What is the meaning of the term theorem

Answers

Answer 1

There are 4 terms in the world of *Mathematical proof*
Lemma, Proposition, Corollary and Theorem.
There is no difference between a lemma,
proposition, theorem, or corollary - they are all claims waiting to be proved. However, we use these terms to suggest different levels of importance and difficulty. A lemma is an easily proved claim which is helpful for proving other propositions and theorems, but is usually not particularly interesting in
its own right. A proposition is a statement which is interesting in its own right, while a theorem is a more important statement than a proposition which says something definitive on the subject, and often takes more effort to prove than a proposition or lemma. A corollary is a quick consequence of a proposition or theorem that was proven recently

Related Questions

Write an equation of four lines that intersect to form the sides of a parallelogram

Answers

To write equations for four lines forming a parallelogram, we use the slope-intercept form ensuring two sets of parallel lines. Opposite lines have equal slopes and by manipulating the y-intercepts, we ensure they intersect appropriately to form a parallelogram.

Writing an equation for four lines that intersect to form the sides of a parallelogram involves ensuring that opposite sides are parallel and equal in length. One straightforward approach is to use the slope-intercept form of a line, y = mx + b, to define the lines.

Let's start by defining two lines with slopes 'm' and 'm' (since opposite sides of a parallelogram are parallel) and two lines with slopes '-1/m' to ensure they are also parallel to each other but perpendicular to the first set of lines. If we assume lines have y-intercepts at 'b' and '-b' respectively (to ensure symmetry and simplify calculations), our equations would be:

y = mx + b (Line 1)y = mx - b (Line 2) - Parallel to Line 1y = (-1/m)x + k (Line 3) - Perpendicular to Line 1y = (-1/m)x + l (Line 4) - Parallel to Line 3

Here, m represents the slope of the first set of parallel lines, b represents the y-intercept of line 1, -b represents the y-intercept of line 2, and k and l are the y-intercepts of lines 3 and 4. By adjusting 'b', 'k', and 'l' we ensure the lines intersect to form a parallelogram.

These lines will form a parallelogram as long as 'k' and 'l' are chosen such that the distances between the y-intercepts of lines 1 and 2, and lines 3 and 4, are equal, satisfying the condition for parallel lines in a parallelogram. This way, we can visually imagine or draw a parallelogram with these four lines as its sides.

Mikayla withdraws $20 on 4 different days during a week. Find the total change in her account balance after the withdrawals.

Answers

20 times 4 = 80

so the change in her account would be negative 80 dollars

The change in her account after 4 withdrawals of $20 the change in her account will be $(D - 80)

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given that Mikayla withdraws $20 on 4 different days during a week.

Assuming she had $D before she had made any withdrawals.

∴ The situation can be represented numerically as,

(D - 20 - 20 - 20 - 20) dollars.

= (D - 80) dollars.

learn more about numerical expressions here :

https://brainly.com/question/14642484

#SPJ2

solve this system of linear equations. separate the x- and y- values with a coma. -x=29-14y
-9x=-19+14y

Answers

We are given the two equations:

(1) -x=29-14y
(2) -9x=-19+14y

Multiply (1) by 9:

-9x = 261 – 126y

Subtract the two equations:

-9x = 261 – 126y

-9x=-19 + 14y

0 = 280 – 140y

140y = 280

y = 2

From (1):

-x = 29 – 14 (2)

x = -1

Answers:

x = -1

y = 2

can someone help with my homework

Answers

Answer: seconds

-----------------------------------------------------------
-----------------------------------------------------------

With conversion fractions, the denominator unit is always what you want to cancel out. In this case, we want to cancel out "seconds" because we want to effectively replace "seconds" with "minutes" (which is what conversions are really). The numerator is the unit we want to convert to. Take care to note that sometimes you'll need multiple conversions, and sometimes it's not going to involve one conversion fraction only.

Have a look at the attached image to get a better sense of what is going on. Note the red slash marks to indicate cancellations.

In the year 2001, a total of 7.2 million passengers took a cruise vacation. The global cruise industry has been growing at 9% per year for the last decade. Assume that this growth rate continues.

How many cruise passengers (in millions) are predicted in the year 2002?

Answers

To find the number of passengers for the next year (2002), take the prior value (7.2 million) and multiply it by 1.09. This will give the predicted value for 2002. In this case, it would be (7,200,000 * 1.09 = 7.848 million). This would show that there is a predicted rise of 0.648 million passengers for the year 2002.

Final answer:

To predict the number of cruise passengers in 2002, multiply the growth rate by the previous year's number of passengers and add that to the previous year's total.

Explanation:

To predict the number of cruise passengers in the year 2002, we need to apply the growth rate of 9% to the number of passengers in the previous year (2001).

Therefore, the predicted number of cruise passengers in the year 2002 is

7.848 million

Learn more about prediction here:

https://brainly.com/question/5958146

#SPJ3

what is the cost of painting the walls and ceiling of a room with walls 30 foot by 25 foot by 1st foot with paint that covers at $9.50 per square yard, allowing for 1275 square feet for doors, windows, and baseboards?

Answers

what I can make out is, check the picture, that'd be the dimensions of the room.

therefore, the surface area of that room is

2 10x25 rectangles, front and back

2 30x10 rectangles, left and right

and 2 25x30 rectangles, top and bottom

so the area will be (2*10*25) + (2*30*10) + (2*25*30), which gives us 2600 square feet though, not yards.

let's add the doors, windows and others which is 1275, so 2600 + 1275, that gives us 3875 square feet.

now, the paint is 9.5 for square yard, no feet, so let's do some conversion then,

[tex]\bf \begin{array}{ll} yards&feet\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1yd&3ft\\ (1yd)^2&(3ft)^2\\ yd^2&3^2ft^2\\ &9ft^2 \end{array}[/tex]

so, if there are 9 square feet in one square yard, how many square yards are there in 3875 square feet?

[tex]\bf \begin{array}{ccll} yd^2&ft^2\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&9\\ x&3875 \end{array}\implies \cfrac{1}{x}=\cfrac{9}{3875}\implies \cfrac{3875}{9}=x[/tex]

that's how many yd² are there in 3875 ft².

now, we know for every yd², is $9.50, so then the cost will be

[tex]\bf 9.5\cdot \cfrac{3875}{9}\implies \cfrac{95}{10}\cdot \cfrac{3875}{9}\implies \cfrac{73625}{18}~~\approx~~ \stackrel{\$}{4090.2778}[/tex]

What is the reciprocal of 6 4/5?

A.) 5/34

B.) 29/5

C.) 34/5

D.) 15/5

Answers

Answer:

Step-by-step explanation:

The denominator in the original question is 5.

Therefore the answer must have 5 in the numerator. The answer can only be A.

6 4/5 = (30 + 4) / 5 = 34/5 This is the original fraction. The upside down of the original fraction is the reciprocal. Upside down of 34/5 is 5/34. You can come to this conclusion by doing this.

The formal definition of a reciprocal is 1/a where a is a fraction.

In this case a = 34/5. The reciprocal is 1/a = 1 // 34/5. You don't change anything by making it 1/1 // 34/5

1/1 // (34/5) Invert and multiply the bottom.

1/1 * 5/34 = 5/34

Qual é a diferença entre a população de Toledo e Umuarama?
Toledo - 119 207
Umuarama - 100 716

Answers

E preciso subtrair.

119207
- 100716
----------------
18491

What is a 6% increase to $62,900

Answers

6% = 0.06

multiply:

62900*0.06 = 3,774 ( Would be the amount of increase)

add:

62900 + 3774 = 66,674 (would be the new total)

Chad has 6 fewer sandwiches than Sarah.chad had 7 sandwiches. how many sandwiches did Sarah made?

Answers

Sarah made 1 sandwiches

Sarah made total 13 sandwiches.

What is an algebraic expression?

An algebraic expression is consists of variables, numbers with various mathematical operations.

Given that,

The number of sandwiches chad have = 7

Also, Chad has 6 fewer sandwiches than Sarah,

Let the number of sandwiches Sarah have = x,

According to condition,

Sarah has 6 more sandwiches than Chad,

⇒x = 7 + 6

⇒x = 13

The number of sandwiches that Sarah made is 13.

To know more about Algebraic expression on:

https://brainly.com/question/19245500

#SPJ5

A seamstress has one-fourth of a foot of thread. Then she uses one-fifth of a foot of thread to sew a hole. How much of the thread is left?

Answers

1/4 - 1/5 =
first make a common denominator
5/20 - 4/20 = 1/20

complete the calculation how to find partial products

1 2 4
× 2
----------

Answers

The first step is to write each factor in expanding notation.

This is:

- 124 = 100 + 20 + 4
- 2 = 2

Now muliply 2 times each term of the terms 100, 20 and 4

=> 2 * 100 = 200

2 * 20 = 40

2 * 4 = 8

Then,

    (100 + 20 + 4 )
x                     2
-----------------------
                       8
               40
                   200
------------------------
                   248

In a classroom of 32 students 14 are male. What percentage in the class is female

Answers

18 females.
18+14= 32

Well, if the classroom has 32 students in total and 14 of them are male, then that means that 18 are female, and 18 percent of 32 is 56.25%, so that would be 56% of the students in the classroom are female. Hope that helped! :D

A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is π/3 , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?

Answers

check the picture below.

notice, the "x" distance, whilst the balloons are moving up up and up, is not changing, thus, is a constant.

[tex]\bf tan(\theta )=\cfrac{y}{x}\implies tan(\theta )=\cfrac{y}{3}\implies tan(\theta )=\cfrac{1}{3}y \\\\\\ \stackrel{chain~rule}{sec^2(\theta )\cfrac{d\theta }{dt}}=\cfrac{1}{3}\cdot \cfrac{dy}{dt}\implies \cfrac{1}{cos^2(\theta )}\cdot \cfrac{d\theta }{dt}=\cfrac{1}{3}\cdot \cfrac{dy}{dt}[/tex]

[tex]\bf \cfrac{3\cdot \frac{d\theta }{dt}}{cos^2(\theta )}=\cfrac{dy}{dt}\quad \begin{cases} \frac{d\theta }{dt}=0.1\\\\ \theta =\frac{\pi }{3} \end{cases}\implies \cfrac{3\cdot 0.1}{cos^2\left( \frac{\pi }{3} \right)}=\cfrac{dy}{dt}\implies \cfrac{0.3}{\left( \frac{1}{2} \right)^2}=\cfrac{dy}{dt} \\\\\\ \cfrac{0.3}{\frac{1}{4}}=\cfrac{dy}{dt}\implies \stackrel{rad/min}{1.2}=\cfrac{dy}{dt}[/tex]

The observer and the balloon form a right triangle (see attachment).

The balloon is rising at 1.2 rad per min

Using tangent rule, we have:

[tex]\mathbf{tan(\theta) = \frac{y}{x}}[/tex]

Substitute 3 for x

[tex]\mathbf{tan(\theta) = \frac{y}{3}}[/tex]

Differentiate both sides with respect to time (t)

[tex]\mathbf{sec^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{3} \cdot \frac{dy}{dt}}[/tex]

Make dy/dt, the subject

[tex]\mathbf{\frac{dy}{dt} = 3 \cdot sec^2(\theta) \cdot \frac{d\theta}{dt} }[/tex]

Substitute [tex]\mathbf{\theta = \frac{\pi}{3}\ and\ \frac{d\theta}{dt} = 0.1}[/tex]

So, we have:

[tex]\mathbf{\frac{dy}{dt} = 3 \cdot sec^2(\pi/3) \cdot 0.1 }[/tex]

Using a calculator, we have:

[tex]\mathbf{\frac{dy}{dt} = 3 \cdot 2^2 \cdot 0.1 }[/tex]

Multiply

[tex]\mathbf{\frac{dy}{dt} = 1.2}[/tex]

Hence, the balloon is rising at 1.2 rad per min

Answers

40 because you get the 10 and the 4 and multiply it together

An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.

The unequal side is the base of the triangle.

The length of the base of the isosceles triangle is

10 cm or 4 cm.

What is an isosceles triangle?

An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.

The unequal side is the base of the triangle.

We have,

Two sides of an isosceles triangle have lengths:

= 10 cm and 4 cm

The unequal side of the isosceles triangle is the base and the other two sides have to be equal.

We can have two cases-

Case 1.

If the equal two sides are 10 cm.

Base = 4 cm

Case 2.

If the equal two sides are 4 cm.

Base = 10 cm.

Thus the length of the base of the isosceles triangle is

10 cm or 4 cm.

Learn more about the isosceles triangle here:

https://brainly.com/question/22532714

#SPJ2

James built a small electric car and recorded the distance it traveled. The table below shows the distance traveled (n) during the first 4 seconds after starting (f). Elapsed Time (seconds) Distance Traveled (feet) 1 6.2 2 12.4 3 18.6 4 24.8 Which of the following equations represents the relationship between the distance traveled and the elapsed time? f = 6.2 + n n = 6.2 + f f = 6.2n n = 6.2f

Answers

Elapsed Time (Seconds) Distance Travelled (Feet)
1 6.2
2 12.4
3 18.6
4 24.8

To form an equation, we first need to check whether the changing rate is a linear or non-linear.

A linear rate would give the same changing rate every one second traveled

Distance traveled between second 1 and second 2 = 12.4 - 6.2 = 6.2
Distance traveled between second 2 and second 3 = 18.6 - 12.4 = 6.2
Distance traveled between second 3 and second 2 = 24.8 - 18.6 = 6.2

Since the increase is the same every second, 6.2 feet, our equation would be the linear equation which is in the form y = mx + c
Where 'm' represents the gradient (changing rate) and c represents the distance traveled when the time is zero, which is also zero

n = 1 ⇒ d = 6.2
n = 0 ⇒ d = 6.2 - 6.2 = 0

We have m = 6.2 and c = 0
The equation is f = 6.2n

Answer: Option 3

Round $8.0443 to the nearest cent

Answers

$8.04 because the four is rounding down, therefore it should be $8.04.

I hope this helps.

To round $8.0443 to the nearest cent, we leave the second decimal at 4, since the third decimal is also a 4, resulting in $8.04

To round $8.0443 to the nearest cent, you need to look at the third decimal place, which is a '4'. Since we are rounding to the nearest cent, we only keep two decimal places. If the third decimal place is 5 or more, we would round up the second decimal place. However, because it is 4, we do not round up. Therefore, $8.0443 rounded to the nearest cent is $8.04

If a truck hauls 5 loads per week how many loads would it haul in a 1 year period

Answers

1 year = 52 weeks

52 * 5 = 260 loads

Debbie's city took a survey about a plan for a new park. The city surveyed 600 people. 60% of the people surveyed liked the plan for the park. How many people liked the plan?

Answers

Hi there.

All we have to do to find out how many people like the plan is multiplication.

We multiply the total number of people by 60% - in decimal form.

600 · 0.6 = 360

360 people liked the plan.

The answer is 360 people liked the survey.

Hopefully that answer it

The perimeter of a college athletic field is 104104 meters and the length is 1414 m more than the width. find the length and width.

Answers

The answer is 50,638.

solve this equation
h(t)= -16t+175t+500

Answers

Use the quadratic formula where a = -16, b = 175 and c = 500 to find t. See picture for quadratic formula.

Miki has a sheet of paper with a length of 104 centimeters and a width of 88 centimeters. She wants to divide it into the largest squares possible without wasting any paper. How many squares of the largest size will she be able to cut from the paper? 13 squares, 26 squares, 143 squares, or 572 squares

Answers

First, find the area of the rectangular paper: 104 × 88 = 9152 cm²

Since we want to find the number of the largest square that we can cut from the paper, we need to investigate if there's any square number is the factor of 9152

We can use the prime factor tree to find the factors of 9152 that is also a square number as shown below

9152 = 2 × 2 × 2 × 2 × 2 × 2 × 11 × 13

after trying few combinations, we have:
2 × 2 × 2 × 2 = 16
2 × 2 × 2 × 2 × 2 × 2 = 64

The largest square number is 64, and we will have 9152 ÷ 64 = 143 squares of papers

Justin is going on a 2000 kilometer road trip with two friends. The car consumes 6 liters of gas for every 100 kilometers and gas costs $1.20 per liter. If Justin and his two friends want to spilt it evenly, how much should each pay and how many liters of gas do they need

Answers

2000 / 100 = 20

20 * 6 = 120 liters total gas

120 * 1.20 = $144 total for gas

144 / 3 = $48 each

Cereal costs $2.79 for 16.4 ounces. At this rate how much does 25 ounces of cereal cost?

Answers

425 sksbsjsnwksnaianueenjwneeidnsinw

the value of a particular investment follows a pattern of exponential growth. in the year 2000 you invested money in a money market account. the value of your investment t years after 2000 is given by the exponential growth model A=2600e^0.052t. how much did u initially invest in the account? please show work

Answers

the 2600 is the constant so you initially invested $2600

In Ms. Hendricks class, there are 10 boys and 12 girls. What is the ratio of boys to girls? Express your answer as a fraction in simplest form.

Answers

The ratios is 10:12 and if you were to write it in a fraction you get 10/12 which is simplified as 5/6

The ratios is 10:12 and if you were to write it in a fraction you get 10/12 which is simplified as 5/6 hope this helped

Bottles of water sell for $1.50 each. Graph the relationship between the number of bottles of water sold and the total cost.

Answers

draw a graph with number of bottles on the x axis ( and number it 1 through 10 )

put price on the y axis and label it in increments of $1.50 ( 1.50, 3.00 , 4.50, 6.00, etc.

Then put dots on the intersection of price with the number of bottles and then draw a straight line through the dots.

for every 1 bottle of water sold the price increases by 1.50

so at x 1 y = 1.50

at x 2 y = 3.00

at x 3 y = 4.50

and so on

there are 207 students in 9 classes at east middle school at this rate how many students are in six classes

Answers

Hi Officiallylilly!
So 207 students in 9 classes, how many are in 6 classes? OK this is easy to solve so we do 207/9 to find out how many is in one class which is 23 in one class. Ok so if 23 is one class now we need to find out how many is in 6 classes which all we do is 23*6 which is 138.
Hope this helps!

the sum of 5 consecutive integers is 110. what is the fourth number in the sequence

Answers

Let's divide 110 by 5, that equals 22. That is our middle number. Now, we will use the 2 numbers below that (22.) and the 2 numbers above that.
20+21+22+23+24= 110.
So, the 4th number is 23.

Which of the following statements describes the process for solving 4 x ≥ -24?

Divide both sides of the inequality by -24 and flip the symbol.

Divide both sides of the inequality by -24 but don't flip the symbol.

Divide both sides of the inequality by 4 and flip the symbol.

Divide both sides of the inequality by 4 but don't flip the symbol.

Answers

Divide both sides of the inequality by 4 but don't flip the symbol.

First, you have to isolate the x, and so you divide by 4

However, because you are not dividing by a negative number, you will keep the sign the way it is

hope this helps :D

Hello Charlie!

The correct answer is option D

Divide both sides of the inequality by 4 but don't flip the symbol.

------------------------
Note: The only time you flip the symbol is when we divide by negative sign.

I hope this helps!

Other Questions

In _____, a person or a device intentionally or unintentionally interferes with your wireless network transmissions. select one: a. rf jamming b. war driving c. eavesdropping d. telemetry e. installing rogue access devices a class has 27 students.15 are boys the rest are girls. what is the ratio of girls to total students? passes through (-1,4) and m=4 Name the cell structures that are needed for photosynthesis and cellular respiration What places can you visit in California?Spanish missionsSalvadoran restaurantsArgentine dance studiosGuatemalan bakeries Two-thirds of a number is negative six. Find the number.a. -9b. -8c. -4 Which steps has the government taken in an effort to reduce second hand smoke exposure?A.Banned smoking on domestic airplane flights.B.Banned smoking in restaurants.C.Banned employers from creating smoking sections in offices.D.none of the above What is the role of the prosecution in criminal proceedings? 1) To file a complaint and convince the jury that the defendant is guilty. 2)To file a notice of appeal and convince the judges that the defendant is guilty. 3)To file a lawsuit and defend the person accused of the crime. 4)To file a lawsuit as a representative of the court. What is the solution of the equation x^2 + 6x + 6 = 0? A _________ works outside established organizational divisions and has greater flexibility to apply innovative approaches to new products and markets. 1.2 divided by .3 in the model Match the words in the left column to the appropriate blanks in the sentences on the right. make certain each sentence is complete before submitting your answer. help reset skin epidermis tendon smooth muscle cardiac muscle 1. : moves food through the gi tract 2. : moves blood through the body 3. : has a surface to which nothing is attached 4. : derived from mesenchyme 4. How might Douglass' reliability as an author be called into question for his piece Narrative of the Life of Frederick Douglass? Q 9.37: when should the gross profit method of inventory valuation not be used because it is invalid? The role of federal agencies is to ___________. develop, create, and implement the law interpret, administer, and enforce the law facilitate greater communication between courts render decisions in court cases regarding employment law If 4/5 of a population of a certain town is considered to be middle class and the population of the town is 2000 how many people are considered middle class which of these is a chemical property of a substance?A.textureB.ductilityC.reactivityD.conductivity Jane is saving her money in order to purchase a new racing bike. She initially saves $3 and plans to double the amount she saves each month. The bike Jane wants is $1,536 at the local bike shop.Which equation represents this situation, and after how many months, t, will Jane have enough money to purchase the bike?A, 3(2)t = 1,536; t = 11B, 3(1.2)t = 1,536; t = 35C, (3 2)t = 1,536; t = 9D, 3(2)t = 1,536; t = 9 is it true that Kilogram is a unit of volume. How is alphonse different from most of the other kapos? Steam Workshop Downloader