Write an explicit formula for each sequence. 4,1.5,-1,-3.5, . . . . .

y = x² , y = 2 x are  the region enclosed by the given equations is revolved about the y -axis.

What exactly is a closed area?

All space between a floor and ceiling that is enclosed on all sides by solid walls or windows, except doors that stretch from the floor to the ceiling, is referred to as an enclosed area.

What do you mean by the region that a closed curve encloses?

The sum of all infinitely thin rectangles with height f(x), enclosed by the curve y=f(x), and the x-axis between x=a and x=b, is what we mean when we write baf(x)dx.

Whether contained or not?

The graph is attached in equation y = x² , y = 2 x

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A consistent system of equations has at least one solution.

A consistent system is considered to be an independent system if it has a single solution, such as the example we just explored. The two lines have different slopes and intersect at one point in the plane.

A consistent system is considered to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide so the equations represent the same line. Every point on the line represents a coordinate pair that satisfies the system. Thus, there are an infinite number of solutions.

Another type of system of linear equations is an inconsistent system, which is one in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no points common to both lines; hence, there is no solution to the system.

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Answer:

16.97

Step-by-step explanation:

[tex]BF=\sqrt{(-2-0)^2 + (1-3)^2}=2\sqrt{2} \\ \\ BC=\sqrt{(0-4)^2 + (3-(-1))^2}=4\sqrt{2}[/tex]

So, the perimeter is

[tex]2(4\sqrt{2}+2\sqrt{2})=12\sqrt{2} \approx 16.97[/tex]

Using elimination method, the solution of the given system of equations is (-4/7, 1/14)

A system of equation can be solved using:

The given system of equations:

2 = 4y - 3x   ............   (1)

5x = 2y - 3  .............. (2)

Re-arrange the equations so that all variables are on the left sides:

2 = 4y - 3x  

⇔ -3x + 4y = 2   .......  (3)

5x = 2y - 3

⇔  5x - 2y = -3  ....... (4)

Choose one variable to eliminate. Let us choose y. Multiply equation (4) by 2, we get:

10x - 4y = -6   ....... (5)

Add equation (3) and (5)

-3x + 4y = 2

10x - 4y = -6 +

7x          = -4

 x          = -4/7

Substitute back  x = -4/7 into equation (3):

-3x + 4y = 2

-3.(-4/7) + 4y = 2

12/7 + 4y = 14/7

4y = 2/7

y = 2/28 = 1/14

Hence, the solution is (-4/7, 1/14)

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The following set of numbers, 10, 16, and 18, can be the measures of the sides of an acute triangle.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 10, b = 16, and c = 18

a + b > c     10 + 16 > 18     26 > 18     True

a + c > b     10 + 18 > 21     28 > 16     True

b + c > a     16 + 18 > 21     34 > 10     True

To know what type of triangle based on the length of its side:

1. Take the sum of the squares of the two smaller sides.

10^2 + 16^2 = 356

2. Compare it to the square of the largest side.

18^2 = 324

324 < 356

If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.

if they are equal, it is a right triangle

if they are smaller, then it is an obtuse triangle.

Hence, 10, 16, and 18 can be the measure of the sides of an acute triangle.

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Answer:

x = 6

Step-by-step explanation:

x² - y² is a difference of squares and factors as (x + y)(x - y)

given

x² - y² = 20 , then

(x + y)(x - y) = 20 ← substitute x + y = 10

10(x - y) = 20 ( divide both sides by 10 )

x - y = 2 → (1)

x + y = 10 → (2)

add (1) and (2) term by term to eliminate y

2x + 0 = 12

2x = 12 ( divide both sides by 2 )

x = 6

The average rate of change of the equation is 35

The equation is given as

y  = 35x^1

Evaluate the quotient x^1

So, we have

y  = 35x

The above equation is a proportional linear equation

A proportional linear equation is represented as

y = mx

Where

m represents the average rate of change

By comparison, we have

m = 35

Hence, the average rate of change of the equation is 35

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Complete question

Given the equation y = 35x^1 where x is distance and y is height, calculate the average rate of change

The Simplified value of the expression 2(b-a)+5(b-a) is 7b-7a .

Distributive property for real numbers "a", "b" and  "c" is defined as

a(b-c)=a*b-a*c.

In the given question

=2(b-a)+5(b-a)

Applying Distributive Property

=2*b-2*a+5*b-5*a

=2b-2a+5b-5a

Combining the like terms together

=2b+5b-2a-5a

=7b-7a                          (adding the like terms )

Therefore , the Simplified value of the expression 2(b-a)+5(b-a) is 7b-7a .

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The following set of numbers, 20, 21 and 31, can be the measures of the sides of an obtuse triangle.

A triangle is a polygon with three sides and three vertices.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 20, b = 21, and c = 31

a + b > c     20 + 21 > 31     41 > 31     True

a + c > b     20 + 31 > 21     51 > 21     True

b + c > a     21 + 31 > 21     52 > 20     True

To know what type of triangle based on the length of its side:

1. Take the sum of the squares of the two smaller sides.

20^2 + 21^2 = 841

2. Compare it to the square of the largest side.

31^2 = 961

961 > 841

If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.

if they are equal, it is a right triangle

if they are smaller, then it is an obtuse triangle.

Hence, 20, 21 and 31 can be the measure of the sides of an obtuse triangle.

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Answer:

109 x 3 = 327

Step-by-step explanation:

Answer:

17.25 < 17.252

Step-by-step explanation:

17.25 means 17.250. So, 17.250 is less than 17.253, which is correct. The other answer choices are incorrect because the sign is pointed the wrong way. 29.60 is not greater than 29.65, so that's incorrect. 21.51 is greater than 21.49. That is not an answer choice though, so that answer choice is incorrect. 7.602 is not greater than 7.612, so that is incorrect.

Hope this helps! :)

The new mural created by Rhianon, which is 33 inches longer, has a perimeter of 1024 inches.

Perimeter refers to the total distance around a two-dimensional figure. The perimeter of a rectangle is the sum of all its 4 sides and is given by the formula

P = 2l + 2w

where l = length

w = width

If a rectangular mural measures 234 inches by 245 inches, length is usually longer than the width, and Rhianon creates a new mural that is 33 inches longer, then the length of Rhianon's mural is:

l = 245 inches + 33 inches

l = 278 inches

If the new mural is the same as the width of the rectangular mural and its length is 278 inches, then the perimeter can be solved using the formula for the perimeter of a rectangle.

P = 2l + 2w

P = 2(278 inches) + 2(234 inches)

P = 556 inches + 468 inches

P = 1024 inches

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Answer:

22.8 blocks

Step-by-step explanation:

We can think of your path as traveling on a coordinate plane. You start by walking 6 units in the positive y direction, then 22 units in the negative x direction, then walking from this point (-22, 6) back to (0, 0)

This path draws a right triangle. The shorter leg is 6 units long, and the longer end is 22 units long. You want to find the hypotenuse of this triangle.

The hypotenuse is found using the Pythagorean theorem:

[tex]a^2+b^2=c^2[/tex]

A and B represent the sides of the triangle, and c represents the hypotenuse!

Before plugging in the functions, isolate c, since that's the answer we're looking for:

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

Now, plug in the side lengths of the triangle:

[tex]c=\sqrt{6^2+22^2}[/tex]

Now simplify!

[tex]c=\sqrt{36+484} \\x=\sqrt{520} x=22.8[/tex]

It is 22.8 blocks back to your house! Hope this helps!

The dimensions of the base are 180 feet in length and 165 feet in width.

The whole length of any closed shape's boundary is known as its perimeter. Let's use an illustration to try to comprehend this. You may have a sizable square-shaped farm, for instance. You now decide to fence your farm in order to protect it from stray animals. Finding the entire length of the farm's boundary is as simple as multiplying the length of one side of the farm by 4. There are a lot of situations like this when we can be applying the perimeter-finding notion without even realizing it.

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Answer:

A= Q/d +N

Step-by-step explanation:

First you want to move the d term over by dividing both sides

Next you can move the N over by adding it to both sides.

Step-by-step explanation:

adventures

Q

d and d will cancel and

it let d= A-N

Q

Answer:22.05

hope it help

and have a good day

Answer:

45

Explanation

35% is 63

so 5% is 9

so 100% is 180 cuz 5 multiplied by 20 is 100

so 25 % is 25 divided by 100 is 0.25×180 which is 45

hope that helps

The measure of the given angle is 10 degrees.

Supplementary angles are those angles that sum up to 180 degrees.

Complimentary angles are those angles that sum up to 90 degrees

The supplement of the angle is 10° more than twice it's complement.

Therefore,

180 - x = 2(90 - x) + 10

open the brackets

180 - x = 2(90 - x) + 10

180 - x = 180 - 2x + 10

180 - 180 - 10 = -2x + x

-10 = -x

divide both sides by - 1

x = -10 / -1

x = 10

Therefore, the measure of the given angle is 10 degrees.

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Answer:

Step-by-step explanation:

you did that correctly but it will equal 90

How much would the commission be on a 650,000 house? $39,000

Given:

Rate of the house 1= $8,00,000

Commission for the house 1=$48,000

Rate of the house 2= $6,50,000

Commission for the house 2=x

What is the commission for the house 2?

8,00,000 ⇒48,000

6,50,000 ⇒ x (directly proportional)

On cross multiplication,

[tex]8,00,000 *x= 48,000*6,50,000\\\\x=\frac{48,000*6,50,000}{8,00,000} =39,000[/tex]

Commission for the house 2 = $39,000

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Answer:

19

I first do plus 2and 7 and 10=z

Answer:

The rabbit will get hit because the car takes too long to break

Step-by-step explanation:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Multiplication and Division - whatever comes first from left to right (i.e. 6*7*2, do 6*7 first)

Addition and Subtraction - same thing as multiplication and division, whatever comes first

The First Amendment to the Constitution affect American society as D. The right to a free press allows Americans to have access to many independent sources of news and information.

It should be noted that Constitution simply refers to the rules and laws that guide a group of people especially a country.

In this case, the First Amendment to the Constitution affect American society as The right to a free press allows Americans to have access to many independent sources of news and information.

In conclusion, the correct option is D.

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The correct answer is "The right to a free press allows Americans" to have access to many independent sources of news and info

Explanation:

The First Amendment to the constitution was ratified in 1791, in this it was established government could not interfere in the right to exercise religion or assemble as well as the rights of freedom of speech and freedom of the press. This last aspect implies the government cannot interfere in the circulation of information, according to this, citizens have the right to create sources of news and information to report news or express opinions. Thus, the First Amendment affects American society because "the right to a free press allows Americans to have access to many independent sources of news and info".

Answer:

Parallelogram S: b = 7, h = 6

Parallelogram T: b = 3, h = 6

Area of Parallelogram S = 42

Area of Parallelogram T = 18

Step-by-step explanation:

The bases and heights of each parallelogram are given by the arrows, just count the number of boxes you see.

Area = base × height, so you just multiply these numbers. Area of parallelograms is found the same way as area for squares/rectangles.

7 × 6 = 42 and 3 × 6 = 18

The solving for the Segment CE is congruent to segment BC is bellow.

Congruent segments are those with the same length. Collinear points are those that are on the same line. A theorem is a mathematically proven proposition. A segment's midway is a point that divides one segment onto two congruent segments.

Congruent lines are two line segments that have the same length. For example, if we possess two 6 cm line segments AB as well as PQ, we may say AB PQ and so they are congruent.

Solving for the right column:

C is the midpoint of segment AE

C is the midpoint of segment BD

Segment AE is congruent to segment BD(given)

2. BC = EC

   BC=CD

3. AE=BD

4. BD = BC + CD

   AE=AC+CE

5. AC+CE=BC+CD

6. CE+CE=BC+BC

7. 2CE=2BC

8. CE=BC

9. Segment CE is congruent to segment BC.

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The pattern exists described as a sequence of repeating objects, shapes, or numbers. Patterns can also occasionally be referred to as a series.

The pattern follows the rule = Σn+(n+1)

The next three numbers in the pattern be 3, 6, 10, 15, 21, 28, 36.

A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.

Let the numbers in the pattern be 3,6,10,15, . . .

t1 = 1 + 2 = 3

t2 = 3 + 3 = 6

t3 = 6 + 4 = 10

t4 = 10 + 5 = 15

t5 = 15 + 6 = 21

t6 = 21 + 7 = 28

t7 = 28 + 8 = 36

The pattern follows the rule = Σn+(n+1)

Therefore, the next three numbers is 21, 28, 36.

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Answer: 1/3

Step-by-step explanation:

Answer:

⬤ = 8

⬛ = 6

Step-by-step explanation:

⬤ = x

⬛ = y

x + y = 14

x - y = 2

add the numbers on top of each other together:

add x to x = 2x , y + -y = 0 , 14 + 2 = 16

2x = 16

divide both sides by 2

x = 8, plug this back into the equation

8 + y = 14

8 - y = 14

y = 6

Kepler had 9 wooden edges to make for the cube.

As it is given in the data that the platonic solids are related to the orbits of the planets, and he made models of each of the Platonic solids. Kepler made a frame of each of the platonic solids by fashioning together wooden edges. At that time six planets were discovered and out of the six, two platonic solids were considered as cube. A cube is a three dimentional structure which has 8 corners and 12 edges.

So the number of edges = 4 x 2 + 1

= 9

Kepler has 9 wooden edges to make for the cube, to make a frame of each of the platonic solids by fashioning together wooden edges.

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The order of the sides from smallest to largest is: WX, XY, YW

Given: [tex]\angle[/tex] X = 90° (right angle) and [tex]\angle[/tex] W = 51°

The sum of the interior angles of any triangle is 180°, then

[tex]\angle[/tex] W + [tex]\angle[/tex] X + [tex]\angle[/tex] Y = 180°

Replacing the given values then we get

51° + 90°+ [tex]\angle[/tex] Y = 180°

141° + [tex]\angle[/tex] Y = 180°

Solving for  [tex]\angle[/tex] Y

Subtracting 141° both sides of the equation:

141° + [tex]\angle[/tex] Y - 141°=180° - 141°

[tex]\angle[/tex] Y = 39°

The order of the angles from smallest to largest is:

[tex]\angle[/tex] Y = 39°, [tex]\angle[/tex]  W = 51°, [tex]\angle[/tex] X = 90°

The opposite sides to these angles must be ordered in the same way:

Opposite side to  [tex]\angle[/tex] Y: WX

Opposite side to  [tex]\angle[/tex] W: XY

Opposite side to  [tex]\angle[/tex] X: YW

The order of the sides from smallest to largest is: WX, XY, YW

Therefore, the correct answer is option C. WX, XY, YW

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