Approximate the critical numbers of the function shown in the graph. Determine whether the function has a relative maximum, a relative minimum, an absolute maximum, an absolute minimum, or none of these at each critical number on the interval shown. (Enter your answers as a comma-separated list.)

factor x2 − 2xy − 10y2 is (x+2y)(x−5y) .

A polynomial is an expression made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x.

Therefore,

phrase reordering

x2−10y2−2xy

Rearrange 10y2 and 2xY.

x2−2xy−10y2

Subtract 3 from 3xy.

x2−2(xy)−10y2

Write 2as 2 plus 5 x2+(25)(xy)10y2 instead.

The distributive property should be used.

x2+2(xy)−5(xy)−10y2

Delete any extra parentheses.

x2+2xy−5(xy)−10y2

Delete any extra parentheses.

x2+2xy−5xy−10y2

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅ c=1⋅−10=−10 and whose sum is b=−2

Put the first and last two terms together.

(x2+2xy)

−5xy−10y2

Subtract each group's GCF, or greatest common factor.

x(x+2y)−5y(x+2y)

Remove the polynomial's x+2y largest common factor to factor it.

(x+2y)(x−5y)

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Answer:

Step-by-step explanation:

degree 6 -- triple root, double root, single root

leading coefficient is negative -- it opens downward

3 distinct roots

3 relative extrema

Tucker is painting his pool deck over the weekend. The area of the deck is 76 1/2 square meters. He paints 2/3 of the deck before stopping to eat lunch. How many square meters does Tucker have left to paint after lunch?

Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.

we have that

total area=76 1/2 m2

Convert to an improper fraction

76 1/2=76+1/2=153/2 m2

1-(2/3)=1/3

Multiply the total area by 1/3

(153/2)*(1/3)=51/2=25.5 m2 ------> 25 1/2 m2

The equation to show the change in temperature between 9 a.m. and noon is given as d = x - y.

An equation contains two mathematical expressions that state that they are equal or equivalent.

We use the equation mark (=) to show that two expressions possess equality.

Air temperature at 9 a.m., y  -5.8 degrees Celsius

Air temperature at noon, x = -1.6 degrees Celsius

Change in temperature, d = 4.2 degrees Celsius (-1.6 - -5.8)

The equation to show the change is d = x - y, where d is the change in temperature, x is the final temperature, and y is the initial temperature.

Thus, based on the equation, the temperature increased by 4.2 degrees Celsium from the earlier -5.8 degrees Celsius to result in a final temperature of -1.6 degrees Celsius at noon.

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In this problem the total price (p) will be equal to the price per kilogram (p) times the number of kilograms of food (k) so the equation will be:

Consider that the general form of a line can be written as follow:

y = mx + b

where m is the slope and b the y-intercept.

Take into account that if two lines are parallel, then, the slopes of the line are equal. Based on the given equations, you can notice that the slopes are different, m1 = 2 and m2= -3.

Two lines are perpendicular if:

m1 = -1/m2

you can notice, based on the given equations that m1 is not equal to -1/m2, that is, 2 ≠ -1/(-3).

Hence, the lines are neither perpendicular nor parallel

ANSWER:

k = 4, y = 4/x

STEP-BY-STEP EXPLANATION:

Since they are inverses they have the following form the equation

now, x = 2 and y = 2, therefore, replacing and solving for k:

We replace and we would have the equation

The domain of the function f is [-5. -2] U [ 1, 2].

The range of the function f is [-4, 3].

A function is defined as a relation between a set of inputs having one output each.

The inputs are called the domain of the function.

The outputs are called the range of the function.

We have,

A graph of the function f.

We can see two curves on the graph.

One curve:

Domain = [1, 2]

Range = [-4, 0]

Another curve:

Domain = [-5, -2]

Range = [-3, 3]

We can combine both the curves domain and the range.

Domain = [-5. -2] U [ 1, 2 ]

Range = [-4, 3]

Thus,

The domain of the function f is [-5. -2] U [ 1, 2].

The range of the function f is [-4, 3].

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The y-intercept of the equation y = 3x − 2 is (0, -2).

y-intercept

In Mathematics, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx + c, where m is slope and c is the y-intercept.

Equation of a line

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y. The values of x and y represent the coordinates of the point on the line represented in the coordinate plane.

Given that lies on the graph of the equation y = 3x − 2.

We know that

In an equation of line

y = mx + c

m = slope of a line

c = y intercept

So therefore in given equation of line the y intercept is (0, -2).

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Answer:

  8 miles

Step-by-step explanation:

You want to know the distance Alan traveled for $29 in a taxi that charges a fee of $5 plus $3 per mile.

The amount of the $29 that paid for mileage was $29 -5 = $24.

At $3 per mile, that will pay for ...

  $24/($3/mile) = 8 miles

Alan traveled 8 miles for a total fare of $29.

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The fraction of cookies left for Suzanne will be equal to 2/5 of the total number of cookies.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. Example -  5/9. Here, (5) is called numerator and (9) is called denominator.

Given is Melinda who ate 3/5 of the cookies and left the rest for Suzanne.

Assume that the fraction of cookies left for Suzanne is represented by [x].

Fraction of cookies ate by Melinda = [y] = 3/5

The sum of the fractions representing the cookies eaten by both Suzanne and Melinda will be equal to 1. Mathematically -

x + y = 1

x + 3/5 = 1

x = 1 - 3/5

x = (5 - 3)/5

x = 2/5

Therefore, the fraction of cookies left for Suzanne will be equal to 2/5 of the total number of cookies.

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To solve this question we are going to need to define an equation with the data that the problem gives us

The first part (rate of growth) shows us a derivate, this is equal to 9 square root of t or:

where P is the population size and t is the time in days

Now we need the population after 7 days, so we need the P(t) formula, which means that we need the integration

First, we send the dt to the other side to have something to integrate

Solving

We know that P(0)=600 so

Now we replace the t by 7

Answer: 711

The equation of line is y = 8/5x-26/5.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

Equation 8x-5y=4 is given.

-5y = 4-8x

y = 8/5x-4/5 and we are aware that the line's equation is y = mx+b

m = 8/5

Nowadays, coordinates are (2,-2)

Y=-2, X=2, and m=8/5

y = mx+c

-2 = 8/5(2)+c

c = -26/5

Consequently, the line's equation is

y = 8/5x-26/5

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Answer:

1) 6000/30=200

2)5820/28=207.9 (1dp)

Step-by-step explanation:

5^3 = 5x5x5 = 125

6^2 = 6x6 = 36

2^7 = 2x2x2x2x2x2x2 = 128

From least to greatest

36 - 125- 128

6^2- 5^3 - 2^7

The total distance from Washington DC to Dulles airport is 15 miles

The total cost of the cab ride is $25. 50

The cabbie charges $1.50 per mile for the entire trip

Let T be the total cost of the entire trip

Let x represents the number of miles traveled

Let y be the flat rate of the cab ride

Total cost = flat rate + charge per trip x number of miles covered

Mathematically,

T = y + 1.5 * x

T = y + 1.5x

Where, 1.5 is the charge per trip.

The equation becomes

T = y + 1.5x

B

To calculate the flat rate of the cab ride?

The total cost = $25.50

Charges per mile = $1.5

Total number of miles = 15

Substitute the above values into the equation

25.50 = y + 1.5 x 15

25.50 = y + 22.5

Make y the subject of the formula

y = 25.50 - 22.5

Y = $3

The flat rate of the cab ride is $3

C

How much does it cos

Given:

Lan pays,

A semiannual premium of ​$650 for automobile​ insurance.

A monthly premium of ​$150 for health​ insurance.

An annual premium of ​$350 for life insurance.

To find:

The monthly expense.

Explanation:

According to the problem,

The amount paid for automobile​ insurance per year will be,

The amount paid for health​ insurance per year will be,

The amount paid for life insurance per year will be,

The total expenses in a year are,

So, the monthly expense is,

Therefore, the monthly expense is $287.50.

Final answer:

The monthly expense is $287.50.

Price = 72.87

The markup is 30% or 30/100 = 0.3

Let's find the markup of the price:

The retail price, or selling price, is the price + markup.

Thus, retail price is:

Answers:

To detremine the ordered pairs that represent the system of inequalities given, from the choices given, the corredct ordered pairs are:

(x, y) ==> (-6, 3), (-4, 2), (-6, 6), (-4, 0)

Solution:

A quadratic expression is said to be a perfect square trinomial if it has repeated factors.

Given the expression below:

By factorization, we have

Since the above expression has a repeated factor of

We can conclude that the expression is a perfect square trinomial.

Answer:

Yes

Step-by-step explanation:

Any number divided by 1 equals itself. This rule tells us simply that if we have a number divided by 1, our answer will equal that number regardless of what that number is.

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For the value of c = 0,c=1 then A is not invertible

For given matrix  A is invertible if  c≠ 0 and c≠ 1

[tex]Given \ $A=\left[\begin{array}{ll}1 & 1 \\ c & c^2\end{array}\right]$ \\A matrix $A$ is invertible if $|A|={det}(A) \neq 0$.\\Now consider $|A|={det}(A)=0$.[/tex]

[tex]$$\begin{aligned}&\Rightarrow\left|\begin{array}{ll}1 & 1 \\c & c^2\end{array}\right|=0 \\&\qquad \quad \text { If } A=\left[\begin{array}{ll}a & b \\c & d\end{array}\right] \text { then }|A|={det}(A)=a d-b c\end{aligned}$$[/tex][tex]$$\begin{aligned}&\Rightarrow c^2-c=0 \\&\Rightarrow c(c-1)=0 \\&\Rightarrow c=0, c=1\end{aligned}$If $c=0$ or $c=1$ then \A \is \\not \ invertible. \\$\therefore$ Given matrix $A$ is invertible iff $c \neq 0$ and $c \neq 1$. \\ie Given marix $A$ is invertible for $c \in \mathbb{R}-\{0,1\}$.[/tex]

Matrix, a collection of numbers arranged in rows and columns forming a rectangular array. The number is called the elements or entries of the matrix. Matrices have wide applications in engineering, physics, economics and statistics, as well as in various areas of mathematics. Matrices also have important applications in computer graphics, where they have been used to represent image rotations and other transformations.

Different types of matrices are

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A polynomial function is a function that only employs non-negative integer powers or only positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, etc. For instance, the exponent of the polynomial 2x+5 is 1.

 A polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial equations.

The variable t in the formula b(t) stands for the number of years following 2008. This function's range of application is. More over 258.7 wouldn't make sense as a range. The function's graph is continuously drawn at all times.

Explanation:

Since 2008, the provided function b(t) displays the bobcat population in Northern Arizona. The number of years following 2008 is therefore represented by the variable t.

The domain of this function is because t stands for the number of years after 2008, which can be either positive or zero.(0,∞)

Provided that the given function is a quadratic function with a negative coefficient, it is a descending parabola. There is no meaning in the range above the vertex's y-coordinate.

Vertex function is (4.2,258.7)

This is polynomial function so the graph of the function always continuous

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ANSWER

(a). Average Rate of Change = - 4

(b). Average Rate of Change =

EXPLANATION

(a).

Step 1: Given

Step 2: Determine the Average Rate of Change

Let x be the total of students in their Junior Year.

So, 84% of x =378

84% = 0.84

0.84x=378 (divided by 0.84)

x= 450 students.

The ones that chose not to take spanish will be:

450-378=72

72 students chose not to take spanish in their junior year.

Domain:

we know that a root cannot have negative values ​​inside so

the domain is X >= 0

Range:

we solve the equation for y

and we replace the condition that x must be greater than or equal to 0

so

now solve y

so the range is Y >= -5

then the right option is A

1) ∠4 ≅∠1

Vertically opposite angle

2) ∠4 ≅∠5

Alternate angle

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

An acute angle is one that is smaller than 90 degrees. Right Angle: An angle with a 90 degree exactness. More than 90 degrees but less than 180 degrees is referred to as an obtuse angle. A straight angle is one that has a 180 degree angle. An angle that is more than 180 degrees but less than 360 degrees is called a reflex angle.

Given Data

∠1 ≅∠5

1) ∠4 ≅∠1

Vertically opposite angle

2) ∠4 ≅∠5

Alternate angle

3) p ║r

When a transversal cuts two lines so that the accompanying angles are congruent, the lines are said to be parallel. When a transversal cuts two lines so that their opposing interior angles coincide, the lines are said to be parallel.

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We want to select the graph that represents the equation;

Let's rewrite this equation as;

This equation has a slope of 2/5, an x-intercept of -5. and a y-intercept of 2, lets inspect the graphs to see which one matches it.

Going through the options, we see that the matching graph-the correct graph is Option A.

The formula for the expected value from an event is given as;

From the table given, we can obtain the expected value of winning as;

Therefore, the expected value of winning is $5.2