Use proof by contradiction to show that there are no integers a
and b such that a^2 − 4b − 2 = 0. Make sure the first lines of your
proof very clearly state the assumption ¬P.
Answers
There are no integers a and b such that a^2 - 4b - 2 = 0.
Given that a^2 - 4b - 2 = 0. We need to prove that there are no integers a and b such that this equation holds true using proof by contradiction.Proof by contradiction: Assume that there are integers a and b such that a^2 - 4b - 2 = 0Let P be the statement, a^2 - 4b - 2 = 0.It can be re-written as a^2 = 4b + 2.We can also say that a^2 is an even number. There are two cases to consider:Case 1: a is an even integer. a = 2k for some integer k.If a = 2k, then a^2 = 4k^2, which is divisible by 4. Hence, b = (a^2 - 2) / 4 should be an integer.But 4b + 2 = a^2 is an even number and an odd integer cannot be expressed as the sum of an even number and an even number plus 2. This means that b cannot be an integer.Case 2: a is an odd integer. a = 2k + 1 for some integer k.Then a^2 = 4k^2 + 4k + 1 = 2(2k^2 + 2k) + 1 is odd. But we know that a^2 = 4b + 2 is even, which is a contradiction.Hence, the assumption ¬P that there are integers a and b such that a^2 - 4b - 2 = 0 is false.Therefore, there are no integers a and b such that a^2 - 4b - 2 = 0.
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Related Questions
To create the flower gardens, Wendell bought six pieces of wood. Pieces A and B are 6 feet long, pieces C and D are 8 feet long, piece E is 3 feet long, and piece F is 2 feet long.
Part A
Can Wendell make a triangular garden using pieces A, B, and F? Why or why not?
Part B
Can Wendell make a triangular garden using pieces D, E, and F? Why or why not?
Part C
Can Wendell make a rectangular garden with the pieces of wood he has? If yes, which pieces can he use?
Part D
Describe how Wendell can use all six pieces of wood to create either two rectangular gardens or two triangular gardens. Assume the gardens do not share a common side.
Part E
Wendell’s dog, Jordan, was getting in his way as he worked in the backyard. So, Wendell chained him to a pole. If the chain is 12 feet long, about how much area does Jordan have to walk around?
Don't bother to answer if you're not gonna get them right or just guessing.
Answers
Answer:
i only know A and B
Step-by-step explanation:
Part A: Yes because the total is 6 pieces and can be used for each to find the answer
Part B: To create the flower gardens, Wendell bought six pieces of wood. Pieces A and B are 6 feet long, pieces C and D are 8 feet long, piece E is 3 feet long, and piece F is 2 feet long
Sorry but at least its something
A company sells lab equipment. The daily revenue and costs are modeled by the functions below where x is the number of units sold.
Revenue: R(x) = -0.32x^2 + 270x
Costs: C(x) = 70x +52
Answers
The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.
The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:
R(x) = -0.32x^2 + 270x
The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:
C(x) = 70x + 52
To determine the company's profit, we subtract the costs from the revenue:
Profit = Revenue - Costs
P(x) = R(x) - C(x)
Substituting the given revenue and costs functions:
P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)
Simplifying the equation:
P(x) = -0.32x^2 + 270x - 70x - 52
P(x) = -\(0.32x^2\)+ 200x - 52
The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.
To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:
x = -b / (2a)
For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.
x = -200 / (2 * -0.32)
x = 312.5
Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.
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graph the solution to the inequality on the number line m >-3
Answers
Answer:
sorry I can't remember this
Which one? (The first answer gets Brainly) (HAS TO BE CORRECT)
Answers
Answer:
Cytoplasm
Step-by-step explanation:
Answer:
Cytoplasm
Step-by-step explanation:
A card is randomly selected from a standard deck. What is the probability that a club or the queen of hearts is selected?
Answers
Answer:1/52 One out of 52 (there are 52 cards in a deck, right?)
Step-by-step explanation:
f a rectangle is not a square, what is the greatest number of lines of symmetry that can be drawn?A. 1B. 0C. 2D. 3 or more
Answers
If the rectangle is not a square, then the sides must not be equal.
Thus, the rectangle can be cut horizontally, vertically, and diagonally. Therefore, it must be option D, which is "3 or more".
A rectangular table is measured to be 264 centimetres long and 1.55 metres wide.Convert the length of the rectangular table to metres. Write your answer as a decimal.
Answers
Answer:
2.64m
Step-by-step explanation:
A rectangular table is measured to be 264 centimetres long and 1.55 metres wide.Convert the length of the rectangular table to metres. Write your answer as a decimal.
100cm = 1m
so
264cm = 2.64m
The annual salaries of all employees at a financial company are normally distributed with a mean Mu = $34,000 and a standard deviation Sigma = $4,000. What is the z-score of a company employee who makes an annual salary of $28,000?.
Answers
Answer:
see the attachment.
Answer:
C, -1.5
Step-by-step explanation:
edge
For what value of x is the rational expression below equal to zero?
X-4
(x+5)(x-1)
A. 4
B. -5
O
O
C. 1
O D.-4
Answers
Answer:
\(\boxed{\textsf{ The value of x is \textbf{4}.}}\)
Step-by-step explanation:
For complete solution kindly refer to the attachment .
Do what the picture says.Right answer gets brainilest!!!!
Answers
Answer:
142.5 ft^2
Step-by-step explanation:
You need to calculate each figure separately
area of the first rectangle = 5 x 4 = 20
area of the second rectangle = (5+6)x(4) = 44
area of 1/4 circle = 1/4π(10^2) = (1/4) x 3.14 x 100 = 78.5
area of figure: 78.5 + 20 + 44 = 142.5
Answer:
To find the area of this figure, we need to first determine its shape. The lengths given do not form a clear shape, so we need more information to determine the shape.
Assuming that the shape is a trapezoid with the bases of 6ft and 10ft, and a height of 5ft, we can use the formula for the area of a trapezoid:
Area = (b1 + b2) / 2 * h
where b1 and b2 are the lengths of the two parallel bases, and h is the height of the trapezoid.
Plugging in the values, we get:
Area = (6ft + 10ft) / 2 * 5ft
Area = 8ft * 5ft
Area = 40 sq ft
Area ≈ 3.73 sq m (rounded to two decimal places)
Therefore, the area of this figure is approximately 3.73 square meters.
(If it wasn't in decimals, it would be 40 square feet.)
Hopefully this helped! I'm sorry if it's wrong. If you need more help, ask me! :]
PLZZ HELP I WILL GIVE 100 points to whoever gets it right
Answers
Answer:
34
Step-by-step explanation:
A coach is buying snacks for 22 players at a soccer match. She pays a total of $77 to
buy each player a bottle of water and an energy bar. The price of one energy bar is $2.
Let w equal the price of a bottle of water. Write an equation that
represents the situation.
Answers
Answer: 22( w + 2 ) =77 and the amount of the water bottle would be 1.50
Step-by-step explanation: i dont know what to write??
What's the predicted number of runs for the player with only 86 hits? Show your equations, plugging in the values, and your steps to the solution. (2 points)
Answers
The predicted number of runs for the player with only 86 hits can be calculated using the equation Runs = Hits + Walks - Home Runs. Plugging in the values given, we get: Runs = 86 + Walks - Home Runs. Therefore, the predicted number of runs for the player is dependent on the number of walks and home runs they have.
To solve for the predicted number of runs, we can use the following steps:
Therefore, the predicted number of runs for the player with only 86 hits can be calculated by plugging in the values of the number of walks and home runs into the equation Runs = Hits + Walks - Home Runs.
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Pls pa Answer po❤️!!!!!
Answers
Answer:
1) 4
2) 40
3) 22
4) 3
5) 9.5
6) 4
7) 14.2
8) 7
9) 12
10) 11
Step-by-step explanation:
1) 14 + 6 = 16
so, 16 - 12 = 4
2) 58 - 18 = 40
3) 30 - 8 = 22
4) 10 + 2= 12
so, 12 - 9 = 3
5) 15 + 3 = 18
so, 18 - 7.5 = 9.5
6) 22 - 8 = 14
so, 14 - 10 = 4
7) 19.6 - 5.4 = 14.2
8) 17 - 9 = 8
so, 8 -2 = 7
9) 54 + 8 = 62
so, 62 - 50 = 12
10) 32 - 16 = 16
so, 16 - 5 = 11
Answer:
1. 4
2. 40
3. 22
4. 21
5. 10.5
6. 4
7. 14.2
8. 6
9. 12
10. 11
Step-by-step explanation:
If 0<=k<(pi/2) and the areas under the curve y=cosx from x=k to x=(pi/2) is 0.1, then k=
Answers
Answer: The integral of the function y = cos(x) from x = k to x = π/2 represents the area under the curve of the function between those limits. We can evaluate this integral as follows:
∫[k, π/2] cos(x) dx = sin(k) - sin(π/2) = sin(k) - 1
We are given that this area is 0.1, so we can write:
0.1 = sin(k) - 1
Adding 1 to both sides gives:
1.1 = sin(k)
To solve for k, we take the inverse sine (or arcsine) of both sides, keeping in mind that k is between 0 and π/2:
k = arcsin(1.1)
However, arcsin(1.1) is not a real number since the sine function is only defined between -1 and 1. Therefore, there is no value of k that satisfies the given conditions.
how many different collections of 40 coins can be chosen if there are at least 40 of each kind of coin?
Answers
Using the combination formula, there are approximately 2.77 x 10^21 different collections of 40 coins that can be chosen if there are at least 40 of each kind of coin.
To solve this problem, we can use a combination formula. We have to choose 40 coins from a set of coins where there are at least 40 of each kind.
Let's assume that we have four types of coins - quarters, dimes, nickels, and pennies. Since we have at least 40 of each type, we have a total of 160 coins.
Now, we have to choose 40 coins from these 160 coins. This can be calculated using the combination formula:
nCr = n! / (r! * (n-r)!)
where n is the total number of coins (160) and r is the number of coins we want to choose (40).
Plugging in the values, we get:
160C40 = 160! / (40! * (160-40)!)
Simplifying this expression, we get:
160C40 = 2,771,436,503,423,282,717,080
So, there are approximately 2.77 x 10^21 different collections of 40 coins that can be chosen if there are at least 40 of each kind of coin.
In conclusion, using the combination formula, we can calculate the total number of collections that can be formed from a given set of coins. This formula is useful in solving a variety of problems related to probability and combinatorics.
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how many one-half cubes are needed to fill the gap in the prism? a prism has a length of 3 and one-half, height of 3, and width of 2. a one-half unit cube has a length of one-half, width of 1, and height of 1. 2 4 6
Answers
42 one-half cubes are needed to fill the gap in the prism.
To find the number of one-half cubes needed to fill the gap in the prism, we need to calculate the volume of the gap and then divide it by the volume of a one-half cube.
The volume of the prism can be calculated using the formula: V = length * width * height.
In this case, the length is 3 and one-half (3.5), the width is 2, and the height is 3.
V = 3.5 * 2 * 3
V = 21
The volume of a one-half cube can be calculated using the formula: V = length * width * height.
In this case, the length is one-half (0.5), the width is 1, and the height is 1.
V = 0.5 * 1 * 1
V = 0.5
To find the number of one-half cubes needed to fill the gap, we divide the volume of the gap by the volume of a one-half cube:
Number of cubes = Volume of gap / Volume of one-half cube
Number of cubes = 21 / 0.5
Number of cubes = 42
Therefore, 42 one-half cubes are needed to fill the gap in the prism.
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Simplify the following expression: NEEED HELP PLLZ:(
2x − 8y + 3x2 + 7y − 12x
A 3x2 − 14x − y
B 3x2 − 10x − y
C 3x2 − 10x − 15y
D 3x2 + 10x − y
Answers
Step-by-step explanation:
I'm pretty sure that it is C.3x2-10x-15y
Anybody knows the answers to the monomial functions ?
Answers
Step-by-step explanation:
A monomial function is an expression with only one term. ... For example, a polynomial function is the sum of many monomial functions; If there's only one term in a polynomial function, then it is a monomial function [2]. Monomial functions can take many forms: A monomial (a number by itself is a “monomial”).
Can you Help me please
Answers
Answer:
They can buy only 40 shirts with $435.
They can buy the 52 shirts if the price is $ 7.28
Step-by-step explanation:
9.25x + 56 = 435
9.25x = 435 - 56
x = 379/9.25
x = 40
435-56=379
$379/52 shirts
$ 7.28
13 more than three times a number is less than or equal to 7 inequality
Answers
Answer:
x * 3 + 13 ≤ 7
Step-by-step explanation:
three times a number
x * 3
13 more than that
x * 3 + 13
less than or equal to 7
x * 3 + 13 ≤ 7
Please mark as brainliest
csct (csct-sin t) +sint - cost/sin t+ cott = csc² t
Answers
Answer:
Step-by-step explanation:
Explanation:
Left Hand Side:
cot
2
t
csc
t
=
cos
2
t
sin
2
t
1
sin
t
=
cos
2
t
sin
2
t
⋅
sin
t
1
=
cos
2
t
sin
2
t
⋅
sin
t
1
=
cos
2
t
sin
t
Use identity:
sin
2
t
+
cos
2
t
=
1
=
1
−
sin
2
t
sin
t
=
1
sin
t
−
sin
2
t
sin
t
=
1
sin
t
−
sin
2
t
sin
t
=
csc
t
−
sin
t
∴
=
Right Hand Side
how many variables are in the data set? b. which of the following variables are categorical, and which are quantitative? overall score - select your answer - recommended - select your answer - owner satisfaction - select your answer - overall miles per gallon - select your answer - acceleration () sec - select your answer - c. what percentage of these vehicles are recommended? round your answer to one decimal place. d. what is the average of the overall miles per gallon across all vehicles? round your answer to one decimal place.
Answers
All parts of the problem given have been explained and provided below.
Variables in any particular dataset are defined as any characteristics, numbers, or quantity that can be measured or counted to give information about any object, on which the dataset is based.
So, the variables in this given dataset are;
Overall score
Recommended
owner satisfaction
Overall miles per gallon
Acceleration (0-60) sec
Categorical or qualitative variables are those which can't be quantified or measured. Their values are defined by an order relation between the different categories.
the categorical variables in this dataset are,
Recommended
Owner satisfaction
Quantitative variables are those which can be measured in an order to provide information about an object.
the quantitative variables in this dataset are,
Overall score
Overall miles per gallon
Acceleration (0-60) sec
In the given dataset, 7 vehicles are recommended,
So their percentage would be,
7/15 × 100 = 46.67%
The average overall miles per gallon of these 15 vehicles is 25.4.
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Give the names of two other statistics that have the same value as the 50 th percentile. Choose the correct answer below. A. Second quartile; median B. Second quartile; mean C. Third quartile; mode D. First quartile; midrange
Answers
The 50th percentile is a commonly used statistic in data analysis. It represents the value below which 50% of the data falls.
In other words, it divides the data into two equal parts. There are two other statistics that have the same value as the 50th percentile, namely the second quartile and the median. The second quartile is the middle value of the data when it is arranged in ascending or descending order.
It is also known as the 50th percentile or the median. The first quartile is the value below which 25% of the data falls, and the third quartile is the value below which 75% of the data falls.
The mean is another commonly used statistic in data analysis. It is the sum of all the values in the data divided by the total number of values. Unlike the median, the mean is affected by extreme values or outliers in the data. This means that if there are outliers in the data, the mean may not be a good measure of central tendency.
The mode is the value that occurs most frequently in the data. It is another measure of central tendency that can be used in addition to the median and mean.
In summary, the 50th percentile is equivalent to the second quartile and the median. These statistics are all measures of central tendency that help to describe the distribution of data. The choice that best answers the question is option A: Second quartile; median.
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Someone help me with this
Answers
Answer:
81
Step-by-step explanation:
Any number, wether it is negative or postive, will always be postive when there is a even exponent.
In this case, we have a -9, and a exponent thats 2.
Since 2 is a even number, -9^2 will be a postive value.
Now, what is the actual value of this?
Well, a exponent of 2 basiclly means 2 numbers being multiplied together.
Or in this case, 2 negative 9s being multiplied together.
THis will be:
-9*-9
=
As I said above, a even exponent makes a negative number postive.
You see here that a negative 9 is being multiplied by -9. When two negative numbers multiply together, they make a postive.
THis is why a even exponent makes a postive.
Hope this helps!
how do i solve this
Answers
Answer:
m <E = 134
Step-by-step explanation:
Triangle DEF looks like an isosceles triangle to the base angles are the same measure.
6x+11 = 10x+3
Subtract 11 from both sides
6x = 10x-8
Subtract 10x from both sides
-4x = -8
Divide -4 from both sides
x = 2
Substitute 2 into both equations to make sure it works
6 (2) + 11
12+11
23
10 (2) +3
20+3
23
Both angles equal 23 degrees.
Now subtract both angles from the total angle measure of 180.
180-23-23=134
TIMED, 100 POINTS. What is the reciprocal of TanB in the triangle below?
Answers
Answer:
tanA
Step-by-step explanation:
Answer:
b) tanA
Step-by-step explanation:
The tangent is the opposite side to the angle over the side next to it.
In the case of angle B, the tangent would be the opposite side, AC, over the adjacent side, BC.
tanB = opposite/adjacent = AC/BC
The reciprocal of this would be BC/AC (this is just the fraction flipped around)
The only one that equals this would be tanA since the opposite/adjacent of that one is BC/AC.
Given: ABCD is a rhombus.
Prove: Triangle AEB is congruent to triangle CEB.
Answers
Answer:
Maybe right angle theorem? All right angles are congruent.
Answer:
Yes Triangle AEB is congruent to triangle CEB.
They are congruent by S.S.S axiom.
Solve - 12x ≤ 72 and then plot the solution set on the number line.
Answers
Answer:
(6,0)
Step-by-step explanation:
Used Desmos Scientific calculator.
Need help!!! Don’t understand at all…
Answers
Cos A = 9/26 = 0.346