Prove by contradiction that in a right triangle with integer sides, the two shorter sides cannot both be odd.
Assume that the two shorter sides, a and b, of a right triangle are both odd integers. Then the hypotenuse, c, must also be an integer. From the Pythagorean theorem, we know that c2 = a2 + b2. We can rewrite this as c2 = (2m + 1)2 + (2n + 1)2, where m and n are integers. We can expand the left-hand side of the equation to get c2 = 4m2 + 4n2 + 4m + 4n + 1. Since c2 is an even integer, 4m2 + 4n2 must be an even integer as well. But, since 4m + 4n + 1 is odd, the only way to make the left-hand side of the equation an even integer is if 4m2 + 4n2 is an odd integer, which is impossible.
Therefore, our initial assumption that a and b are both odd integers is false. Thus, in a right triangle with integer sides, the two shorter sides cannot both be odd.
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If you flip a coin 8 times, what is the best prediction possible for the number of times it will land on tails?
Solve this problem pls
The simplification of the given expression
[tex]3 \frac{1}{5} x + 10 \frac{7}{9} - 2 \frac{2}{5} x - 10 \frac{8}{9} [/tex]
is
[tex]\frac{4}{5}x - \frac{1}{9}x[/tex]
How to simplify expressions?[tex]3 \frac{1}{5} x + 10 \frac{7}{9} - 2 \frac{2}{5} x - 10 \frac{8}{9} [/tex]
Change into improper fraction
[tex] = \frac{16}{5} x + \frac{97}{9} - \frac{12}{5}x - \frac{98}{9} [/tex]
[tex] [/tex]
Collect like terms
[tex]= \frac{16}{5}x - \frac{12}{5}x + \frac{97}{9} - \frac{98}{9} [/tex]
Subtract
[tex] = \frac{4}{5}x - \frac{1}{9}x [/tex]
Consequently, the solution to the expression is
[tex] = \frac{4}{5}x - \frac{1}{9}x [/tex]
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Answer:
= 36x - 5.
Step-by-step explanation:
Sorry for my cancellation
What is the equation of this graph
In this equation, the value of x is fixed at 2, which means that every point on the graph will have the same x-coordinate value of 2. This creates a vertical line that passes through the point (2, y), where y can be any real number.
Therefore, the proper equation for the graph presented is:
[tex]x=2[/tex]
If m∠A = 50° and m∠B = 45°, what is m∠H?
(If anyone knows all the answer to any of these please provide a link.)
(It's called Chapter 5 Test, 3B Ratio, Proportion, and Similar Figures)
The measure of m∠H in the triangle is 85°.
How to find the measure of m∠H?
Similar triangles are two triangles that have the same shape but can have different sizes. More specifically, two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.
Since ΔABC and ΔFGH are similar, we can say:
m∠A = m∠F
m∠B = m∠G
m∠C = m∠H
m∠A + m∠B + m∠C = 180° (sum of angles in a triangle)
We have m∠A = 50° and m∠B = 45°
50° + 45° + m∠C = 180°
m∠C = 180° - 50° - 45°
m∠C = 85°
Since m∠C = m∠H
Thus, m∠H = 85°
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Three friends go to a book fair. Allen spends $2.60. Maria spends 4 times as much as Allen. Akio spends $3.55 less than Maria.
How much does Akio spend?
PLS NEED THE HELP!!
Answer:
$6.85
Step-by-step explanation:
$2.60 x 4 is 10.4 and that is how much Maria spends. Akio spends $3.55 less than Maria. So, 10.4 - 3.55 which is 6.85 and that is the answer.
Three numbers are given below. Use prime factorisation to determine the HCF and LCM 1848, 132 and 462
Answer:
The HCF is the highest common factor of 1848, 132 and 462, which is 14.Step-by-step explanation:
Prime factorisation is a mathematical method that breaks a number down into its prime factors, the smallest positive integers that are multiples of that number.The highest common factor of 1848, 132 and 462 is the smallest number that divides all three.The lowest common multiple is the smallest number that multiples all three numbers!Need help!
Use the Savings plan to find the amount A=? if monthly payments are $250 with APR=4% for 10 years.
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
The required formula is :
[tex] \qquad \dashrightarrow \sf \: A = P \times \dfrac{{\bigg(1 + \dfrac{APR}{n} \bigg) }^{ny} - 1}{\dfrac{APR}{n}}[/tex]
[tex] \textsf{A = Total accumulated savings } [/tex][tex] \textsf{P = regular deposit } [/tex][tex] \textsf{APR = annual percentage rate } [/tex][tex] \textsf{n = number of payment period per year} [/tex][tex] \textsf{y = number of years } [/tex]Now, plug in the values ~
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1 + \dfrac{0.04}{12} \bigg) }^{(12 \times 10)} - 1}{\dfrac{0.04}{12}}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1 + 0.0033 \bigg) }^{(12 0)} - 1}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1.0033 \bigg) }^{(12 0)} - 1}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{1.4908- 1}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{0.4908}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.249[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.2498[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.2498[/tex]
[tex] \qquad \dashrightarrow \sf \: A =\$ 36812.45[/tex]
That's the required value ~
What are the zeros of the function f(x) = x² - 4x² - 5?
+√5 ti
±2, ti
±5, ti
O +√2 ti
You must check the box below prior to submitting your exam!
The zeros of the function f(x) = x² - 4x - 5 are given as follows:
x = -1 and x = 5.
How to solve the quadratic function?The quadratic function for this problem is defined as follows:
f(x) = x² - 4x - 5
The coefficients are given as follows:
a = 1, b = -4, c = -5.
Then the discriminant is given as follows:
D = b² - 4ac
D = (-4)² - 4(1)(-5)
D = 36
Hence the zeros are given as follows:
x = (4 + sqrt(36))/2 = 5.x = (4 - sqrt(36))/2 = -1.More can be learned about quadratic functions at https://brainly.com/question/1214333
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When a number is increased by 5%, the result is 25. What is the original number to the nearest tenth?
Anwser : 23.8
Step 1: Subtract 5% from 25.
25 - (5% of 25) = 25 - (0.05 x 25)
Step 2: Simplify the equation.
25 - (0.05 x 25) = 25 - 1.25
Step 3: Subtract 1.25 from 25.
25 - 1.25 = 23.75
how to calculate the median in excel?
Answer:
Step-by-step explanation:
By using the Median Function in Excel =Median()
i need help. thank you
The following compositions are shown below:
Case 1
f ° g (x) = x, g ° f (x) = x
The two functions are inverses of each other.
Case 2
f ° g (x) = x, g ° f (x) = x
The two functions are inverses of each other.
How to find the composition between two functions and determine if the two functions are inverses or not
In this problem we need to determine the composition between two functions and determine if both functions are inverses of each other. A composition is defined below:
f ° g (x) = f [g (x)]
Where the independent variable of the function f(x) is substituted by function g(x). Two functions are inverses if and only if the following condition is fulfilled:
f[g (x)] = g[f (x)]
Now we proceed to determine the compositions and relationships for each case:
Case 1
f(x) = 3 · x
g(x) = x / 3
f ° g (x) = 3 · (x / 3)
f ° g (x) = x
g ° f (x) = (3 · x) / 3
g ° f (x) = x
Functions f(x) and g(x) are inverses of each other.
Case 2
f(x) = (x - 3) / 2
g(x) = 2 · x + 3
f ° g (x) = [(2 · x + 3) - 3] / 2
f ° g (x) = 2 · x / 2
f ° g (x) = x
g ° f (x) = 2 · [(x - 3) / 2] + 3
g ° f (x) = (x - 3) + 3
g ° f (x) = x
Functions f(x) and g(x) are inverses of each other.
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A student has a collection of 72 baseball cards. All of the cards are stored in
an album with 8 cards on each page. Which expression can be used to find the
total number of pages of baseball cards in the student's album?
The required expression that can be used to find the total number of pages of baseball cards in the student's album is P = 72 / 8.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
To find the total number of pages of baseball cards in the student's album, we need to divide the total number of cards by the number of cards per page.
Let's call the number of pages "P". Then we have:
P = 72 / 8
So, the number of pages is equal to 9.
So, the expression that can be used to find the total number of pages of baseball cards in the student's album is P = 72 / 8.
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Is 1/3(36m+12) and 12m+4 equivalent expressions
The expressions 1/3(36m+12) and 12m+4 are equivalent
What are equivalent expressions?
Equivalent expressions are defined as algebraic expressions that have the same solution but differ in the mode of the arrangement of values.
These expressions are known to have variables, constants, terms, coefficients, and factors.
They are also made up of mathematical operations.
We have the expression;
1/3(36m+12)
Now, expand the bracket
36m/3 + 12/3
Divide the values
12m + 4
Hence, the expression is 12m + 4
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Find the radius of each circle. round your answer to the nearest tenth
area=64π ft²
Answer: 64 MBS/43XY
Step-by-step explanation:
courseeeeeeeeee
Answer: r =[tex]\sqrt{4/\pi } =\sqrt{64/\pi } =4.51352[/tex]
Step-by-step explanation:
help me answer this pls
Since [tex]1 - \sin^{2}{\theta} = \cos^{2}{\theta}[/tex], the trigonometric expression [tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \tan{\theta}[/tex] is proven.
How to prove the trigonometric expression?The trigonometric expression for this problem is defined as follows:
[tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \tan{\theta}[/tex]
The identity used for the proof is given as follows:
[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]
Hence:
[tex]1 - \sin^{2}{\theta} = \cos^{2}{\theta}[/tex]
Replacing on the left side of the expression, we have that:
[tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \frac{\sin{\theta}}{\sqrt{cos^{2}{\theta}}}[/tex]
Taking the square root:
[tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]
The tangent is given as the division of the sine by the cosine, hence:
[tex]\frac{\sin{\theta}}{\cos{\theta}} = \tan{\theta}[/tex]
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What is 76 degree F in C?
76 degrees Fahrenheit was found to be equal to approximately 24.4 degrees Celsius using the formula of conversion.
To convert Fahrenheit to Celsius, you can use the following formula:
Celsius = (Fahrenheit - 32) x 5/9
Plugging in 76 degrees Fahrenheit, we get:
Celsius = (76 - 32) x 5/9
Celsius = 44 x 5/9
Celsius = 220/9
Celsius ≈ 24.4
Therefore, 76 degrees Fahrenheit is approximately 24.4 degrees Celsius.
On the Fahrenheit scale, water freezes at 32 degrees Fahrenheit (°F) and boils at 212 °F, at standard atmospheric pressure.
On the Celsius scale, the freezing point of water is defined as 0 degrees Celsius (°C), and the boiling point of water is defined as 100 °C, at standard atmospheric pressure.
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Help please the question is in the picture
Answer:
a) [tex]W(x) = 0.50 (3^x)[/tex]
W = tickets worth in $
x = number of balloons popped
b) For 8 balloons popped, number of tickets = 6,561
Tickets worth = [tex]\$ 3,280.50[/tex]
Step-by-step explanation:
The relation between number of balloons popped(x) and the number of tickets is
[tex]f(x) =3 ^ x\\\\f(1) = 3^1 = 3\\\\f(2) = 3^2 = 9\\\\f(3) = 3^3 = 27\\\\f(4) = 3^4 = 81[/tex]
each ticket is worth 50 cents
So for x tickets
[tex]W(x) = 0.50 (3^x)[/tex]
Number of tickets for 8 balloons popped
f(x) = 3^8
= [tex]f(x) = 3^8 = 6,561[/tex]
Ticket worth = [tex]0.5 \times 6,561 = \$ 3,280.50[/tex]
Given the following cash inflow at the end of each year, what is the future value of this cash flow at 5%, 8%, and 17% interest rates at the end of year 7? What is the future value of this cash flow at 5% interest rate at the end of year 7?
A $1000 cash inflows at the end of each year would have a future value of $8,142.01, $8,922.80 and $11.772012 at the end of the year 7 for interest rates of 5% , 8% and 17% respectively.
Future Value:Annuities are a financial instrument that generates a regular stream of cash. They have both a present and future value dependent upon the value of the cash payment, the number of payment periods and the interest rate. This question does not specify the cash inflow amount so an answer will be generated that can be scaled on multiples of $1000.
Let C represent the cash inflow at the end of each year. The future value (FV) of this cash inflow is given by:
FV = [tex]C[((1+i)^n-1)/i][/tex]
where i is the annual interest rate and n is the number of years.
(a) For i = 5% and n = 7
FV = [tex]C [((1+0.05)^7-1)/0.05][/tex]
FV= C[(1.047100-1)/0.05]
FV = C [8.142008]
(b) For i = 8% and n = 7
FV = [tex]C [((1+0.08)^7-1)/0.08][/tex]
FV = C[(1.713824 - 1)/0.08]
FV = C[8.922803]
(c) For i = 17% and n = 7
FV = [tex]C [((1+0.17)^7-1)/0.17][/tex]
FV = C[(3.001242 - 1)/ 0.17]
FV = C[11.772012]
Therefore, A $1000 cash inflows at the end of each year would have a future value of $8,142.01, $8,922.80 and $11.772012 at the end of the year 7 for interest rates of 5% , 8% and 17% respectively.
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which one of the following best describes the notion of the significance level of a hypothesis test?The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true
The probability of the type I error
The probability of the type II error
The Hypothesis test of probability of the type I error is True.
The Hypothesis test probability of the type II error is False.
The notion of the significance level of a hypothesis test is best described by the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true. This is also known as the "p-value." A significance level is often set beforehand, such as alpha (α) = 0.05, and if the p-value is less than alpha, the null hypothesis is rejected.
The probability of a type I error is related to the significance level. A type I error occurs when the null hypothesis is rejected when it is actually true. The probability of a type I error is represented by alpha (α) and is the level of significance that was set for the test.
The probability of a type II error is the probability of failing to reject a false null hypothesis. It is represented by beta (β) and depends on the sample size, the true value of the parameter being tested, and the level of significance set for the test.
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Why is the lac curve called the envelope curve?
The lac curve, also known as the envelope curve, is a curve that shows the maximum amount of work that can be done in a given period of time.
It is defined by the equation: W = min {W1 + W2, W3, W4, ..., Wn}, where W1, W2, W3, W4, ..., and Wn are the individual work tasks. The envelope curve is called such because it forms an envelope that encompasses all of the individual tasks on the graph, visually representing the maximum amount of work that can be done within the given timeline. This curve can be used to assess the efficiency of a task or project, as well as to analyze the impact of changes in the workload, deadlines, and resources.
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Can someone help me with this aleks question
The value of angles are,
∠ H = 20°
∠ G = 100°
∠ I = 60°
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Two triangles are similar.
Now, We have in triangle XYZ,
∠Y = 20°
∠Z = 100°
Hence, ∠ X = 180 - (100 + 20)
∠ X = 60°
Thus, By definition of similarity;
∠ H = ∠ Y = 20°
∠ G = ∠ Z = 100°
∠ X = ∠ I = 60°
Thus, The value of angles are,
∠ H = 20°
∠ G = 100°
∠ I = 60°
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Can y’all help me and solve for x
and I’m not sure if my answer is right
What value for x makes the equation −13(x + 11) + 12x = -26 true
Answer:-117
Step-by-step explanation:
-13x-143+12x=-26
-x=-26+143=117
x=-117
based on each set of triangles or parallel lines crest a proportion and solve it to find the missing value
pls help
The value of the x in the given triangle is 7.5 units.
What is proportion?Proportion definition, comparative relation between things or magnitudes as to size, quantity, number.
Given is a triangle having sides, 12, 4 and 10 there is a missing side x we need to find is value,
Using the concept of parallel lines crest a proportion,
x / 10 = 12 / 16
x = 120 / 16
x = 7.5
Hence, the value of the x in the given triangle is 7.5 units.
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In 2015 the highest tower in the world is the tower Burj Khalifa in Dubai.
It measures 828 meters of height
Alex have represented this tower at the scale 1=4000
What is the height of the tower in his draw ?
The height of the tower in Alex's drawing is 20.7 centimeters.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We need to find the height of the tower in Alex's drawing.
Let us multiply the actual height of the tower by the scale factor.
Scale factor = 1 : 4000
Height of the actual tower = 828 meters
Height of the tower in Alex's drawing = 828 meters x (1/4000) = 0.207 meters or 20.7 centimeters.
Therefore, the height of the tower in Alex's drawing is 20.7 centimeters.
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The graph represents y = −1/4 x − 3. Which coordinate pair is NOT a solution for the equation? Responses A(−8, −1) (−8, −1) B(0, −3) (0, −3) C(−2, −4) (−2, −4) D(4, −4) (4, −4) Question 2
The equation given in the problem is shown below:
[tex]y=-\frac{1}{4} x-3[/tex]
Here are the answer choices:
a) (-8,-1)
b) (0,-3)
c) (-2,-4)
d) (4,-4)
We are asked to choose the coordinate pair that is NOT a solution, so let's just test each option!
To test answer choice "a", plug in [tex]x=-8[/tex] and [tex]y=-1[/tex] into the original equation, then simplify:
Plug in values: [tex]-1=-\frac{1}{4} (-8)-3[/tex]
Multiply: [tex]-1=2-3[/tex]
Subtract: [tex]-1=-1[/tex]
Notice that we now have a true expression, therefore option "a" IS A SOLUTION, and is thus not the correct answer.
Repeat for option "b" (0, -3):
Plug in values: [tex]-3=-\frac{1}{4}(0)-3[/tex]
Multiply: [tex]-3=-3[/tex]
Notice that we now have a true expression, therefore option "b" IS A SOLUTION, and is thus not the correct answer.
Repeat for option "c" (-2, -4):
Plug in values: [tex]-4=-\frac{1}{4}(-2)-3[/tex]
Multiply: [tex]-4=\frac{1}{2} -3[/tex]
Subtract: [tex]-4=-\frac{5}{2}[/tex]
Notice that we now have a false expression, therefore option "c" IS NOT SOLUTION, and is thus the correct answer.
To ensure we have the right option, check option "d" as well (4, -4):
Plug in values:[tex]-4=-\frac{1}{4} (4)-3[/tex]
Multiply: [tex]-4=-1-3[/tex]
Subtract: [tex]-4=-4[/tex]
Notice that we now have a false expression, therefore option "d" IS A SOLUTION, and is thus not the correct answer.
Notice that we have now checked all possible options and only option "c" was evaluated as a false expression, therefore option C is the correct choice in regard to this question.
Let me know if you have any questions!
If the measure of angle f g h is 64 degrees and the measure of angle e g d is (4 x + 8) degrees, what is the value of x?.
By the help of congruent , the measure of angle f g h is 64 degrees and the measure of angle e g d is (4 x + 8) degrees and the value of x is 14
Things that have precisely the same size and shape are said to be congruent. The shapes and sizes need to hold true regardless of how we flip, spin, or rotate the forms. Two triangles that are identical in size and shape are said to be congruent triangles. Even if we flip, turn, or rotate one of two congruent triangles, the other two remain congruent.Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.The equal sides and angles may not be in the same location if there is a turn or flip, but they are still there.
The are congruent So,
4x+8=64
Solve for x
X=14
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Use the Exterior Angle Theorem to find the measure of each angle.
mangleC =
°
mangleD =
°
mangleDEC
The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles. That means that the measure of angle DEF is equal to the sum of measure of angle C and measure of angle D. Substituting known values gives you 2y + 9 + 6y + 10 = 115, then you can solve
8y + 19 = 115
8y = 96
y = 12
The measure of angle C is 33 degrees, the measure of angle D is 82 degrees, and because the measure of angle DEF is 115 degrees, its supplement angle (DEC) measures 65 degrees.
6) Brand X sells 25 kg bags of mixed nuts
that contain 41% peanuts. To make their
product they combine Brand A mixed nuts
which contain 35% peanuts and Brand B
mixed nuts which contain 45% peanuts.
How much of each do they need to use?
HELP ASAP compare these
1.) 2 (1/5)x-5
2.) y=2x
Both the equations cut at the point (- 3.125, - 6.25).
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equations are,
1) 2(1/5)x - 5
2) y = 2x
Now, We can draw the equations by using tool,
Hence, We get the graph of function 2(1/5)x - 5 shows by green line and y = 2x shows by red line.
Clearly, Both the function are cut at the point (- 3.125, - 6.25).
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