A postulate becomes a theorem through logical deduction and proof, starting with the postulates and leading to an indisputably true conclusion. Each step in a proof must follow logically from the ones before it, and the end result is a statement that holds true without premises, recognized universally in mathematics.
A postulate becomes a theorem through a process of logical deduction and proof. In mathematics, a postulate is an assumed statement used as a starting point for further reasoning and arguments. When we begin with our starting definitions and postulates, we can logically deduce new conclusions or theorems. If we can provide a proof of a statement A and show that it is definitely true based on the postulates and previously established theorems, then A becomes a theorem. Each line in a proof must follow from the rules cited, which are based on earlier lines of the proof or established logic. Once we derive the final conclusion, if every line of the proof is legitimate, then the whole proof is legitimate, and the sentence can be considered a theorem.
Moreover, a theorem is a statement that is true without any premises, meaning it derives from logical deductions of the initial assumptions. A theorem is proven via indisputable, step-by-step logical deductions. To illustrate, if an experiment or an established fact contradicts existing theories, it may lead to the development of a new theorem, as was the case with the postulates of Special Relativity. Ultimately, something is recognized as a theorem if it is a tautology—true in all possible models—thus making it a universally accepted truth in mathematics.
What is the product?
(5r + 2)(3r − 4)
15r2 + 8
15r2 − 8
15r2 + 14r − 8
15r2 − 14r − 8
15r² -14r -8 is the product of (5r + 2)(3r − 4). Thus, option D is correct.
What is a product?A product is an outcome of multiplying two or more numbers in mathematics. It is a crucial idea in algebra and is applicable to solution-solving.
The multiplication sign (x) designates the product, which is typically represented by a mathematical formula or a statement. The item is able to be employed to solve equations and discover their unsolved values.
= (5r + 2)(3r − 4)
= 5r(3r − 4) +2(3r − 4)
= 15r² - 20r + 6r - 8
= 15r² -14r -8
Therefore, option D is the correct option.
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.
Which is the conclusion of this statement?
If a and b are negative, then a + b is negative.
A. If a and b are negative, then a + b is negative.
B. If a + b is negative, then a and b is negative.
C. a and b are negative.
D. a + b is negative.
which ordered pair is a solution of y=-6x-7
Gcf of 24 60 and 72 i need it for my test tomorrow
How do i prove lines are parallel
Use the graph of the function h below to find the following.All values at which h has a local minimum
All local minimum values of h
If there is more than one answer, separate them with commas.
Don't want an answer, just want to know what I'm looking for, maybe an example.
The local minimum values of h are -3 and 0, and occur at the points (-2,-3) and (3,0).
From the graph, we can see that:
Local minimum values of h occur at (-2,-3) and (3,0)
Local minimum values of h are -3 and 0 respectively.
To find the local minimum values of h, we look for the points on the graph where the function changes from decreasing to increasing. These points are called local minimums.
From the graph, we can see that h changes from decreasing to increasing at the points (-2,-3) and (3,0). Therefore, these are the local minimum values of h.
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What is the eighth term in the arithmetic sequence defined by the explicit formula an=2n+7
Answer:
a8= 23
Step-by-step explanation:
work out the value of 5x-2y when x=-2 and y=-3
what is √6 over √5 in simplest radical form
HELP PLEASE?!???
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A rectangle is transformed according to the rule R0, 90º. The image of the rectangle has vertices located at R'(–4, 4), S'(–4, 1), P'(–3, 1), and Q'(–3, 4). What is the location of Q?
(–4, –3)
(–3, –4)
(3, 4)
(4, 3)
The location of Q in the rectangle is D. (4, 3).
How to illustrate the information?
Graph images undergo transformations, one of the types of transformations is rotations. Rotation is done when each point of the image rotates 90° around a point in a counterclockwise manner.
When rotation is done, (x,y) -> (-y,x), therefore when taking points from image to original then the reverse is done (-y,x) --> (x,y)
The coordinates of image point q' is (-3,4), hence, before rotation then the coordinates are (4,3).
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Every ten years, the Bureau of the Census counts the number of people living in the United States. In 1790, the population of the U.S. was 3.93 million. By 1800, this number had grown to 5.31 million. Write an exponential function that could be used to model the U.S. population y in millions for 1790 to 1800. Write the equation in terms of x, the number of decades since 1790.
write a fraction with a denominater of 6 that is greater than 4/2
If two triangles are congruent, then the six ___ parts are congruent.
Answer:
If two triangles are congruent, then the six corresponding parts are congruent.
Step-by-step explanation:
If two triangles are congruent, then each part of the triangle is congruent to the corresponding part in the other triangle.
With reference to the above congruent triangle rule, we get;
If two triangles are congruent, then the six corresponding parts are congruent.
What is the solution to the equation below? 2(x - 3) = 2x 5?
The planets move around the sun in elliptical orbits with the sun at one focus. The point in the orbit at which the planet is closest to the sun is called perihelion, and the point at which it is farthest is called aphelion. These points are the vertices of the orbit. A planet's distance from the sun is 224,000,000 km at perihelion and 232,000,000 km at aphelion. Find an equation for the planet's orbit. (Place the origin at the center of the orbit with the sun on the x-axis. ...?
Which function represents exponential decay?
f(x) =1/2 (3/2)^x
f(x) =1/2 (-3/2)^x
f(x) =4 (-2/3)^x
f(x) = 4 (2/3)^x
The function [tex]f(x) = 4 (2/3)^x[/tex] represents exponential decay, as the base of the exponent (2/3) is between 0 and 1.
The function which represents exponential decay is the one where the base of the exponent is between 0 and 1 (0 < b < 1). Out of the given options, [tex]f(x) = 4 (2/3)^x[/tex] represents an exponential decay function since (2/3) is a positive fraction less than 1.
In contrast, a base greater than 1, a negative base, or a base of 1 would not represent decay: a base greater than 1 represents exponential growth; a base of 1 would be constant (no growth or decay); and a base that is negative would not be a standard exponential decay because it would lead to oscillation between positive and negative values.
2/17 = x/102 solve the proportion
what is 3,996 + 7899
What is the least common denominator of 5/12 and 4/9
A total of 411 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?
The number of tickets sold to adults is 274 and of tickets sold to students is 137.
What is the system of equations?A system of equations is a set of one or more equations involving a number of variables.
Let the number of tickets sold to adults be x.
And the number of tickets sold to students be y.
A total of 411 tickets were sold for the school play.
x + y = 411
The number of student tickets sold was two times the number of adult tickets sold.
x = 2y
Substitute the value of x in equation 1
[tex]\rm x + y = 411\\\\2y+y=411\\\\3y=411\\\\y =\dfrac{411}{3}\\\\y= 137[/tex]
Substitute the value of y in equation 2
[tex]\rm x = 2y\\\\x= 2\times 137 \\\\x =274[/tex]
Hence, the number of tickets sold to adults is 274 and of tickets sold to students is 137.
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Using the figure above, if< A = <D, then< B ___ <E.
Choose the relationship symbol that makes the statement true.
Answer:
The relationship symbol that makes the statement true is '>'.
Step-by-step explanation:
Given,
In triangles ABC and EDF,
∠A = ∠D
Since, the sum of all interior angles of a triangle is supplementary,
⇒ ∠A + ∠B + ∠C = 180° and ∠D + ∠E + ∠F = 180°
⇒ ∠A = 180° - ∠B - ∠C and ∠D = 180° - ∠E - ∠F,
By substituting the values,
180° - ∠B - ∠C = 180° - ∠E - ∠F
- ∠B - ∠C = - ∠E - ∠F
∠B + ∠C = ∠E + ∠F
∠B + 20° = ∠E + 30° ( given ∠C = 20° and ∠F = 30° )
∠B = ∠E + 10°
⇒∠B > ∠E
Hence, the relationship symbol that makes the statement true would be '>'.
A spherical water tank holds 10500ft^3. What is the diameter of the tank? Use V=pie/6*d^3
The diameter of the sphere having a volume 10500 ft³ is 27.2 feet.
What is a sphere?In geometry, a sphere is a three-dimensional solid figure, which is round in shape.
The surface area is 4πr².
The volume is (4/3)πr³.
The diameter is 2×radius of the sphere.
Given, A spherical water tank holds 10500ft³.
The formula for the volume of the sphere is to be used is V = (π/6)d³, where 'd' is the diameter.
Therefore,
(π/6)d³ = 10500.
d³ = (10500)×(6/π).
d³ = 20063.7
d = 27.2 feet.
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Which statement correctly describes the end behavior of y = -3x5 + 5x2 +2x + 1
A)
The graph rises to the left and falls to the right.
B)
The graph falls to the left and rises to the right.
C)
The graph rises to the left and rises to the right.
D)
The graph falls to the left and falls to the right.
Rishi Maharan’s charge account statement shows an unpaid balance of $6,752.22. The monthly finance charge is 1.85% of the unpaid balance. After the finance charge was applied, Rishi has made new purchases of $150.75. What is the new account balance?
$7,027.89
$7,030.67
$6,902.97
$6,877.14
The requreid new account balance is approximately $7,027.89, which is option A.
What is a finance charge?A finance charge is a fee charged by a lender or creditor for the use of credit or the extension of existing credit. It is typically calculated as a percentage of the unpaid balance on a credit account or loan and is added to the account balance as an additional cost to the borrower.
The finance charge can be calculated as:
1.85% of $6,752.22 = 0.0185 x $6,752.22 = $124.98
Adding this finance charge to the unpaid balance gives:
$6,752.22 + $124.98 = $6,877.20
Finally, adding the new purchases to this balance gives:
$6,877.20 + $150.75 = $7,027.95
So, the new account balance is approximately $7,027.89, which is option A.
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A science experiment calls for mixing 3 2/3 cups of distilled water with 1 3/4 cups of vinegar and 2/3 cups of liquid detergent. How much liquid, in all, in cups, is needed?
Answer:
D) 6 1/12
Have a good day.
Answer:
D. It’s right
Step-by-step explanation:
One book costs £2.98. how much do 4 books cost?
Find the most general antiderivative of the function.
g(t) = (5 + t + t^2)/ square root of t
To find the most general antiderivative of the function g(t) = (5 + t + t^2) / sqrt(t), rewrite the function using inverse trigonometric functions and integrate it with respect to x, before substituting x back in terms of t to get the most general antiderivative.
Explanation:To find the most general antiderivative of the function, g(t) = (5 + t + t^2) / sqrt(t), we can rewrite the function using inverse trigonometric functions. Let x = sqrt(t), then t = x^2. Substituting this into the function gives us g(x^2) = (5 + x^2 + x^4) / x. Now, we can integrate this function with respect to x to find the antiderivative. The antiderivative of (5 + x^2 + x^4) / x is 5x + (x^3/3) + (x^5/5) + C, where C is the constant of integration. Finally, we substitute x back in terms of t to get the most general antiderivative of g(t).
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Each figure represents a Real Number and no denominators are zero. Choose the
correct statement and briefly explain why the others are not correct.
A) a/b+ c/d= a+c/bd
B) a/b+c/d= a+c/b+d
C) a/b+c/d= ad+bc/bd
Which pairs of angles below are alternate interior angles? Check all that apply.
A. ∠1 and ∠3
B. ∠7 and ∠2
C. ∠4 and ∠5
D. ∠8 and ∠2
E. ∠6 and ∠4
F. ∠7 and ∠1