Determine, whether each set of measures can be the sides of a right triangle.
1) 3,4,5
2) 5,5,10
3) 8,12,13
4) 26,24,10

The addition of the polynomial P(x) and Q(x) is  5x³ - 13 x² + 3x - 19.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.

Given:

P(x) = 3x³ - 7x² + 3x-4 and Q(x) = 2x³ - 6x² - 15.

Now, adding the both Polynomials

P(x) + Q(x)

= 3x³ - 7x² + 3x-4 + 2x³ - 6x² - 15.

Now, solving the like terms

= 3x³ + 2x³ - 7x² - 6x² +3x -4 -15

= (3+ 2) x³ + (-7-6) x² +3x -4 - 15

= 5x³ - 13 x² + 3x - 19

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[tex]V= [0,16] \int\limits {4y^2 \sqrt{(256 - y^2)} } \, dy[/tex] would be the integral that gives the volume of the solid.

What is Disk method of integration?

Disc integration is a method for estimating the volume of a solid of revolution of a solid-state material when integrating along an axis "parallel" to the axis of revolution in integral calculus.

The volume of the solid can be found using the disk method of integration. In this method, we consider thin slices of the solid perpendicular to the x-axis, each of which is a disk with a square cross-section.

The volume of each slice is equal to the product of the area of its cross-section and its thickness, which is equal to the difference in x-coordinates between the top and bottom of the slice.

Let's call the top-right corner of the square cross-section (x, y, z). We k[tex]x^2 + y^2 = 256[/tex]

And we also know that the side length of the square is equal to 2y. So, the area of the cross-section is equal to [tex](2y)^2 = 4y^2.[/tex] The volume of the slice is equal to [tex]4y^2 dx.[/tex]

Since the semicircle is centered at the origin, the value of y ranges from 0 to 16.

The value of x ranges from 0 to the square root of [tex]256 - y^2.[/tex]Using these ranges, the volume of the solid can be calculated as follows:

[tex]V=\int\limits {[0,16] 4y^2 \sqrt{(256 - y^2)} } \, dy\\V= [0,16] \int\limits {4y^2 \sqrt{(256 - y^2)} } \, dy[/tex]

This is the integral that gives the volume of the solid.

Therefore, [tex]V= [0,16] \int\limits {4y^2 \sqrt{(256 - y^2)} } \, dy[/tex] would be the integral that gives the volume of the solid.

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Note that a system of two linear inequalities in two variables is made up of at least two inequalities in the same variables.

Consider the following scenarios: highway speed restrictions, minimum credit card payments, the quantity of text messages you may send each month from your cell phone, and the time it will take to commute from home to school.

All of these may be expressed mathematically as inequalities. A linear inequality's solution is the ordered pair that is a resolution to all inequalities in the system, and the graph of the linear inequality is the graph of all system solutions.

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The midpoint is given by the coordinates M ( 6 , 7.5 )

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

Measure the distance between the two end points, and divide by 2.

Let A ( x₁ , y₁ ) be the first point

Let B ( x₂ , y₂ ) be the second point

The midpoint between A and B is M ( a , b ) where

a = ( x₁ + x₂ )/2

b = ( y₁ + y₂ ) / 2

Given data ,

Let the midpoint of gazebo and the ice cream shop in town be M ( a , b )

Now , the equation will be

The coordinates of the point Gazebo = G ( 10 , 12 )

The coordinates of the point Ice Cream = C ( 2 , 3 )

Now , midpoint between A and B is M ( a , b ) where

a = ( x₁ + x₂ )/2

b = ( y₁ + y₂ ) / 2

Substituting the values in the equation , we get

a = ( 10 + 2 ) / 2

a = 12 / 2

a = 6

b = ( 12 + 3 ) / 2

b = 15 / 2

b = 7.5

So , the coordinates of the midpoint is M ( 6 , 7.5 )

Hence , the midpoint is M ( 6 , 7.5 )

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Therefore , the solution of the given problem of function comes out to be Since 4 > 2, function A has a greater rate of change than function B.

The mathematics curriculum covers the study of numbers or rather their variations as well as in our environment, buildings, and both actual and imagined locations. A function presents a graph representation of the relationship between input and output quantities. A function, expression simply, is a collection of sources that, when combined, result in particular outputs by each input. There is a locale, territory, or range assigned to each job.

Here,

The rate of change of a linear function is the slope of the line.

Function A is y = 4x - 3, so the rate of change (slope) is 4.

To find the rate of change of function B, we can calculate the slope of the line passing through the points given in the table. Using the two points (1,4) and (5,12), we get:

slope = (change in y) / (change in x) = (12-4) / (5-1) = 2

So the rate of change of function B is 2.

Since 4 > 2, function A has a greater rate of change than function B.

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Answer:

55%

Step-by-step explanation:

To find the percentage of juveniles in the local deer population, we need to calculate the proportion of juveniles in the total population and convert it to a percentage.

First, find the total number of deer in the population by adding the number of juveniles and adults:

110 juveniles + 90 adults = 200 deer

Next, divide the number of juveniles by the total number of deer and multiply by 100 to convert to a percentage:

110 juveniles / 200 deer * 100 = 55%

Therefore, 55% of the local deer population were juveniles.

Solving the provided question, we can say by Pythagorean theorem b = [tex]\sqrt{a^2 + b^2}[/tex] = [tex]\sqrt{32.49 + 92.16}[/tex] = 11.231meters

The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.

By Pythagorean theorem

a = 5.7 meters and c = 9.6

b = [tex]\sqrt{a^2 + b^2}[/tex]

b = [tex]\sqrt{32.49 + 92.16}[/tex]

b = [tex]\sqrt{124.65}[/tex]

b = 11.231meters

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Answer: 2 pounds of flour

Step-by-step explanation:

1/2 of four is two,

4 * 1/2 = 2

Answer:

Jessie used 1/2 of the 4-pound bag of flour, so she used 1/2 * 4 pounds = 2 pounds of flour to bake her cake.

Answer:

3C ÷ 21 = 63 C = 21

great question BTW

Answer:

Addition with the number 3.

Next numbers will be 15, 18, 21,...

Answer:

not sure but slope doesn't belong

Step-by-step explanation:

We can use the two points given to find the slope of the line (which represents the population growth) and then use the point-slope form of the equation of a line to write an equation.

The population at time t=4 is 1580, which means P(4) = 1580. The population at time t=7 is 2000, which means P(7) = 2000. We can use these two points to find the slope:

slope = (P(7) - P(4)) / (7 - 4) = (2000 - 1580) / 3 = 140

So the slope of the line representing population growth is 140. Now we can use the point-slope form of the equation of a line to write an equation:

P - 1580 = 140(t - 4)

Simplifying and rearranging, we get:

P = 140t - 380

So the correct equation that represents the situation is:

P(t) = 140t - 380.

The choices if multiplied by √36 would result in an irrational number are

3.454545... and 2.828427... the correct options are A and D.

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Rational numbers are numbers which can be written in the form of \dfrac{a}{b} where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.

Irrational numbers are those real numbers which are not rational numbers.

Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.

Given;

The number is multiplied by √36

√36=6

3.454545*6=20.72727

-5*6=-30

3/4*6=9/2

2.828427*6=16.970562

√18*6=  6√18

Therefore, the irrational numbers will be 3.454545... and  2.828427...

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The probability that the discrete random variable x takes a value less than or equal to 50 is 0.50, since F(50) = 50/100 = 0.50.

F(x) = x/100

Then, the probability that x takes a value less than or equal to 50 is 0.50, since

F(50) = 50/100 = 0.50

The cumulative distribution function (CDF) of a random variable is a function that gives the probability that the random variable is less than or equal to a certain value. In this case, the CDF of the random variable x is given by F(x) = x/100.

Therefore, to find the probability that x takes a value less than or equal to 50, we simply need to evaluate the CDF at x = 50. This is done by substituting 50 into the CDF, which gives us F(50) = 50/100 = 0.50. This means that the probability that x takes a value less than or equal to 50 is 0.50.

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The value of proportionality is not same.So the it is not proportional.

Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.

Let

y ∝ x

y = kx , k is constant

Take x = 2, y = 3

3 = k(2)

k = 3/2 = 1.5

At x= 4, y = 7

7 = k(4)

k = 7/4 = 1.75

The value of proportionality is not same.So the it is not proportional.

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In response to the query, x is equal to 60°, 120°, 240°, and 300°. These four options are the answer to the equation.

A mathematical equation is a statement that two amount or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. An equation is applied when several or more factors must be considered jointly in order to understand or explain the whole situation.

This equation can be solved using the trigonometric identity:

[tex]sinx = \sqrt{ (1 - cos^2x)}[/tex]

This identity can be used as a substitution in the equation:

5 sinx - 5 cosx = 2

5 [tex]\sqrt{(1 - cos^2x) }[/tex] - 5 cosx = 2

5 sqrt[tex](1 - cos^2x)[/tex]) = 7 + 5 cosx

Squaring both sides:

25([tex]1 - cos^2x[/tex]) = 49 + 70 cosx + 25 [tex]cos^2x[/tex]

25 - 25 [tex]cos^2x[/tex] = 49 + 70 cosx + 25 [tex]cos^2x[/tex]

0 = 74 + 45 cosx

45 cosx = -74

cosx = -74/45 = -2/3

The inverted cosine function can be used to determine that x = cos-1(-2/3). x must be within the range of 0° to 360°, hence x must be 300°.

5 sin - 5 cos - 5(-1/2) = 5 sqrt(3)/2 + 5/2 = 2 + 2.5 = 2.5

Since the left side of the equation is not equal to 2, x = 300° is not a solution to the equation.

We can repeat this process for the other solutions to the equation:

x = 60°, x = 120°, x = 240°, and x = 300°

These are the four solutions to the equation for 0° <= x < 360°.

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Before any taxes, deductions, and other adjustments, she earns $98.40 per week.

Gross pay refers to the total amount of money an employee earns before any deductions or taxes are taken out. It is the total amount of money earned by an employee for the hours worked, including any overtime or bonuses.

here, we have,

To calculate Talia's gross pay for a week, we need to know how many hours she works per day and her pay rate.

You've provided that information:

Talia works 6 hours per day on Fridays and Saturdays each week.

Her pay rate is $8.20 per hour.

First, we need to find out how many hours she works a week. As she works 6 hours on Friday and 6 hours on Saturday, the total hours she works in a week is 6 hours/day x 2 days/week = 12 hours/week.

Next, we need to multiply her hourly rate by the number of hours she works per week to find her gross pay. Her pay rate is $8.20/hour and she works 12 hours/week, so her gross pay is:

$8.20/hour x 12 hours/week = $98.40/week

So, Talia's gross pay for a week is $98.40.

Therefore, before any taxes, deductions, and other adjustments, she earns $98.40 per week.

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Answer:

y = 14x - 1

Step-by-step explanation:

By equation of the line, we mean the slope intercept form equation [tex]y=mx+b[/tex] where m is the slope and b is the y intercept. As a result, we are given the slope and the y intercept in the problem. So we can use this to write our equation

[tex]y=14x-1[/tex]

Hope this helps!

Answer:

A=F/M

Step-by-step explanation:

m=f/a ......,,, cross product

f= ma......,..., both sides divided by m

then the answer is a=f/m

The factors of the quadratic function  x² - 2x - 4  is equal to

(x + 1 + √5)(x - 1 + √5)

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, The zeros of the quadratic function x² - 2x - 4  are,

(1 + √5) and (1 - √5). (As they occur in conjugate pairs).

Therefore, The factors of (x + (1 + √5))(x + (x - (1 - √5))

x² - 2x - 4 = (x + 1 + √5)(x - 1 + √5)

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Answer:

956 centimeters is equal to 9.56 meters.

How many meters are in 956 centimeters?

Well, first, we must understand the conversion from meters to centimeters and centimeters to meters.

1m=100cm and 1cm=0.01m. So multiply by 100 if converting from m to cm and divide by 100 if converting from cm to m.

In this problem, we're looking at cm to m.

Take 956cm and divide that by 100. You'll get 9.56m. That's your answer.

Hope this helped!

The total number of children that ordered Sandwiches  is 1 5/6

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

Class 1 = 5/6 Hamburger

Class 2 = 2/4 Hot days

Class 3 = 1/2 Chicken wings

So, the total number of children that ordered Sandwiches is

Total =  5/6 + 2/4 + 1/2

Evaluate

Total = 1 5/6

Hence, 1 5/6 of the three classes ordered sandwiches

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The cumulative distribution function (CDF) of U is also well known and is given by:

F(u) = 1 - [tex]e^{(-u/2)}[/tex] × γ(1/2, u/2)

where γ is the lower incomplete gamma function.

What is the chi-squared distribution?

The chi-squared distribution is a continuous probability distribution that is widely used in statistics and other fields.

The random variable U = Y1^2 + Y2^2 has a well-known distribution called the chi-squared distribution with two degrees of freedom. The density function of U is given by:

[tex]f(u) = (1 / (2 \times \pi)) \times e^{(-u/2)} \times (u/2)^{(1/2 - 1)}[/tex]

where e is the base of the natural logarithm and π is the mathematical constant pi. This distribution has a positive support on the interval [0, +∞).

The cumulative distribution function (CDF) of U is also well known and is given by:

F(u) = 1 - [tex]e^{(-u/2)}[/tex] × γ(1/2, u/2)

where γ is the lower incomplete gamma function.

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Answer:

x=2

Step-by-step explanation:

4x+4=12

   -4   -4

_______

4x=8

_____

4     4

x=2

Michael writes, "Triangle ABC is congruent to triangle CDA'',

if the segment AC ≅ AC.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given the parallelogram below,

Michael writes, "Triangle ABC is congruent to triangle CDA''.

By the parallelogram property:

AB ≅ CD

BC ≅ AD.

If triangle ABC is congruent to triangle CDA,

then the segment AC ≅ AC.

Therefore, the segment AC ≅ AC.

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The amount of money put by Shannon in her account is $300.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific amount of time.

Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to calculate interest, the principal amount in simple interest remains constant.

Given that Shannon put some money in her savings account. After 6 months, she earned $10.50 in interest. If the interest rate was 7%,

The amount will be calculated as:-

SI = ( P x R x T ) / 100

10.50 = ( P x 7 x 1 ) ( 2 x 100 )

P = ( 10.50 x 2 x 100 ) / ( 7 )

P = $300

Therefore, $300 has been deposited into Shannon's account.

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The area needed to be iced is 263.76 inches².

The circular cake is 12 inches in diameter and 4 inches high. The side and top of the cake are to be covered with icing. The area of the cake that will be iced can be found as follows;

The area to to be iced is the top and the lateral area.

Therefore,

area to be iced = πr² + 2πrh

area to be iced = πr(r + 2h)

Therefore,

r = 12 / 2 = 6 inches

h = 4 inches

Hence,

area to be iced = 6π(6 + 2(4))

area to be iced = 6π(14)

area to be iced = 84π

area to be iced = 263.76 inches²

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Step-by-step explanation:

Classmate Conjecture

John | All circles are similar if they have the same center and can be dilated or contracted to the same size.

Teresa | All circles are similar if their corresponding radii have a constant ratio.

Evaluate the Conjectures:

2. Yes, it makes intuitive sense that all circles are similar because they all have the same shape and form.

Construct the Circles:

3. [Diagram not provided]

[Diagram not provided]

The hypotenuse of △ABC is the diameter of the smaller circle.

[Diagram not provided]

The hypotenuse of △XYZ is the diameter of the larger circle.

The two triangles, △ABC and △XYZ, are similar because they are both isosceles right triangles with the same angle measures.

The ratio of the lengths of their sides are equal, therefore the ratio of their radii is a constant.

Making a Decision:

10. Both John and Teresa were right as all circles are similar if they have the same center and can be dilated or contracted to the same size (John's method) and also if their corresponding radii have a constant ratio (Teresa's method).

Further Exploration:

11. The circumference of the circle that circumscribes a triangle with side lengths 3, 4, and 5 can be found using the Pythagorean theorem to find the diameter of the circle, which is equal to the sum of the lengths of the three sides. The diameter is equal to 5, so the circumference is equal to 2 * pi * (5 / 2) = 5 * pi

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