Match each of 1 -6 with its appropriate definition from the list A - F below.

1. Axiom
2. Corollary
3. Contradiction
4. Tautology
5. Theorem
6. Lemma

a. An elementary mathematical truth that is assumed self-evident and not in need of proof.
b. A theorem that is an immediate consequence (and perhaps special case) of another theorem.
c. A proposition that is always false.
d. A proposition that is always true.
e. An important true mathematical statements.
f. A theorem that is needed as a stepping stone to prove a greater theorem.

Answers

Answer 1

Answer:

1. Axiom

Appropriate definition: An elementary mathematical truth that is assumed self-evident and not in need of proof (a).

2. Corollary

Appropriate definition: A theorem that is an immediate consequence (and perhaps special case) of another theorem (b).

3. Contradiction

Appropriate definition: A proposition that is always false (c).

4. Tautology

Appropriate definition: A proposition that is always true (d).

5. Theorem

Appropriate definition: An important true mathematical statements (e).

6. Lemma

Appropriate definition: A theorem that is needed as a stepping stone to prove a greater theorem (f).


Related Questions

Complete the statement for the equation y=-1/2x-1/2.
Enter the correct answer in the box.
The graph crosses the y-axis at (0,?)

Answers

9514 1404 393

Answer:

  -1/2

Step-by-step explanation:

The constant in the equation is the value that y has when x=0, because the x-term evaluates to zero when x=0. The constant term in this equation is -1/2, so that is the y-value when x=0.

  (x, y) = (0, -1/2) . . . . where the graph crosses the y-axis

-4x+9y=9
x-3y=-6
Solve using Elimination

Answers

Answer:

Step-by-step explanation:

Multiply the first equation by 4,and multiply the second equation by 1.

4(x−3y=−6)

1(−4x+9y=9)

Becomes:

4x−12y=−24

−4x+9y=9

Add these equations to eliminate x:

−3y=−15

Then solve−3y=−15for y:

−3y=−15 (Divide both sides by -3)

y=5

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

x−3y=−6

Substitute5foryinx−3y=−6:

x−(3)(5)=−6

x−15=−6(Simplify both sides of the equation)

x−15+15=−6+15(Add 15 to both sides)

x=9

Jennifer serves the volleyball to Deb with an upward velocity of 10.5ft/s. the ball is 5 feet above the ground when she strikes it. how long does debra have to react before the volleyball hits the ground ​

Answers

Answer:

Step-by-step explanation:

ddsfaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaafewwwaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefgtssssssssssssssssssccccccccccccccccccfgre

frstgsrgr

grgrgtegehhaaaaaaaaa

Please Help!! ASAP thank you

Answers

Answer:

(-4,-6)

Step-by-step explanation:

7TH GRADE MATH IF YOU HELP ILL GIVE BRANLIEST AND 10 POINT//PROBABILITY

Answers

Answer:

1. 1 in 5

2. There are 5 colors it could land on, and orange is one of them.

3. 40 different combinations

4. There are 5 colors with 8 corresponding numbers. 5x8=40

Step-by-step explanation:

1) 20%

2) Assuming that on the spinner with color, every section has an equal share, then the probability of landing on orange is [tex]\frac{1}{5}[/tex] or 20%. This is because, the orange section is one of the five equal sections, or [tex]\frac{1}{5}[/tex] or the spinner. [tex]\frac{1}{5}[/tex] in decimal form is 0.2, to convert to a percent, multiply by 100. Hence one gets, 20%.

3) 40

4) There are 5 sections on the spinner with color, hence 5 possible outcomes when one spins the spinner. On the black and white spinner, there are 8 sections, hence 8 possible outcomes when one spins the spinner. To find the total number of outcomes resulting from the two events, one must multiply the total outcomes from one event by the total outcome of the other event. When one does this, they get that there are 40 possible events.

Grandma's Recipe for Sugar Cookies
1 cups kutter
2 cups sugar
4 eggs
12 teaspoon baking powder
1% cups flour
4 teaspoon salt

Your sister wants to make more cookies and decides to use 4 cups of sugar. She says that she
will need to use 3 1/4 cups of flour. Do you agree with her? Explain your reasoning.

Answers

Answer:

I agree

Step-by-step explanation:

The sugar sweetens the cookies and also because it's a sugar cookie the sugar content should be a little bit more. And when the flour is too much it makes the cookie bumpy because of its dry content. The sugar should be more to give the cookie its expected taste

See the picture of the question

Answers

Answer:

(1, 3)

(2, 6)

(4, 12)

(6, 18)

Step-by-step explanation:

Time represents s, or the x value when plotting (x, y) and distance represent m or the y value when plotting.

For the first one, plot it at (1, 3), so look where time is, the horizontal line, and find one. Then from there, go up three places. That is where you will plot your first point.

The second one will be plotted at (2, 6). Find two on the horizontal line, and then go up six spaces. That is where you will plot your second.

Do the same thing for the last two. You should plot your points at:

(1, 3)

(2, 6)

(4, 12)

(6, 18)

Answer:

1,3  2,6  4,12  6,18

Step-by-step explanation:

A box has length 7 feet width 4 feet and height 5 inches find the volume of the box in cubic feet and in cubic inches

Answers

Answer:

20160in3

Step-by-step explanation:

1.) Convert all measurements to inches

7ft = 84in

4ft = 48in

5in = 5in

2.) Multiply all of the values to find the volume

84in x 48in x 5in = 20160in3

One person earns $53,000 per year. Another person earns $3700 per month how much more does the first person earn in a year than the second

Answers

they earn 8,600 more than the second

Solve the equation and check your solution. (If an answer does not exist, enter DNE. If all real numbers are solutions, enter REALS.)
2 − 4x = 34

Answers

Answer:

x= -8

Step-by-step explanation:

2-4x=34

-4x=32

x=-8

Find slope. plzz help me ​

Answers

Hello!

[tex]\large\boxed{slope = 2}[/tex]

Find the slope using the slope formula:

[tex]slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

We can use two points from the table and plug these into the equation. Use the points (5, 10) and (10, 20) to solve:

[tex]slope = \frac{20 - 10}{10 - 5}[/tex]

Simplify:

[tex]slope = \frac{10}{5}[/tex]

[tex]slope = 2[/tex]

In the graph of an inequality, the region below a dashed horizontal line through the point (4,1) is shaded. What inequality does the graph
represent?
cy1
D.X4

Answers

Answer:

Step-by-step explanation:

D

The graph represents the inequality y < 1.

Option B is the correct answer.

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

The horizontal line through the point (4, 1).

This horizontal line passes through y = 1.

The region below this horizontal line will be y < 1.

Thus,

The graph represents y < 1.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ2

The base of a pyramid is a square whose perimeter is 836m. What is the length of each side of this square

Answers

209m is the correct answer .

What's equivalent to 4(y – 3)

Answers

Answer:

that's

Step-by-step explanation:

+4y -12 thank you

Answer:

see below

Step-by-step explanation:

4y -12 hope it helps u

A single die is rolled twice find the probability of rolling a 1 the first time and a 6 the second time.

Answers

1/36 Ibaiwisjshaujsijj it’s 1/6 times 1/6

A child's ticket for the aquarium is 0.45 times the cost of an adult's ticket. An adult ticket costs $13.00. Mr. and Mrs. Lewis took their two children to the aquarium. How much did the Lewis family spend to enter the museum? help?​

Answers

i believe they would have to spend 37$$

Draw a number line . Locate each integer on the number line.
- 5
2
0
-4
3


PLEASE HELP DUE IN 15 MIN!!!!!

Answers

-5, -4, 0, 2, 3. From smallest to largest
Sorry for my messy handwriting. Here you go :)

solve for x in simplest form 10=3/5(x+5)

Answers

Answer:

x = 35/3

or

x = 11.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666

Step-by-step explanation:


Suppose f(x) = 3x + 5. Describe how the graph of g(x) = f(x) + 12 compares to f

Answers

Answer:12

Step-by-step explanation:

i know

Answer:

Given

f(x) = 3x + 5

The graph g(x) = f(x) + 12 is:

g(x) = 3x + 5 + 12 = 3x + 17

This function is translation up of f(x) by 12 units

g(x) has y-intercept greater than f(x) by 12 units

The equation above can be used to calculate the volume V, of a cone with a height h and radius r.

If the volume of a cone is 243πft3, and the height is equal to the radius of the base, what is the height of the cone in feet?

Select one:
A. 6
B. 9
C. 16
D. 13

Answers

Answer:

9

Step-by-step explanation:

i just did it

What is the prime factorization of 420?

Answers

we have the factors 2 x 2 x 3 x 5 x 7 = 420. It can also be written in exponential form as 22 x 31 x 51 x 71.

Step-by-step explanation:

Answer:The prime factors are 2 x 2 x 3 x 5 x 7 .

Step-by-step explanation:

6x+3(-2+4) when x=-2

Answers

Answer:

-8

Step-by-step explanation:

Calculate the slope of the line.

Answers

Answer:

Slope is -2/5

Step-by-step explanation:

here, (x1,y1)=(-5,5) and (x2,y2)=(5,1)

then,using formula

y2-y1

= ---------

x2-x1

1-5

= --------

5+5

-4

= --------

10

-2

= ----------

5

Javier teaches yoga classes at his community center. In a 60-minute class last night, he taught 30 poses. Today, he has a 30-minute class.
If he teaches at the same rate, how many poses will Javier teach in today's class?

Answers

Answer:

I'm guessing 15 poses because 30/60 half and 15/30 half so basically in the 60 minute lesson Javier spend 1 minute teaching them how do to each pose, so in the 30 minute lesson he'll spend 1 minute on the other poses.

Step-by-step explanation:

this was a little confusing and sorry if i dont make since

Answer:a minute !!!!!

Step-by-step explanation:

Please help me with this one

Answers

Answer:

the first one 2x -2

Step-by-step explanation:

It’s the first one I’m sure

f(x) = 3x^2 + 4x - 6
g(x) = 6x^3– 5x^2 - 2
Find (f +g)(x).

Answers

Answer:

(f+g)(x)=6x^3-2x^2+4x-8

I'm sorry if I'm wrong!!

3/4 + 3/8 how do I do this I messed the last one up

Answers

Answer:

1 1/8

Step-by-step explanation:

We need to add the fractions; 3/4 and 3/8

Step 1, get the LCM of 4 and 8. The LCM of 4 and 8 is 8

Step 2, 3/4 + 3/8 = 6 + 3/8 = 9/8 = 1 1/8

Hence, 3/4 + 3/8 = 1 1/8

In September Gill paid £62 for her electricity.
In October she will pay 15% more for her electricity.
Work out how much Gill will pay for her electricity in October.

Answers

71.3 UK£

Step-by-step explanation:

Can the following question be represented by 1/2 x5?

Jada has 5 bottles that each contain 1/2 liter of water.how many liters of water is that total??

Answers

Answer: yes i think

Step-by-step explanation:

What is 3785 divided by 30?

Answers

Answer: 126.166666667



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