of carbonic acid (H2CO3) and bicarbonate (HCO3-) is: H2CO3 ⇌ H+ + HCO3- and equation for the equilibrium of bicarbonate (HCO3-) and carbon dioxide (CO2) is: HCO3- ⇌ H+ + CO2.

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Answer:

The answer is 18.

Step-by-step explanation:

You need to divide 144 by 8 to end up with 18.

The amount borrowed with 4% interest was 1100, and the amount borrowed with 3.5% interest was 6000 - 1100 = 4900.

Let x be the amount of the loan with 4% interest and y be the amount of the loan with 3.5% interest. Then, x + y = 6000, because the total amount borrowed is 6000.

The interest owed on the 4% loan after 5 years is 4% of x per year, so the total interest owed after 5 years is 5 * 0.04x = 0.20x.

Similarly,

The interest owed on the 3.5% loan after 5 years is 3.5% of y per year, so the total interest owed after 5 years is 5 * 0.035y = 0.175y.

The total interest owed after 5 years is $1062.50, so 0.20x + 0.175y = 1062.50.

Now we have two equations, so we can solve for x and y.

First, substitute x + y = 6000 into the second equation, and we get,

0.20x + 0.175(6000 - x) = 1062.50

Expanding the second term, we get,

0.20x + 1035 - 0.175x = 1062.50

0.025x = 27.50

Dividing both sides by 0.025,

x = 1100

So the amount borrowed with 4% interest was 1100, and the amount borrowed with 3.5% interest was 6000 - 1100 = 4900.

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The greatest common monomial factor of this polynomial will be 14x²y³.

Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).

The polynomial is given below.

⇒ 14x³y⁵z² - 98x²y⁴x² + 28x²y³

⇒ 14x²y³(xy²z² - 7x²y + 2)

The greatest common monomial factor of this polynomial will be 14x²y³.

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Step-by-step explanation:

To find the ratio of the payment for gas to the payment for electricity, we can use the following formula:

(Payment for gas) : (Payment for electricity) = (Gas payment) : (Electricity payment)

We know that the total bill was $55 and the payment for electricity was $30.

So, the payment for gas would be: $55 - $30 = $25

Therefore, the ratio of the payment for gas to the payment for electricity is:

($25) : ($30) = 25 : 30

You can simplify this ratio to 5:6 or you can write it as 25:30

Answer:

Mistake: From line 4 to 5

Correct Solution:

7x - 5 = 5x + 9

2x = 14

x = 7

Step-by-step explanation:

On line 4 to 5, Ms.Shreve should've subtracted 5 to 7, and add 5 to 9, not vice versa.

Answer:

3.125 cm

Step-by-step explanation:

cos50 ≈ 0.64 = b/h
b = 2
∴ h = 2/0.64 = 3.125 cm

The center of dilation of the triangle is (7, 5)

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

Two triangles

The center of dilation of the triangles is the center of both triangles

From the figure, we can see that the center is located at (7, 5)

Hence, the center is (7, 5)

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The probability that the machine is up at times n = 5, 10, 15, and 20 can be calculated as n = 5: 0.773797, n = 10: 0.60653065, n = 15: 0.47000363 and n = 20: 0.35831814.

For the machine described in Conceptual Problem 2.8, the probability that the machine is up at times n = 5, 10, 15, and 20 can be calculated using the formula:

P(machine is up at time n) = P(machine was up at time n-1) * p

Given that the machine is initially up and p = 0.95, the probabilities are as follows:

As for the transition probability matrix of the DTMC {Xn, n > 0}, the possible transitions are:

Thus, the transition probability matrix and the transition probability matrix of the DTMC {Xn, n > 0}  can be represented as attached in the below image:

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Answer:

36 inches.

There are 12 inches in 1 foot, and snce there are 3, then you will multiply:

12 * 3 = 36

Step-by-step explanation:

Hope it helps! =D

The linear inequality will be 2.5x+1.5y<=9, where x=boxes of popcorn and y=no. of drinks.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

Given that  Shiloh and Mario went to the movies. At the theater a small box of popcorn costs $2.50 each and each drink costs $1.25 each.

Shiloh and Mario only have $9 to spend.

So, let  x=boxes of popcorn and y=no. of drinks

Therefore, given statements can be satisfied by linear inequality given

as 2.5x+1.5y<=9.

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No conclusion can be drawn with the given information regarding function.

No conclusion can be drawn about whether f is defined at x=1 or whether f(1)=5 based solely on the statement "lim f(x) = 5." The limit of a function only describes the behavior of the function near a particular value, not necessarily the value of the function at that point.

It is possible for a function to have a limit at a point without being defined at that point, or for a function to be defined at a point but have a different value there than its limit.

Hence, no conclusion.

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Using fractions subtraction, we know that the original fraction in the given situation is -7/8.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole.

A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

Proper fractions, improper fractions, mixed fractions, like fractions, unit fractions, equivalent fractions, and same numerator fractions are the seven different types of fractions.

So, we have the fraction:
1/8

Now, the original fraction would be:

1/8 - 4/4

1-8/8

-7/8

Therefore, using fractions subtraction, we know that the original fraction in the given situation is -7/8.

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The radius of each of the sphere is 1.1 centimetres.

Fifteen solid spheres are made by melting a solid metallic cone of base diameter 2cm and height 15cm. Therefore, let's find the volume of the cone to know the radius of the sphere.

Hence,

volume of a cone = 1 / 3 πr²h

where

Therefore,

volume of the cone = 1 / 3 × π × 1² × 15

volume of the cone = 5π cm³

Therefore, let's find the radius of the sphere.

volume of a sphere = 4πr³

where

5π = 4 × π × r³

r³ = 5 / 4

r = ∛5 / 4

r = 1.07721734502

Therefore,

radius of each sphere = 1.1 cm

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Answer:

PR is equal to 3

Step-by-step explanation:

line QR is 0.6 bigger than line SR. So I did SR + 0.6 = 2.4 + 0.6 = 3

Therefore, our answer is 3

Answer:

[tex]\frac{1}{5}[/tex] are red

Step-by-step explanation:

ratio of red : yellow = 1 : 4

total of ratio parts = 1 + 4 = 5 parts

then fraction of red counters is

[tex]\frac{1}{5}[/tex]

fraction of yellow counters is [tex]\frac{4}{5}[/tex]

The x-coordinates of the inflection points of this function are −1 and −1/3.

In this case, we are looking for the open intervals on which the function f(x) = −x⁴ − 9x³ + 4x − 6 is concave up (down) and the x-coordinates of the inflection points of the function.

To find the open intervals on which f is concave up, we must first calculate the second derivative of the function.

The second derivative of the function f(x) is

=> f''(x) = −12x³ − 27x² + 4.

This means that the function f is concave up when f''(x) > 0 and concave down when f''(x) < 0. Solving the equation f''(x) > 0 will give us the intervals on which the function is concave up.

These are the intervals (−∞, −1), (−1, −1/3), and (−1/3, ∞).

Similarly, solving the equation f''(x) < 0 will give us the intervals on which the function is concave down. These intervals are (−1, −1/3) and (−1/3, 0).

We can now determine the x-coordinates of all inflection points of the function f by finding the x-values at which the second derivative is equal to zero.

Solving the equation f''(x) = 0 will give us the x-coordinates of the inflection points, in this case −1 and −1/3.

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Two week ago I bought 10 cupcake last week I bought 7 today id like to follow this pattern so 4 cupcakes are needed.

A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint.

Another example is 2,4,16,256 in this pattern each term is the square of the previous term and this will become its specific pattern.

As per the given,

Number of cupcakes in two weeks ago = 10

Number of cupcakes in last weeks ago = 7

Decrement of cupcakes = 10 - 7 = 3

Thus,

Number of cupcakes in today = 7 - 3 = 4

Hence "The number of cupcakes is 10 - 7 = 3 thus with follow this pattern the number of cupcakes today will be 7 - 3 = 4 cupcakes".

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Answer: 122.81

Step-by-step explanation:

If 86 seals dove for a combined total depth of 10,578 meters, each seal would have dove an average of 122.81 meters (10,578 meters / 86 seals)

[tex]10578 \div 86 = 122.81[/tex]

The factors of given polynomial are (2x-1) ( x+2 ) (x-4) (x+2 ) .

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given expression,

2x^4 + x^3 - 29x^2 - 34x + 24 = 0

By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term 24 and q divides the leading coefficient 2. One such root is 4. Factor the polynomial by dividing it by x-4.

(x-4)(2x^3 + 9x^2 + 7x-6)

Consider 2x³+9x²+7x-6. By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term -6 and q divides the leading coefficient 2. One such root is -3. Factor the polynomial by dividing it by x+3.

(x+3) ( 2x^2+3x-2)

Consider 2x²+3x-2. Factor the expression by grouping. First, the expression needs to be rewritten as 2x²+ax+bx-2. To find a and b, set up a system to be solved.

a+b = 3

ab = 2(-2) = -4

As ab is negative, a and b have the opposite signs. As a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -4.

(-1,4)

(-2,2)

Calculate the sum for each pair.

-1+ 4 = 3

-2+2 = 0

The solution is the pair that gives sum 3.

a = -1

b = 4

Rewrite ( 2x^2+3x-2)  as  ( 2x^2-x ) + (4x - 2 )

( 2x^2-x ) + (4x - 2 )

Exclude x in the first group and 2 in the second group.

x (2x-1 ) + 2 (2x-1)

Factor out common term 2x-1 by using distributive property.

(2x-1 ) ( x +2 )

Rewrite the complete factored expression

(2x-1) ( x+2 ) (x-4) (x+2 ) .

Hence, The factors of given polynomial are (2x-1) ( x+2 ) (x-4) (x+2 ) .

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