if n is a positive integer: 1²+ 2² + 3² + ... +n² = 1/6n(n+1)(2n+1) IS 1
What is meant by integer?An integer, which is pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Examples of integers include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are examples. The set of whole numbers and their antipodes is known as the integers. The set of integers excludes fractions and decimals. For instance, 2,5,0,12,244,15, and 8 are all numbers. Any positive or negative number that does not contain fractions or decimal places is known as an integer, often known as a "round number" or "whole number." For instance, the numbers 3, -10, and 1,025 are all integers, whereas the numbers 2.76 (decimal), 1.5 (decimal), and 3 12 (fraction) are not.P(n) :
1²+ 2² + 3² + … +n² = 1/6n(n+1)(2n+1)
P(1) :
[tex]1^2=\frac{1(1+1)(2(1)+1)}{6}[/tex]
[tex]1=\frac{6}{6}=1[/tex]
∴ LHS = RHS
Assume P(k) is true
P(k):
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(x + 7 ) + 3y help me please
Answer:
x+7+3y
Step-by-step explanation:
You just remove the parentheses in this case since you don't have to change any of the operations.
Answer:
Step-by-step explanation:
x+7+3y simplifed
Find volume of cylinder
I really need an answer for this FAST so if anybody can answer id really appreciate it :)
The volume of the cylinder on the image is:
v = 36,424 in³
So the correct option is the second one.
What is the volume of the cylinder?We know that for a cylinder of diameter D and height H, the volume is given by the formula:
V = pi*(D/2)²*H
Where pi = 3.14
Here we know that:
D = 40 inches.
H = 29 inches.
Replacing that in the formula for the volume we will get:
V = 3.14*(40 in/2)²*29 in = 36,424 in³
So the correct option is the second one.
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I need the answer to this question please!
The equivalent expression of 5[tex]x^{3/2}[/tex] is 5√(x³). The correct option is last one.
What are the equivalent expressions?Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Given:
An expression,
5[tex]x^{3/2}[/tex]
To find the equivalent expression:
We have to simplify the expression,
5[tex]x^{3.1/2}[/tex]
= 5(x³)[tex]){1/2}[/tex]
= 5√(x³)
The above expression is an equivalent expression.
Therefore, 5√(x³) is an equivalent expression.
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A line starts at (negative 2, 0), goes to (5, question mark), and then goes down to (6, 0).
What would the height need to be for this curve to be a density curve?
One-fourth
One-half
StartFraction 1 Over 8 EndFraction
StartFraction 1 Over 16 EndFraction
answer is one fourth
What the height would need for this curve to be a density curve is; One-half
How to interpret Density Curves?The criteria for a curve to be a density curve is as follows;
1. The curve must always be non-negative. This tells us that the y-value of the curve must be greater than or equal to 0 at every given point.
2. The area under the curve must always be equal to 1.
Now, we are told that the curve starts at (-2, 0) and then goes to (5, question mark), and then goes down to (6, 0),.
This means that the area under the curve will be a trapezoid that has a height of question mark and then bases of length 3 (from -2 to 5) and length 1 (from 5 to 6).
The area of this trapezoid will be equal to the sum of the bases times the height divided by 2, or:
Area = ((3 + 1) × question mark)/2
Since the area under the curve must be equal to 1, we can set up the equation:
1 = ((3 + 1) × question mark) / 2
Solving for question mark, we will:
The question mark = 2/4
The question mark = 1/2
Therefore, we can conclude that the height of the curve is 1/2
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Solve the following system of equations algebraically:
y = x² - 15x + 60
y=x-3
Since the square root of a negative number does not exist in the real numbers, there are no real solutions for x. Therefore, the system of equations has no solutions.
Define Algebric expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
What is variables and constants ?A constant has a fixed value and does not vary over time. For instance, the size of a shoe, a piece of clothing, or any other article of clothing will never alter. x+y = 8 is an algebraic equation, and 8 is a constant that cannot be altered. Variables are concepts that change or fluctuate throughout time.
To solve this system of equations algebraically, we can substitute y = x-3 into the first equation
y = x² - 15x + 60
x-3 = x² - 15x + 60
x² - 16x + 63 = 0
We know that this quadratic equation has no real solutions because its discriminant (b^2 - 4ac) is negative, so the system of equations has no real solutions.
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test form 1a answers 6th grade three times Geoff's age plus 3 is myrkas age. myrka is 48. what is Geoff's age
Geoff is therefore 15 years old.Rearranging terms in an equation to get the solution is known as "solving by rearranging.
What does a math reshuffle mean?Rearranging terms in an equation to get the solution is known as "solving by rearranging." Keep these guidelines in mind when solving by rearranging: To shift terms from one side to the other, do the reverse operation.Rearranging terms in an equation to get the solution is known as "solving by rearranging." Keep these guidelines in mind when solving by rearranging: To shift terms from one side to the other, do the reverse operation.Geoff is therefore 15 years old.Rearranging terms in an equation to get the solution is known as "solving by rearranging.Age of Myrka = 3x + Age of Geoff
3x + 3 = 48
3x = 48 - 3
3x = 45 x = 15
Geoff is therefore 15 years old.
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A quadrilateral with vertices at A(4, -4), B(4, -16), C(12, -16), and D(12,-4) has been dilated with a center at the
origin. The image of D, point D', has coordinates (36, -12). What is the scale factor of the dilation? 1/9. 1/3
3
9
Answer:
scale factor = 3
Step-by-step explanation:
since the origin is the centre of dilatation then the scale factor is the ratio of corresponding coordinates, image to original.
given D (12, - 4 ) and D' (36, - 12 ) , then
scale factor = [tex]\frac{36}{12}[/tex] = [tex]\frac{-12}{-4}[/tex] = 3
9/10 - 3/10
?????…..
Answer:
Step-by-step explanation:
9 - 3 = 6
6/10 = 3/5
Answer:
6/10 and/or 3/5(this is the answer simplified
Step-by-step explanation:
Subtract: 9/10 - 3/10
= 9 - 3/10
= 6/10
= 2 · 3/ 2 · 5
= 3/5
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 10) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 3/5. In other words - nine tenths minus three tenths is three fifths.
THIS HAS BEEN KILLING ME!!!!!
The function y=-1/3x is reflected across the x-axis. What's the equation of the new function?
- explain step by step, please.
Check the picture below.
let's bear in mind that the -(1/3)x has a negative slope, namely going down, so a reflection over the x-axis will yield the same points pretty much, but instead of the IV Quadrant, on the I Quadrant, above, whilst the slope remains the same, it simply turns positive.
Please answer this by 11/01/22. Thank you.
Answer: a) AE || BC b)AB=BC c)AE⊥ED &ED⊥CD
Step-by-step explanation:
a) The line segments that have the arrow sign on them mean that they are parallel, so AE || BC ( || = parallel to).
b) When two line segments have a dashed line on it, it shows that they are the same length, so AB is equal to BC.
c) when two segments intersect with a 90° angle, they are perpendicular, so AE⊥ED &ED⊥CD(⊥ = perpendicular to).
For the function Y= X +4 what is the output value if three is the input value
Answer: 7
Step-by-step explanation:
1. You need to know that the input value means the x-value, which means x = 3.
2. Input 3 in the function
3. Solve 3+4
4. 3+4 = 7
Answer:
put y=4 then four comes with- and 4-3=2
The table shows the lowest elevations for several countries. The
lowest elevation in the United States is -86 meters. Between the
elevations of which two countries is the elevation for the United
States?
Country
Argentina
China
Egypt
Ethiopia
Libya
Morocco
Lowest
Elevation (m)
-105
-154
-133
-125
-47
-55
What i the lope of the line through (-9,6)(−9,6)left parenthei, minu, 9, comma, 6, right parenthei and (-6,-9)(−6,−9
The slope of the line through (-9,6) and (-6,-9) is -5
Now, According to the question:
Let's know:
What is slope and example?
Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).
The formula for the slope of a line when two points (coordinate pairs)
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are given is :
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] , where m denotes the slope of the line.
Applying this formula, we get:
[tex]m = \frac{-9-6}{-6-(-9)}[/tex]
[tex]m = \frac{-15}{-6+9}[/tex]
m = [tex]\frac{-15}{3}[/tex]
m = -5
Hence, The slope of the line through (-9,6) and (-6,-9) is -5.
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The complete question is this:
What is the slope of the line through (-9,6) and (-6,-9) ?
fill in the following statements with sometimes, always, or never in order to the statements true
Perfect squares NEVER be irrational numbers.
Repeating decimals will ALWAYS be rational numbers.
Irrational numbers will NEVER be able to be written as fractions.
What is a perfect square?A square number, also known as a perfect square, is an integer that is the square of another integer, or the result of multiplying another integer by itself. For instance, 9 is a square number since it equals 3² and is represented by the symbols 3 × 3.
A number whose decimal representation eventually becomes periodic is known as a repeating decimal, also known as a recurring decimal.
All real numbers that are not rational are considered irrational numbers. In other words, it is impossible to express an irrational number as the ratio of two integers.
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Complete question
Fill in the following statements with either "sometimes ", "always ", or "never " in order to make it a true statement.
Perfect squares _______be irrational numbers
Repeating decimals will_____be rational numbers
Irrational numbers will____ be able to be written as fractions
Elizabeth has a loyalty card good for a 10% discount at her local grocery store. What would her total in dollars and cents be, after the discount and before tax, if the total cost of all the items she wants to buy is $37. 60? Round to the nearest cent
The total amount for Elizabeth's purchase after 10 percent discount on her total bill is 33 dollars and 84 cents which is equivalent to 34 dollars.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
Elizabeth bought the grocery for a total of 37 dollars and 60 cents.
She has a coupon of 10% discount.
Which means, she can get 10% discount on her total bill.
The amount of her total bill is $37.60.
So, calculate using percentage, the value of 10% of $37.60.
=(10 × 37.60/100)
= 376/100
= 3.76
So, Elizabeth would get a discount of $3.76 on her total bill -
= 37.60 - 3.76
= 33.84
Therefore, after the discount Elizabeth's total bill is $33.84 ≈ $34.
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3. The difference between the digits in a two-digit numeral is 3. The units’ digit is twice the tens’ digit. Find the numeral.
Answer:
36
Step-by-step explanation:
let the number be 10x+y
x - y = 3 (eq 1)
given: y = 2x (eq 2)
putting 2 in 1
x - 2x = 3
-x = 3 (we can ignore the negative sign for now because we only need to find the absolute value)
y = 6
number is 36
In a classroom, 1 10 of the students are wearing blue shirts , and 2 5 are wearing white shirts. There are 20 students in the classroom. How many students are wearing shirts other than blue shirts or white shirts
Answer:
10 students are wearing shirts other than blue or white.
Step-by-step explanation:
1 10 of the students in the classroom are wearing blue shirts, which is 1/1020 = <<1/1020=2>>2 students.
2 5 of the students in the classroom are wearing white shirts, which is 2/5*20 = 8 students.
Altogether, 2+8 = <<2+8=10>>10 students are wearing either blue or white shirts.
There are 20 students in the classroom, so 20-10 = <<20-10=10>>10 students are wearing shirts other than blue or white.
What is reflex angle class 9?
A reflex angle is an angle which measures more than 180 degrees and less than 360 degrees.
There are different types of angles in geometry, such as obtuse, acute and right angles, which all are under 180 degrees.
Assume, z is an acute or obtuse angle, and r is the reflex angle, then:
z + r = 360
r = 360 - z
Therefore, we can find the related reflex angle(r), if we know the value of the acute or obtuse angle(z).
A reflex angle equals the summation of 180 degrees and any of the primary angles (acute, right and obtuse angles). Therefore,
Reflex angle = 180° + Acute angle
Reflex angle = 180° + Right angle
Reflex angle = 180° + Obtuse angle
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Exit ticket
The length of the sides of two triangles is as follows:
ZY = 14, YX = 9, XZ = 8 PR = 5, RQ = 7, and QP = 4
is AZXY~ AQPR? Use a flowchart to organize your facts and conclusions.
Therefore , the solution of the given question triangle comes out to be
triangle PQR to triangle ZXY is 3/2
Defining a triangleYou can link any three points in a plane to form triangles, which have three sides and three angles. They were among of the first geometric forms to be examined. Since triangles may be divided into any polygon, regardless of whether it has four, five, six, or n sides, they are very significant.
Here,
Consider PR and ZY as a point of comparison.
PR = 5
ZY = 14
Suppose the scaling factor is r and that
5 * r = 14
r = 14 / 5
r = 14/5
examining other sides
RQ to PR
right 5 * 12/3 = 20
To YX, QP
Correct answer is 4 * 9/3 = 12.
Thus,
triangle PQR to triangle ZXY
Therefore , Triangle PQR to Triangle ZXY equals 3/2, which is how the given question's solution is determined.
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. In the cafeteria
3 out of every 5
students prefer
pizza. If there are
200 students in the
cafeteria how many
students prefer
pizza?
Answer:
120
Step-by-step explanation:
3/5 of 200 = 120
A barrel shaped like a cylinder is laid on its side and rolled up a ramp. The barrel has a circular base that is 1.1 inches in diameter. If the barrel turns 47 times in being rolled up the ramp, how long is the ramp?
The length of the ramp is 161.62 inches when the barrel turns 47 times in being rolled up the ramp.
What is the Circumference of a circle?The Circumference of a circle is defined as the product of the diameter of the circle and pi.
C = πd
where 'd' is the diameter of the circle
The circumference of the circular base of the barrel is given by the formula C = πd, where C is the circumference and d is the diameter of the base.
In this case, d = 1.1 inches, so C = π1.1 inches = 3.46 inches.
Since the barrel turns 47 times, the distance it travels is 47 times the circumference of the base,
47 × 3.46 inches = 161.62 inches
Therefore, the length of the ramp is 161.62 inches.
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15. Find the lengths of the sides of the kite KITE. (Answer in simplest radical form and show work)
The lengths of the sides of the kite LM is 13√2.
How does Pythagoras' rule work?According to the Pythagorean theorem, the hypotenuse of a right-angled triangle's other two sides add up to a square whose length equals the hypotenuse's.
The hypotenuse (longest side) of a right-angled triangle's square is equal to the sum of its other two sides, according to the Pythagoras theorem (base and perpendicular). Hypotenuse2 = Base2 + Perpendicular2 is how this is expressed. A2 + B2 = C2 is the formula for the hypotenuse.
According to question:-
LM = 13√2
Hypotenuse = Base 2 + Perpendicular 2.
So,
LM = √7² + 17²
LM = √49 + 289
LM = √338
LM = 13√2.
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What are the 4 ways to solve a quadratic equation?
The four ways are 1) Factoring 2) Completing the Square 3) Quadratic Formula and 4) Graphing
1. Factoring: Factoring is the process of breaking down an expression into its simplest components. To solve a quadratic equation using factoring, you must start by writing the equation in standard form (ax² + bx + c = 0). Then, you must factor the equation into two binomials (x + a)(x + b) = 0. Once this is done, you can solve for x by setting each factor equal to zero and solving for x.
2. Completing the Square: Completing the square is another method of solving a quadratic equation by rewriting it in the form of (x + a)² = b. To do this, you first start by writing the equation in standard form (ax² + bx + c = 0). Then, you must rearrange it so that all the terms are on one side of the equation and the constant is on the other side. Next, divide the coefficient of x² by two and then square this number. Finally, add this number to both sides of the equation, which will then allow you to solve for x.
3. Quadratic Formula: The quadratic formula is a useful tool for solving quadratic equations.
4. Graphing : is another method useful for solving quadratic equation.
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•40 POINTS• don’t explain.
Answer:
ASA-------------------------
We can see two angles marked as same, one of them is a right angle.
The included vertical side is common to both triangles so is a congruent side.
Since we have congruence of two angles and the included side, it is Angle-Side-Angle or ASA.
Use the illustration below to determine which statements are true. Select the two statements that are true statement 1: Points A, E, and C are collinear. statement 2: Lines I and m intersect at point D. statement 3: AE and DC are line segments on line I. statement 4: EA and EC are rays on the line m.
The required true statements for the given lines are 1 and 4.
What is line segments?An element or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.
According to question:Statement A: E and C are co-linear.
It is true, E and C are lie in same line
statement 2: Lines I and m intersect at point D.
It is false, I and m intersect at point E.
statement 3: AE and DC are line segments on line I
It is false,because AE and DC are line segments placed in different line.
statement 4: EA and EC are rays on the line m.
It is true, as EA and EC are in same line m.
Thus, required true statements are 1 and 4.
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Answer:
1 and 4
Step-by-step explanation:
It is a problem about the systems of equations that do not arise.
It is desired to distribute 420 € among three people, so that the first has €40 more than the second, and the third has half of what they have between the first two.
a) It proposes a system of linear equations to calculate what corresponds to each one. b) It solves, using the Gauss method
The solution to the equations is
The value of first x = € 160
The value of second y = € 120
The value of third z = € 140
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first , second and third be represented as x , y , and z
The total amount to be distributed = € 420
So , x + y + z = € 420 be equation (1)
Now , first has €40 more than the second
So , x = y + 40 be equation (2)
And , third has half of what they have between the first two
So , z = ( 1/2 ) ( x + y ) be equation (3)
Substituting the value of x in the equation (3) , we get
z = ( 1/2 ) ( 2y + 40 )
z = y + 20 be equation (4)
Substituting the value of z and x in equation (1) , we get
( y + 40 ) + y + ( y + 20 ) = 420
On simplifying the equation , we get
3y + 60 = 420
Subtracting 60 on both sides of the equation , we get
3y = 360
Divide by 3 on both sides of the equation , we get
y = € 120
Therefore , the value of x = € 160
The value of z = € 140
Hence , the solution to the equation is € 160 + € 120 + € 140 = € 420
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What are the potential solutions to the equation below? 1ln(x+3)=0
A. x = -3 and x = -4
B. x = -2 and x = -4
C. x = 2 and x = -3
D. x = 2 and x = 4
The potential solutions to the equation are x = -2 and x = -4
What is logarithm ?A logarithm is the power to which a number must be raised in order to get some other number .
The given expression is ln(x + 3) = 0
It can be rewritten as
[tex]ln _e (x + 3) = 0[/tex]
[Since base of a natural logarithm is considered as e]
[tex]e^0 = (x + 3)[/tex]
Since in a logarithmic function if log b with base e = c
Then we further solve the expression to get the possible roots.
x + 3 = 1
x = 1-3
x = -2
Therefore, the potential solutions are x = -2 and x = -4
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1. To find members for her skate team, Heather prints flyers to display around town. She posts 6 flyers
at her school and f flyers at each of the 3 nearest skate parks. Write two different expressions that
represent the total number of flyers posted.
Find the total number of flyers posted if f= 5.
Recently, the Town of Aberdeen announced they were going to acquire a large parcel of land for a new park initiative.
What is piecewise function?To fully understand what piecewise functions are and how we can construct our own piecewise-defined functions, let’s first dive into a deeper understanding of how it works.A piecewise function is a function that is defined by different formulas or functions for each given interval. It’s also in the name: piece. The function is defined by pieces of functions for each part of the domain.In mathematics, a piecewise-defined function is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. Piecewise definition is actually a way of expressing the function, rather than a characteristic of the function itself.To learn more about piecewise function refer to:
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If you have 20 balls (10 black, 10 white) and two urns, how could you place the balls into the urns so as to maximize your chance of drawing a black ball
To fill one urn with one white ball and the second urn with the remaining nine white and ten black balls.
Explain about the probability?Probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. A coin flip is the most basic illustration. There are only two outcomes that can occur when you flip a coin: either heads or tails.
The basic probability formula is: Probability = Number of Favorable Outcomes / Total Number of Outcomes. or P(A) = f/N
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In order to summarize qualitative data, a useful tool is a____________.
A) histogram
B) stem-and-leaf diagram
C) scattergram
D) frequency distribution
A (A) histogram is a useful tool for condensing qualitative data.
What is a histogram?An effective tool for summarizing qualitative data is a histogram.
The distribution of numerical data is roughly depicted by a histogram.
Karl Pearson was the person who first coined the phrase.
The first stage in creating a histogram is to "bin" (or "bucket") the range of values, divide it into a series of intervals, and then count the number of values that fall into each interval.
The bins are often defined as a series of discrete intervals that don't overlap.
The bins (intervals) must be close together and frequently, though not always, have the same size.
Therefore, a (A) histogram is a useful tool for condensing qualitative data.
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