Assume to contrary that the sum of the squares of two odd integers can be the square of an integer. Since, [tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex] is odd it shows that sum of the squares of two odd integers cannot be the square of an integer.
What is a square?A quadrilateral with four equal sides is called a square. There are the numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. Let's find out more about square's characteristics, mathematics, and design.
A square has four corners and is closed, two-dimensional (2D) object.
Assume to contrary that the sum of the squares of two odd integers can be the square of an integer.
Suppose that x,y,z∈Z such that [tex]x^{2} +y^{2} =z^{2}[/tex], and x and y are odd.
Let, x=2m+1 and y=2n+1.
Hence,
[tex]x^{2} +y^{2} =(2m+1)^{2} + (2n+1)^{2}[/tex]
=[tex]4m^{2}+4m+1+4n^{2}+4n+1[/tex]
=[tex]4(m^{2}+n^{2}) + 4(m+n)+2[/tex]
=[tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex]
Since, [tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex] is odd it shows that sum of the squares of two odd integers cannot be the square of an integer.
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How do you do question 7 and 8?
Answer:
7.
[tex]y = \frac{a - b \: x {}^{10} \times ln(x) }{x {}^{10} } [/tex]
8.
[tex]y = \frac{12x {}^{3} \times ln(x) - 2x {}^{4} + 1 + 4\pi {}^{2}x {}^{3} }{4x {}^{3} } [/tex]
Write the equation of the line that passes through the points (−9,−4) and (−5,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
[tex](\stackrel{x_1}{-9}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{-5}-\underset{x_1}{(-9)}}} \implies \cfrac{-1 +4}{-5 +9} \implies \cfrac{ 3 }{ 4 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{ 3 }{ 4 }}(x-\stackrel{x_1}{(-9)}) \implies {\large \begin{array}{llll} y +4= \cfrac{ 3 }{ 4 } (x +9) \end{array}}[/tex]
A student ran the Turkey Trot 5K (5 kilometers) race on Thanksgiving Day. Using the ratio 1 mile : 1.61 kilometers, which set-up would correctly convert 5 kilometers to miles
The conversion of 5 kiiometers to miles is 3.11 miles
How to convert the distance from kilometers to milesThe given parameters are
Distance covered by the students = 5 kilometers
The ratio of the distance is given as
1 mile : 1.61 kilometers
Multiply both sides of the ratio by 5
So, we have the following ratio expression
5 * 1 mile : 1.61 kilometers * 5
Evaluate the product in the above expression
So, we have the following ratio expression
5 miles : 8.05 kilometers
Divide both sides of the ratio by 1.61
So, we have the following ratio expression
5/1.61 miles : 8.05/1.61 kilometers
Evaluate the quotient in the above expression
So, we have the following ratio expression
3.11 miles : 5 kilometers
Rewrite as
5 kilometers : 3.11 miles
This means that
5 kilometers = 3.11 miles
Substitute 5 kilometers = 3.11 miles in Distance covered by the students = 5 kilometers
So, we have
Distance covered by the students = 3.11 miles
Hence, the distance covered by the students is 3.11 miles
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The price of a sweater was changed from $20 to $12. This is a(n) of %?
Answer:
If the proton proton chain produces gamma ray photons, why are the majority of photons we observe from the sun at visible wavelengths?
Step-by-step explanation:
Answer:If the proton proton chain produces gamma ray photons, why are the majority of photons we observe from the sun at visible wavelengths?
Step-by-step explanation:
Step-by-step explanation:
the probability of picking a blue marble out of a bag of 50 marbles is 3/25. how many marbles in the bag are not blue?
Answer:
Okay so the probability is 3 outa 25 half the amount in the bag just add 3 and 3 together (cause 25 is half of 50) you get 6 subtract that from 50 you get 44.
. What values of x will make the absolute value equation, 2x - 4= 15, true?
After factorization, the absolute value of the variable 'x' is 9.
What is factorization method?
The factorization method is used for the quadratic based equation whose highest degree is either two or more than two. Depending upon the degree of the variable, the number of factors are calculated. And by substituting the calculated value to check whether the answer is correct or not.
According to the question, the given linear equation is: |2x - 4| = 15
Now, to calculate the value of the variable 'x' by using factorization method. And to remove the bars which represent absolute value that means positive values
Required expression: |2x - 4| = 15
⇒ 2x = 15 + 4 = 19
⇒ x = 19/2 = 9.5
After factorization, the absolute value of the variable 'x' is 9.
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Convert 0.000 000 005 78 to scientific notation
Answer: 5.78 × 10 to the negative ninth power
Step-by-step explanation:
a radio tower is located 350 feet from a building. from a window in the building, a person determines that the angle of elevation to the top of the tower is 42 ∘ and that the angle of depression to the bottom of the tower is 20 ∘ . how tall is the tower? round to the nearest foot.
In linear equation, $ 442.54 tall is the tower.
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Suppose A is the window, B is the top of the tower, C is the bottom of the tower, and D is the point on the tower at the same horizontal level as the window.
Find BD, DC then add these together to give this°.
For BD : AD is 350 ft, the angle CAD is 42.
So BD/350 = tan 42°.
BD = 0.9004 × 350
BD = 315.14
AD/350 = tan20°
AD = 0.364 × 350
AD = 127.4
AD + BD = 315.14 + 127.4 = $ 442.54
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A bird of species A, when diving, can travel four times as fast as a bird of species B top speed. If the total speeds for these two birds is 170 miles per hour, find the fastest speed of the bird of species A and the fastest speed of the bird of species B.
The fastest speed of the bird of species A is 136 mi/hr. and the fastest speed of the bird of species B is 34 mi/hr.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
A bird of species A, when diving, can travel four times as fast as a bird of species B at top speed which is given in the question.
Let b = the speed of bird species B.
So the speed of bird species A is 4b.
If the total speed for these birds is 170, then there is an equation :
⇒ 4b + b = 170.
⇒ 5b = 170
⇒ b = 170/5 = 34 mi/hr.
So the speed of bird species A will be 4×34 ⇒ 136 mi/hr.
Therefore, the fastest speed of the bird of species A is 136 mi/hr. and the fastest speed of the bird of species B is 34 mi/hr.
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Represent the following fractions and decimals in a number line
a. 4/7 b. 7/11 c. 8/5 d 0 /1 e. 2/5 f. 2.5 g. 4.3 h 1.2
Answer:
d, e, a, b, h, c, f, g
Step-by-step explanation:
if you convert them all to decimals you get
a = 0.57
b = 0.64
c = 1.6
d = 0
e = 0.4
f = 2.5
g = 4.3
h = 1.2
in order it goes 0, 0.4, 0.57, 0.64, 1.2, 1.6, 2.5, 4.3
Identify all the sets which each number belongs. 15,-5.075,and π
The sets of numbers which each of the numbers given belong to as required in the task content is as follows;
15; Real, rational and Integers.-5.075; Real, rational and decimal.π; Real, Irrational and decimal.To what sets do all three numbers as given belong?As evident in the task content, the sets to which the three numbers belong is to be determined.
Hence, taking the numbers one after the other; we have;
15 => The number 15 belongs to the set of real numbers, rational numbers and most particularly, integers.
-5.075 => The number -5.075 belongs to the set of real numbers, rational numbers, and most particularly, decimals.
π => The number represented by π belongs to the set of real numbers, irrational numbers and it's numerical value is a non-terminal and non-repeating decimal.
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The linear function m = 50 - 9d represents the amount m (in dollars) of money you have
left after buying d DVDs.
a. Interpret the terms and coefficient in the equation.
b. Find the domain of the function. Is the domain discrete or continuous? Explain.
c. Graph the function using its domain.
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
How can you tell whether a domain is continuous or discrete?A domain's discreteness or continuousness can be determined by examining the function's graph. The domain is continuous if the graph is a line. The domain is discrete if the graph consists of a collection of points.
What is a discrete domain example?Private Domain
The values that will be effective for the function are distinct from one another. The maximum number of children you can have, for instance, has a defined answer. You can have 0 children, 1, 2, 3, etc., but not 2,34.
How can you determine a discrete function's domain?Discrete graphs are those in which no lines connect the points. Start by locating all the x-coordinates in order to determine the domain and range of a discrete graph. The graph's entire set of x-coordinates makes up the domain. The graph's entire range of y-coordinates is considered to be the range.
What does a discrete structure's domain mean?The domain is the collection of all possible inputs for a function. The codomain is the collection of all permitted outputs.
What is an example of discrete structures?Graphs, logical assertions, and combinations are a few examples of discrete structures. Infinite or finite discrete structures are both possible. Contrary to continuous mathematics, which works with structures whose values can span the real numbers or have other non-separable qualities, discrete mathematics deals with discrete objects.
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how do you do these problems
The required value of the function is 2
In the case of a function from one set to the other, each element of X receives exactly one element of Y.
The function's codomain and domain are respectively referred to as the sets Y and X as a whole.When a function is defined, the domain and codomain are not always explicitly specified, and one may just be aware that the domain is a subset of a bigger set without having to conduct any (perhaps difficult) computation. In mathematical analysis, "a function from X to Y" typically refers to a function that may have a valid subset of X as its domain.The given function is of the form :
g(x) = - x² - 7
Now let us find the required values.
g (-3) = - (-3)² - 7 = 2
g (-2) = - (-2)² - 7 = -3
g (1 ) = - ( -1 )² - 7 = -6
Hence the required value of the function is 2 at x = -3 .
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You need a thrust block for the riser for a
fire hydrant. The pyramidal form is 1 foot
high and 18 inches by 16 inches at the
base. How many cubic inches of concrete
will you need?
The number of cubical required are [tex]3456/n[/tex] here n is the area where it is kept.
To find the the number of blocks required, first you are suppose to know the volume of each brick and the area of the place where it is suppose to be kept. The area is not mentioned in this question because it is incomplete.
So, to proceed with it the volume of this block is L×B×H.
Given; length = 18 inches
breadth= 16 inches
and height = 1 foot = 12 inches
Thus Volume of cubical is 18× 16× 12= 3456 inches.
The number of bricks required is [tex]3456/n[/tex] here n represents the area of the place where it is supposed to be kept.
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the shapes below are mathematically similar 10,14,28,x
WE CAN USE THE SIMILARITY THEOREM WHEREIN
[tex] \frac{14}{28} = \frac{10}{x} \\ [/tex]
THE PROPORTIONS OF SIDES OF THE SIMILAR SHAPES A RE EQUAL.
NOW TO SIMPLIFY WE CAN DO CROSS MULTIPLICATION.
[tex]14(x) = 28(10) \\ 14x = 280 \\ \frac{14x}{14} = \frac{280}{14} \\ x = 20 [/tex]
x is therefore 20cman air conditioning and heating repair firm conducted a study to determine if the average outside temperature could be used to predict the cost of an electric bill for homes during the winter months in houston, texas. the resulting regression equation was: y
Finding the numeric value of the regression line, it is found that the electric bill in a month with temperature of 48 degrees is of $157.59.
How to find the numeric value of a function or of an expression?To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.
In the context of this problem, the function is given as follows:
y = 227.19 - 1.45x.
Which y giving the electric bill for a month of temperature x degrees.
The temperature is of 48 degrees, hence to find the electric bill, the lone instance of x in the function is replaced by 48, hence:
y = 227.19 - 1.45(48) = $157.59.
Hence the electric bill in a month with temperature of 48 degrees is of $157.59.
What is the missing information?The regression line is missing in this problem, as is defined as follows:
y = 227.19 - 1.45x.
In which:
y is the electric bill.x is the monthly temperature.The problem asks for the electric bill in a month with temperature of 48 degrees.
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Do the ratios 6:1 and 18:3 form a proportion
Answer:
Yes.
Step-by-step explanation:
18/ 3 = 6
3 / 3 = 1
so, 6 : 1.
what is the common denominator of "-1/4" + "-2/3"
Answer: 12
Step-by-step explanation:
The 4 in “-1/4” can be multiplied by three.
Three 3 in “-2/3” can be multiplied by four.
These give you the common denominator of 12!
Don’t forget to multiply the numerator by the amount you multiplied the denominator by!
Horizontal and parallel lines e and f are intersected by diagonal and parallel lines g and h. At the intersection of lines g and e, the bottom right angle is angle 2. At the intersection of lines h and e, the bottom right angle is angle 1. At the intersection of lines f and h, the top left angle is angle 3.
Statements Reasons
1. g || h 1. given
2. ∠1 ≅ ∠2 2. corresponding angles theorm
3. ∠2 ≅ ∠3 3. given
4. ∠1 ≅ ∠3 4. transitive property
5. e || f 5. ?
What is the missing reason in the proof?
vertical angles theorem
alternate exterior angles theorem
converse corresponding angles theorem
converse alternate interior angles theorem
The line e is parallel to f by converse alternate interior angles theorem.
What is converse alternate interior angle theorem?
Converse alternate interior angle theorem states that states if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.
What is parallel lines?
Two lines are said to be parallel when they do not meet at any point in a plane. Lines which do not have a common intersection point and never cross path with each other are parallel to each other. The symbol for showing parallel lines is ‘||’.
Given,
angle 1 is congruent to angle 2 and g is parallel to h.
similarly, angle 2 is congruent to angle 3,
by transitive property angle 1 is congruent to angle 3.
By converse alternate interior angle theorem, e is parallel to f.
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Which of the following is most likely the next step in the series
18. Angela cleans sneakers on the weekend to make extra money. She has completed 12
pairs of shoes, which is 20% of her total orders. How many total orders does Angela have
to clean?
The total number of orders that Angela has to clean are 60.
How to calculate the Percentage of a number?A percentage is a certain number or part of every hundred. It is a fraction with the denominator 100, and the symbol for it is "%." To determine the percentage of a number use the percentage formula to transform the problem into an equation: P% * X = YGiven:
Number of pairs of shoes cleaned by Angela = 12
Let the total number of shoes to be cleaned be x.
So,12 pairs of shoes are 20% of her total orders.
20% of x = 12
(20/100)x = 12
0.2x = 12
x = 12/ 0.2
x = 60
Therefore, Angela has to clean a total of 60 pairs of shoes.
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Calculate the value of x. Round to the nearest tenth. F 7.8 24 14.8
In this problem bout segment has the same distance so we can write an equation like:
[tex]\begin{gathered} x+7=13+8 \\ x=21-7 \\ x=14\approx14.8 \end{gathered}[/tex]So the answer is 14.8
Solve the equation shown: 14 + 5/7x - 20 = 4/7x - 4
The value of x is determined by solving the equation 14 + 5/7x - 20 = 4/7x - 4, which is: x = 14.
How to Solve an Equation?When given an equation, to solve the equation means to find the value of the variable in the equation.
Given the equation:
14 + 5/7x - 20 = 4/7x - 4
Combine like terms
5/7x - 6 = 4/7x - 4
Add 6 to both sides
5/7x - 6 + 6 = 4/7x - 4 + 6
5/7x = 4/7x + 2
Subtract both sides of the equation by 4/7x:
5/7x - 4/7x = 4/7x + 2 - 4/7x [subtraction property of equality]
x/7 = 2
Multiply both sides by 7
x/7(7) = 2(7) [multiplication property of equality]
x = 14
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Estimate the intercepts of the graph of the function
Answer:
x-intercept equals 5
y-intercept equals -10
Step-by-step explanation:
y-intercept: solve when x=0. y=-2|x-5|= -10
f(x)=(1/7)(7x) what is f(3)
The value obtained for f(3) after substituting x = 3 in the function f(x) is 0.0067.
What exactly is a function?A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.
What are the Function Formulas?The list of function formulas is divided into two categories: formulas for performing numerous arithmetic operations across functions and formulas for performing combined operations involving two or more functions.
The given function is f(x) = (1/7)/(7x)
We need to find the value of f(3) so we will substitute x = 3 in the given function as follows:
f(3) = (1/7)/(7×3)
∴ f(3) = (1/7)/21
∴ f(3) = 0.142/21
∴ f(3) = 0.0067
Therefore, after substituting x = 3 in the function f(x), the value obtained for f(3) is 0.0067.
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Can someone help me solve for
The price of a phone was AED 1,500.
How much will you pay for this phone, after a discount of 22% and a 6% tax?
Answer:
100-22=78
78+6=84
1500 x 84/100= 1260Dhs
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is (6,-2) and (8,-3); (15,9) and (13,8) parallel
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the lines above
[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{6}}} \implies \cfrac{-3 +2}{2}\implies \boxed{-\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{15}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{13}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{13}-\underset{x_1}{15}}} \implies \cfrac{-1}{-2}\implies \boxed{\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \textit{different slopes, \underline{not parallel}}~\hfill[/tex]
how do i identify the slope and y-intercept
y=-6x-8
Answer:
the formula of a line is y=mx+c
mx is the gradient/slope and c is the y intercept
so the slope here is -6
the y intercept is -8
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What is X in this equation
Answer:
13/4 or 3.25
Step-by-step explanation:
Since they are vertical angles, they are equal to each other. Thus, set the two equations together:
8x + 32 = 12x + 19
Isolate x
32 = 12x + 19 - 8x = 4x + 19
32 - 19 = 4x
4x = 13
4x/4 = 13/4 = 3.25