A mathematical proof is an inferential justification for a mathematical claim that demonstrates how the premises logically support the conclusion.
Result for an image A proof formula:
There are numerous techniques to demonstrate something; we'll talk about three of them: direct proof, proof by contradiction, and proof by induction. We'll discuss each of these proofs, including what they are and when and how to use them.
Proof: If n is an integer, then. We shall demonstrate the converse statement, "if n is divisible by 4, then n is divisible by 2," in order to demonstrate that "if n is not divisible by 2, then n is not divisible by 4." Let's say n can be divided by 4.
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A mathematical statement that ________ two quantities using <, >, =
Answer:
compares
Step-by-step explanation:
What is the double of 8 in math?
Using doubles plus one fact the sum of 8 + 8 + 1is equal to 17 it is done by simply adding 1 to the given number.
Doubles plus one fact is used to add numbers which are next to each other.
Doubles plus one fact is simply done by doubling the number and adding one to it.
The sum of 8 + 8 can be determined by using doubles plus one fact as:
Simply add 1 in 8 + 8 + 1 to get the result required.
8 + 8 + 1 = 17
Therefore by using doubles plus one fact the sum of 8 + 8 + 1 is equal to 17.
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HELP ME QUICK PLEASE!!!!!
Which inequality is a true statement?
Select each correct answer.
-3>-1
-3 ≥ -1
-3=-1
-3≤-1
-3 <-1
Answer:
-3 <-1
-3 is less than -1.
−8×(−10+(−7))
Evaluate the following expression.
Answer:
136
Step-by-step explanation:
solve the inside of the parentheses and you get -17, then multiply by -8
What is an equation of the line that passes through the points (-6,6) and (-3,1)?
Answer:
y=-[tex]\frac{5}{3}[/tex]x-4
Step-by-step explanation:
find the slope m = [tex]\frac{y2-y1}{x2-x1}[/tex]
m=[tex]\frac{1-6}{-3+6}[/tex]
m=-[tex]\frac{5}{3}[/tex]
Use the slope and one of the points to solve for the y-intercept
y1=mx1+b
6=-[tex]\frac{5}{3}[/tex](-6)+b
6=10+b
b=6-10
b=-4
plug the values for m and b into y=mx+b
y=-[tex]\frac{5}{3}[/tex]x-4
Answer:
y= -1.6x+12Step-by-step explanation:First find the slope.
m=y2-y1 / x2-x1
m= 1-6
-3-(-6)
m=-5
-3+6
m=-5
3
m= -1.6
y-y1=m(x-x1)
y-6= -1.6(x-(-6))
y-6= -1.6x+6
y=-1.6x+12Does 15 20 25 form a right triangle?
Any triple would still represent the sides of a right triangle if we multiplied it by a constant. Therefore, the sides of a right triangle would be represented by 6, 8, 10, 15, 20, and 25, among countless other numbers.
What is right triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.
Input the Pythagorean Theorem with the given numbers:
c^2 = a^2 + b^2
25^2 = 15^2 + 20^2
625 = 225 + 400
625 = 625
Yes, the numbers 15, 20 and 25 form a right triangle and the Pythagorean triple.
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Are the triangles congruent Why or why not triangle congruence ASA and AAS?
ΔABC and ΔRQM are congruent triangles. They are congruent by either ASA or AAS.
Two triangles are said to be congruent if their all corresponding sides are equal and all corresponding angles are equal in measure.
For the given question,
We know that the sum of all angles of a triangle is 180°.
For ΔABC,
∠A + ∠B + ∠C = 180°
42° + 53° + ∠C = 180°
95° + ∠C = 180
∠C = 85°
For ΔABC and ΔRQM,
∠A = ∠R
∠C = ∠Q
AB = RM
So, by the AAS postulate, ΔABC and ΔRQM are congruent triangles.
For ΔRQM,
∠R + ∠Q + ∠M = 180°
42° + 85° + ∠M = 180°
∠M = 53°
For ΔABC and ΔRQM,
∠A = ∠R
∠B = ∠M
AB = RM
So, by the ASA postulate, ΔABC and ΔRQM are congruent triangles.
Therefore, ΔABC and ΔRQM are congruent triangles. They are congruent by either ASA or AAS.
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The complete question is -
Are the triangles congruent Why or why not triangle congruence ASA and AAS?
Please help! Need this by tonight thanks! Question 7 Click on picture
Answer:
Oh god, I don't really know much about this, but I am going to assume that the 25 represents the mn so maybe you have to put 25mn + 6600 on the first box?
Step-by-step explanation:
I just looked up how to do this. I think the form has to be a C=mn+b format. For the third box, I think you need to solve 54100=25mn+6600. On the second box I think you just need to solve C(3600)=25(3600)+6600. idrk
a rectange has the area of 60 in2. what can its dimentions be? copy and fill in the chart. length 1,2,10,30,120,3,_,5,_ width 60,_,_,_,_,_,5,_,100
PLS HELP FAST
The length and width of the rectangle can be 30 and 2 inches, 1 inches and 60 inches and 12 inches and 5 inches.
How to find the area of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other. Opposite sides of a rectangle is equal to each other.
A rectangle has the area of 60 in².
The dimension of the rectangle can be as follows:
area of a rectangle = lw
where
l = lengthw = widthTherefore,
60 = 30 × 2
60 = 1 × 60
60 = 12 × 5
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In, a city had a population of 310,000 people. Each year since 2007, the population has grown by 4.8%.
Let t be the number of years since. Let y be the city's population.
Write an exponential function showing the relationship between t and y.
The exponential function showing the relationship between t and y is y = 310000(1.048)⁺
How to determine the exponential function?From the question, we have the following parameters that can be used in our computation:
Initial population = 310000
Rate of growth = 4.8%
These parameters can be represeted as
a = 310000 and r = 4.8%
An exponential function is represented as
y = a(1 + r)⁺
Substitute the known values in the above equation, so, we have the following representation
y = 310000 (1 + 4.8%)⁺
Evaluate
y = 310000(1.048)⁺
Hence, the function is y = 310000(1.048)⁺
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Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X=15), n=17, p=0.6
0.01023 is the probability of obtaining a success
How to find the probability of obtaining a success?
Since we are dealing with a binomial probability distribution. We are going to use the binomial distribution formula for determining the probability of x successes:
P(X = r) = nCr . p^r . q^n-r
Given: number of trial (n) = 17, probability of success (p) = 0.6, X=15
probability of failure (q) = 1 - 0.6 = 0.4
P(X = 15) = 17C15 × 0.6¹⁵ × 0.4¹⁷⁻¹⁵
P(X = 15) = 17C15 × 0.6¹⁵ × 0.4²
P(X = 15) = 136 × 0.6¹⁵ × 0.16
P(X = 15) = 0.01023
Therefore, the probability of obtaining a success is 0.01023
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Which graph represents the solution set of the system of inequalities?
y ≤ 2x + 1
y>-21-3
Answer:
see below
Step-by-step explanation:
1. Notice that your inequalities have ≤ and >. So one of the lines on the graph must be dotted, eliminating the bottom two choices.
2. The lines on both of the top choices are graphed identically, so now it's all about shading. The best way to determine correct shading is by testing a point to see if it makes a true statement in BOTH inequalities.
a) Choose a point in the shaded region of the first option (I highly recommend (0,0)!!). Replace x and y in each inequality with the x and y from the point, and evaluate:
0 ≤ 2(0) + 1? ⇒ 0 ≤ 1 TRUE
0 > -2(0) - 3 ⇒ 0 > -3 TRUE
b) Since that point made both true statements, the first option is correct. If EITHER statement had been false, you would need to try a point in the shaded region of the second option. I recommend any where x=0 or y=0.
The monthly rents (in dollars) paid by 10 people are given below. (Note that these are already ordered from least to greatest.) 735, 935, 960, 995, 1005, 1050, 1065, 1075, 1100, 1120 Suppose that one of the people moves. His rent changes from $735 to $535. Answer the following.
The mean will decrease when the rent decrease.
The median will stay the same.
What is a mean?It's important to note that a mean simply means the average of a set of numbers that are given. The mean is the average of the given numbers and is calculated by dividing the total number of numbers by the sum of the given numbers. A data set's mean (average) is calculated by adding all of the numbers in the set and then dividing by the number of values in the set.
Mean = (sum of all observations divided by the total number of observations)
In this case, the rents are 735, 935, 960, 995, 1005, 1050, 1065, 1075, 1100, 1120 and one of the people moves, and his rent changes from $735 to $535.
In this case, changing 735 to 535 will make the average lower.
On the other hand, the median isn't affected as it's still 1057.50.
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A line is parallel to the line y = -x + 5 and passes through the point (4. - 1). Which of the following is an equation of the
line?
Answer:
y = -x + 3; could also be y + 1 = -(x - 4) or y = -(x - 4) - 1 or x + y = 3
Step-by-step explanation:
No options given, so I hope this helps.
1. Identify any of the equations that have the same slope as your given equation (-1). If there's only one, stop here.
2. Find the y-intercept by replacing (x,y)=(4,-1) in the equation y = -x + b and solve for b: -1 = -(4) + b ==> 3 = b
3. Replace b in the equation y = -x + b with 3.
See question in screenshot below:
Answer:
(√2/2)(sin(x) +cos(x))
Step-by-step explanation:
You want sin(x+π/4) written in terms of sine and cosine.
Angle sum identityThe sine of the sum of two angles is found using the identity ...
sin(α +β) = sin(α)cos(β) +cos(α)sin(β)
ApplicationChoosing α=x and β=π/4, this becomes ...
sin(x +π/4) = sin(x)cos(π/4) +cos(x)sin(π/4)
The trig function values are ...
sin(π/4) = cos(π/4) = √2/2, so the expression can be written ...
sin(x +π/4) = sin(x)√2/2 +cos(x)√2/2
sin(x +π/4) = (√2/2)(sin(x) +cos(x))
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5x-1=3x+5 an equation
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
[tex]5x-1=3x+5[/tex]
Get the x's on one side.
Add 1:
[tex]5x-1=3x+5\\\box \ \ +1) \ \ (\ \ \ \ +1)[/tex]
[tex]5x=3x+6[/tex]
Subtract 3x from both sides.
[tex]\ \ \ 5x=\ \: 3x+6\\\underline{-3x} \ \ \ \ \underline{-3x}\\[/tex]
[tex]2x = 6[/tex]
Finally, divide both sides by 2.
[tex]2x / 2 = 6/2[/tex]
[tex]x = 3[/tex]
By rounding each number to the nearest 10, estimate the value of 197 ÷ 10.3
Answer:
20
Step-by-step explanation:
197 rounded to the nearest 10 is 200.
10.3 rounded to the nearest 10 is 10.
So, 200 ÷ 10 = 20
Answer:
20
Step-by-step explanation:
We are rounding to the nearest 10.
197≈200
10.3≈10
After you have rounded the numbers, The equation simplifies a whole bunch.
200/10=20
Please Mark As Brainliestif the probability of selecting the number is 3/10, the what could the question be?
The question can be:
"From the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
What is the probability of randomly selecting a multiple of 3?"
The answer is that the probability is 3/2, as expected.
What could the question be?We want to find a question about probability, such that the answer is 3/10.
So we will have a set of 10 numbers, and 3 of them make a given event true, the probability of selecting one of these 3 numbers out of the whole set is:
P = 3/10
So, for example:
From the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
What is the probability of randomly selecting a multiple of 3?
There are 3 multiples of 3 on that set of 10 numbers, then the probability is P = 3/10.
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help!! i’ve been stuck on this problem!
Answer:
x less than or equal to -2
Step-by-step explanation:
I believe that's the answer
Answer:
x < -2
Step-by-step explanation:
You want the domain of a function graphed as a curve with an open circle at x=-2, which is the right end of the curve.
DomainThe domain is the horizontal extent of the graph. It is the set of values for which the relation is defined.
ApplicationThe open circle at (x, y) = (-2, 0) means that point is not part of the graph. All x-values to the left of that point have corresponding y-values, so the extent of the graph can be said to be ...
x < -2
The domain of the relation is x < -2.
What are rational roots Class 10?
The rational root theorem, as its name suggests, is used to find the rational solutions of a polynomial equation (or zeros or roots of a polynomial function). The solutions derived at the end of any polynomial equation are known as roots or zeros of polynomials. A polynomial doesn't need to have rational zeros.
Rational root theorem, also called rational root test, in algebra, theorem that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the constant term (the one without a variable) must be divisible by the numerator.
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The Science Club has 30 members and needs to elect officers. They will need a President, Vice President, Secretary, Treasurer, and Historian. How many ways can a 5-member committee be formed?
150
3,735
142,506
17,100,720
The ways to select the candidates from the total is (c) 142,506
How to determine the ways of selection?From the question, we have
Total number of members, n = 30
Numbers to selection, r = 5
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 30 and r = 5
Substitute the known values in the above equation
Total = ³⁰C₅
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 30!/25!5!
Evaluate
Total = 142,506
Hence, the number of ways is 142,506
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Answer: The answer is 17,100,720 different ways, or D.
Step-by-step explanation: I took the FLVS test. This situation is a permutation because order DOES matter. If got 142,506, you used the combination formula which is incorrect for this situation.
Solve for w.
2w²-2w+32 = (w-5)²
[tex]2w^2-2w+32=(w-5)(w-5)[/tex]
[tex]2w^2-2w+32=w^2-10w+25[/tex]
Subtract [tex]w^2[/tex] from each side:
[tex]w^2-2w+32=-10w+25[/tex]
Add [tex]10w[/tex] to each side:
[tex]w^2+8w+32=25[/tex]
Subtract 25 from each side:
[tex]w^2+8w+7=0[/tex]
Factor:
[tex](w+1)(w+7)[/tex] =0
Both solutions work, so w=-1 and w=-7Please help asap!!!!!!
A certain shade of light blue paint is made by mixing 1(1/2) quarts of blue paint with 5 quarts of white paint. How much white paint would you need to mix with 4 quarts of blue paint?
a) Set up the table with headings (names of the variables and the units).
b) Show how to use the table to solve the problem.
c) Record your final answer below.
By using Unitary method it can be calculated that
4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint
1 quart of blue paint is mixed with [tex]3\frac{1}{3}[/tex] quarts of white paint
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
a) Here, Unitary method will be used
Blue Paint White Paint
(Quart) (Quart)
[tex]1\frac{1}{2}[/tex] 5
[tex]1\frac{1}{5}[/tex] 4
1 [tex]3\frac{1}{3}[/tex]
5 quarts of white paint is mixed with [tex]\frac{3}{2}[/tex] quarts of blue paint
1 quart of white paint is mixed with [tex]\frac{3}{2} \times \frac{1}{5}[/tex] quarts of blue paint
4 quarts of white paint is mixed with [tex]\frac{3}{2} \times \frac{1}{5} \times 4[/tex] quarts of blue paint
4 quarts of white paint is mixed with [tex]\frac{6}{5}[/tex] quarts of blue paint
4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint
Again
[tex]\frac{3}{2}[/tex] quarts of blue paint is mixed with 5 quarts of white paint
1 quart of blue paint is mixed with [tex]5 \div \frac{3}{2}[/tex] quarts of white paint
1 quart of blue paint is mixed with [tex]\frac{10}{3}[/tex] quarts of white paint
1 quart of blue paint is mixed with [tex]3\frac{1}{3}[/tex] quarts of white paint
c) Finally
4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint
1 quart of blue paint is mixed with [tex]3\frac{1}{3}[/tex] quarts of white paint
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Graph the line for y-6=-4(x+2) on the coordinate plane.
Answer:
x
Step-by-step explanation:
x
Answer:
Step-by-step explanation:
the answer is 8
2. Claire is painting some windows that are all the same size. She used gallon of paint to paint 2 windows. How many gallons of paint are needed to paint 1 window?
Answer:3
Step-by-step explanation:
since 7 is a number and b is to u should just put 3 windows cause u need to add them all up i think, not sure but just do that, why not,
write -1/2x + 4 = 10 in slope intercept form
Answer: y=-1/2x+4
Step-by-step explanation:
How do you solve a proof question?
To solve a proof question, firstly you have to identify the question and visualize it and then try to connect the given conditions.
Mathematical proofs can be difficult, but can be conquered with the proper background knowledge of both mathematics and the format of a proof.
To solve a proof question you have to remember following steps:
Identify the question = You must first determine exactly what it is you are trying to prove. Identify the question. You must first determine exactly what it is you are trying to prove. Draw diagrams = When trying to understand the inner working of a math problem, sometimes the easiest way is to draw a diagram of what is happening. Use the information given in the problem to sketch a drawing of the proof. Label the knowns and unknowns.Study proofs of related theorems = Proofs are difficult to learn to write, but one excellent way to learn proofs is to study related theorems and how those were proveTo know more about proof here
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Please help will mark Brainly
Answer: Horizontal Translation
Step-by-step explanation:
The braking distance y in feet that it takes a car to stop on wet, level pavement can be estimated by y=1/25x^2 , where x is the speed of the car in miles per hour. Find the speed associated with the braking distance of 196 feet.
in essence, find "x" when y = 196
[tex]y = \cfrac{1}{25}x^2\qquad \stackrel{\textit{when y = 196}}{196=\cfrac{1}{25}x^2}\implies (196)(25)=x^2 \\\\\\ \sqrt{(196)(25)}=x\implies {\Large \begin{array}{llll} \stackrel{\frac{m}{h}}{70}=x \end{array}}[/tex]