Answers
(2n + 1)² - (2n + 1) is an even number for all positive integral values of n.
How to simplify an expression?
Expressions are simplified when they are rewritten in a concise manner and without any similar phrases. When we combine like terms in an expression and, if necessary, solve all of the specified brackets, we are only left with unlike terms in the simplified expression that cannot be further reduced.
What is an even number?
An even number is any number that can be divided by 2 precisely. The last digit of an even number is always one of the following: 0, 2, 4, 6, or 8. Even numbers can include 2, 4, 6, 8, 10, 12, and 14. These are even numbers because they are simple to divide by two. It is important to remember that 2 is the smallest positive even natural number.
Given, the equation under consideration is y = (2n + 1)² - (2n + 1)
Upon simplifying and solving for y, we have:
y = (2n + 1)² - (2n + 1) = 4n² + 4n + 1 - 2n - 1 ⇒ y = 4n² + (4n - 2n) + (1 - 1)
⇒ y = 4n² + 2n + 0 ⇒ y = 2 (2n² + n) --(i)
On carefully analyzing (i), we can affirm that y is divisible by 2, thus confirming that (2n + 1)² - (2n + 1) is an even number for all positive integral values of n.
Therefore, (2n + 1)² - (2n + 1) is an even number for all positive integral values of n.
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Related Questions
Tim buys a torch and a battery
The torch costs eleven times as much as the battery
Tim pays with a £10 note and gets £4.84 change
How much does the battery cost?
Answers
The cost of battery is £0.43.
Given,
In the question:
Tim buys a torch and a battery
The torch costs eleven times as much as the battery and
Tim pays with a £10 note and gets £4.84 change.
To find the how much does the battery cost?
Now, According to the question:
Let cost of battery = £ x
So, Cost of torch = £ 11x
Based on the given conditions :
=> x + 11x = £ 10 - £ 4.84
=> 12x = £ 5.16
=> x = £ 5.16/ 12
=> x = £ 0.43
Hence, The cost of battery is £0.43.
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27y over 15y in lowest terms
Answers
Given: 27y over 15y
The expression will be as following:
[tex]\frac{27y}{15y}=\text{?}[/tex]The result of the given expression will be:
[tex]\frac{27y}{15y}=\frac{27}{15}=\frac{3\cdot9}{3\cdot5}=\frac{9}{5}[/tex]The answer is 9/5
It can be written as a mixed number = 1 4/5
Which table shows a function that is decreasing only over the interval (-1, infinity)
Answers
The last table shows the function that is decreasing only over the interval [tex](-1, \infty)[/tex].
From given tables we clearly see that in below table, the functions are decreasing as 'x' increases
x f(x)
-3 -5
-1 -1
-1 -1
0 0
1 -4
2 -8
We need to find interval [tex](-1, \infty)[/tex].
In first table,f(x)=-5,-2,-1,2. Here the functions are in increasing order
In second table, f(x)=-7,-6,1,-1. Here the functions does not follow a specific order
in third table, f(x)=-1,2,1,-6, Here also the functions does not follow a specific order.
In fourth table, f(x)=1,0,-4,-8. Here the functions are in decreasing order.
Hence, the fourth table shows the function that deceases over interval [tex](-1, \infty)[/tex].
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What is the value of x in the triangle?
a 30-60-90 triangle with long leg length x and shorter leg length of 7 times the square root of 3
Answers
Answer:
sin 30 = 7 *3^1/2 / c
sin 60 = x / c definition of 30-60-90 -
sin 30 / sin 60 = 7 * 3^1/2 / x = .5 / .866 = .577
x = 7 * 3^1/2 / .577 = 21
Check: tan 30 = 7 * 3^1/2 / 21 = .577 = tan 30
As Evin is driving her car, she notices that after 1 hour her gas tank has 7.25 gallons left and after 4 hours of driving, it has 3.5 gallons of gas left in it. Assuming the relationship between h, hours, and g, gallons, is linear, write an equation for g in terms of h.
I will mark brainliest to the first person who answers.
Answers
The equation representing the gas left in h hours is g(h) = 8.5 - 1.25h
What is the concept of a linear equation?When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. An equation is an algebraic statement that demonstrates two mathematical expressions are equivalent in algebra, and this is how it is most usually used.
A linear equation is written as
y = mx + b
Where (x, y) is the ordered pair and m is the rate of change and b is the y-intercept.
Let x = time in hours
y = amount of gallons left
So, according to the question, 7.25 gallons of gas is left after 1 hour. So,
(x₁, y₁) = (1, 7.25)
3.5 gallons of gas left after 4 hours, so
(x₂, y₂) = (4, 3.5)
Find the slope
m = (y₂ - y₁) / (x₂ - x₁)
= (3.5 - 7.25)/ (4-1)
= -3.75/ 3
= -1.25
Put values of m = -1.25, (x, y) = (1, 7.25) in y= mx+b
So, 7.25 = -1.25 +b
b = 7.25 +1.25
b = 8.5
So, the linear equation for the situation in terms of g and h is
g(h) = -1.25h + 8.5
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In the figure, assume that angles that appear to be right angles are right angles.What is the area of the figure?Use 3.14 for π.The approximate area is ___ square units.Use 3.14 for π.
Answers
We can break apart the figure into a half-circle, rectangle, and a triangle.
Shown below:
We find the area of each region and sum it up to find the area of the total figure.
Area of Half CircleThe volume of the area of a half circle is
[tex]A=\frac{\pi r^2}{2}[/tex]Given, radius (r) = 3, we find the area:
[tex]\begin{gathered} A=\frac{\pi r^2^{}}{2} \\ A=\frac{\pi(3)^2}{2} \\ A=\frac{9\pi}{2} \\ A=\frac{9(3.14)}{2} \\ A=14.13 \end{gathered}[/tex]Area of RectangleThe area of a rectangle is found by multiplying the length and width.
Given,
Length = 8
Width = 6
The area is:
[tex]\begin{gathered} A=8\times6 \\ A=48 \end{gathered}[/tex]Area of TriangleThe area of a triangle is given by the formula,
[tex]A=\frac{1}{2}bh[/tex]Where
b is the base length and h is the height
Given,
b = 3
h = 6
The area of the triangle is,
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}(3)(6) \\ A=9 \end{gathered}[/tex]The total area of the figure >>>14.13 + 48 + 9
= 71.13 square unitswhich value represents between 11% and 17%?
Answers
0.159 - A
It is between 11% and 17%
19. highlight where values show g(x) = 0 and what is the answer20. highlight where values show f(x) > g(x) and what is the answer
Answers
19) g(x)=0 is the value of x at points where the line cuts the x-axis
From the graph that is at:
x=-7, x=1, x=3, and x=9
20) f(x)>g(x) where the curve f(x) is higher than the curve g(x), and this is at:
x<-3, 07
Find the sum (3.2+4x)+(18.25+6x)
Answers
Answer:
10x+21.45
Step-by-step explanation:
3.2+4x+18.25+6x
we combine like terms
4x+6x+3.2+18.25
10x+21.45
hopes this helps please mark brainliest
First write the equation without parentheses:
3.2 + 4x + 18.25 + 6x
Then combine like terms:
4x + 6x = 10x,
18.25 + 3.2 = 21.45
Plug the results and rewrite the expression:
21.45 + 10x
Finally, 21.45 + 10x should be your answer.
I’m pretty sure since this is an expression (because there’s no equal sign) and not an equation, you don’t determine the actual value of x or the sum of the numbers. In order to do that, you would need to be provided with the value of x or a number with an equal sign that the problem would equal to, so that’s why it’s still written with a plus sign as an expression.
I hope this helps! Please correct me if I’m wrong! :)
what is the line segment addition to fall the distance of the given line segment
Answers
By looking at the number line we got:
AB =5
BC=5
CD=35
So:
AC = AB+BC = 5+5=10
AD =AB+AC+CD =5+5+35=45
BD = BC+CD = 5+35 =40
which value of x below will solve equation 3/4x+10=4
Answers
3/4x+10=4
Then solve for x
3/4x = 4 - 10
x = (4-10)/(3/4)
. = -6/3/4
. = -24/3
. = -8
In consecuence , answer IS
x= -8
The graph shown shows the supply and demand for a widget. What mappens if the price is set at $25.00? Include in your answer how retailers will react to a $25.00 price point.
Answers
From the graph, if the price increases to $25
The quantity demand will decrease
Quantity supply increases --------This is the reaction from the retailers
Round the number to the place of the underlined digit. 50.633 The rounded number is
Answers
According to the rules of rounding to the nearest numbers, 50.633 rounded to the nearest whole number is equal to 51.
To round 50.633, we have to consider
The tenths’ value of the number 50.633 which is equal to 6 and it is also equal to or more than 5.
Therefore, we have to round up the part of 50.633
50, when increases by 1 results in 51
Here, the decimal point and all the following digits (.633) get removed.
Therefore, 50.633 rounded to the nearest number is equal to 51.
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Jason is a high school basketball player. In a particular game, he made some free
throws (worth one point each) and some two point shots. Jason made a total of 13
shots altogether and scored a total of 20 points. Write a system of equations that
could be used to determine the number of free throws Jason made and the number of
two point shots he made. Define the variables that you use to write the system.
Answers
The total number of free throws shots Jason made was 6 and the total number of two point shots Jason made was 7.
First, let us understand the variables:
Any number, vector, matrix, function, its argument, set, or one of its elements can be specifically represented by a variable.
Let x and y be the quantity of shorts.
x is the number of attempts at the free throw line.
y is the quantity of two-point attempts.
According to the question, we have;
x + 2y = 20 ............equation 1
x + y = 13 ............equation 2
From equation 2 we can take out the value of x;
x = 13 - y ............equation 3
substituting the value of x in equation 1, we will get;
(13 - y) + 2y = 20
13 - y + 2y = 20
13 + y = 20
y = 20 - 13
y = 7
putting the value of y in equation 3, we will get
x = 13 - 7
x = 6
Thus, the total number of free throws shots Jason made was 6 and the total number of two point shots Jason made was 7.
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A mixture of orange paint contains 8 tsp of red paint and 12 tsp of yellow paint. To make the same color of orange paint using 18 tsp of red paint, how much yellow paint would you need to use? Consider using the double number line to help
with your thinking.
Answers
After doing some mathematical operations, we know that 27 tsp of yellow colors will be needed with 18 tsp of red paint.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).So, yellow paint is used in 18 tsp of orange paint:
So,
Tsp of orange: 8 tsp of red + 12 tsp of yellowMake new but the same orange paint: 18 tsp of red + x tsp of yellowNow, form and solve an equation as follows:
8/12 = 18/x12(18) = 8x8x = 216x = 216/8x = 27Therefore, after doing some mathematical operations, we know that 27 tsp of yellow colors will be needed with 18 tsp of red paint.
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Multiply binomial by polynomials
Answers
In this case the answer is very simple . .
We must apply the distributive property of multiplication.
[tex](d^2+3)\cdot(d^2\text{ + 2d + 1) }[/tex][tex]d^2\cdot d^2+d^2(2d^{})+d^2+3(d^2\text{) + 3(2d) + 3}[/tex][tex]d^4\text{ + }2d^3+d^2+3d^2+6d+3[/tex][tex]d^4+2d^3+4d^2+6d+3^{}[/tex]That is the solution. .
Rita is playing a game by rolling a rectangular prism made up of cubes. The prism is 6 cubes wide, 3 cubes high, and 4 cubes deep. Rita rolls the cube and says that the top view is a 6-unit by 4-unit rectangle.
Which statement explains whether Rita could be correct?
Rita could be correct because the cube could land so the 3-cube height and the 4-cube depth make up the top face of the cube.
Rita could be correct because the cube could land so the 6-cube width and the 4-cube depth make up the top face of the cube.
Rita could not be correct because the top face of the cube is made up of the 6-cube width and the 4-cube depth.
Rita could not be correct because the top face of the cube is made up of the 6-cube width and the 3-cube height.
Answers
Answer:
Step-by-step explanation:
Answer:
Option B: Rita could be correct because the cube could land so the 6-cube width and the 4-cube depth make up the top face of the cube.
Step-by-step explanation:
We are told the dimensions of the prism are;
Width = 6 cubes wide
Height = 3 cubes high
Depth = 4 cubes deep.
?
Find the Area of the figure below, composed of a rectangle and a semicircle. The
radius of the circle is shown. Round to the nearest tenths place.
Area of Irregular Shapes
Nov 03, 2-44:03 PM
Answer:
9
3
20 POINTS PLEASE HELP !!!!!
Answers
Area of irregular shape is 41.13m².
Define area.The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat.
Given,
Area of irregular shape = Area of rectangle + Area of semicircle
Area of rectangle = Length × Breadth
Area of rectangle = 9 × 3
Area of rectangle = 27 m²
Area of semicircle:
1/2πr²
1/2 × 3.14 × 3²
14.13 m²
Area of irregular shape = 27 + 14.13
Area of irregular shape = 41.13
Area of irregular shape is 41.13m².
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According to the rules of significant figures:1.25 × 200 = 300True orFalse
Answers
According to the rules of significant figures:
1.25 × 200 = 300
the answer is
TRue
Solve the quadratic equation using the quadratic formula or completing the square. Show exact answers in simplified, radical form; no rounded decimals 2x^2-4x+3=0
Answers
The value of x = x = 1 - [tex]\frac{2\sqrt{2i} }{4}[/tex] and x = 1 + [tex]\frac{2\sqrt{2i} }{4}[/tex] by using quadratic formula
Given,
In the question:
The equation is :
2x^2-4x+3=0
To solve by using the quadratic formula :
Now, According to the question;
[tex]2x^2 -4x+3=0[/tex]
Identify the coefficients
a = 2, b = -4 , c = 3
Use the quadratic Formula :
x = (-b±√(b²-4ac))/(2a)
Substitute into values above formula :
x = -(-4) +√(-4)²-4x 2 x 3))/(2x2) or
x = -(-4) -√(-4)²-4x 2 x 3))/(2x2)
Determine the sign for exponential or radical expressions
x = -(-4) -√(-4)²-4x 2 x 3))/(2x2)
x = 4 -√16-4x 2 x 3))/(2x2)
Calculate the product or quotient
x = 4 -√16-24/4
x = 4 -√-8/4
x = 4 - √-8 x √-1/ 4
x = [tex]\frac{4\sqrt{2^2.2 } }{4}[/tex] x [tex]\sqrt{-1}[/tex]
Simplify the radical expression:
x = [tex]\frac{4 - 2\sqrt{2} . \sqrt{-1} }{4}[/tex]
Rewrite by definition i = [tex]\sqrt{-1}[/tex]
x = [tex]\frac{4-2\sqrt{2i} }{4}[/tex]
x = 1 - [tex]\frac{2\sqrt{2i} }{4}[/tex]
Hence, The value of x = x = 1 - [tex]\frac{2\sqrt{2i} }{4}[/tex] and x = 1 + [tex]\frac{2\sqrt{2i} }{4}[/tex] by using quadratic formula .
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3 times x increased by 20 as a algebraic expression
Answers
Answer:
3x+20
Step-by-step explanation:
“3 times x” means 3x
and “increased by 20” means to add 20 to the equation.
if you were to solve this equation, the answer to the first step would be 6.666!
divide each side by 3. 3/3 is 1, and 20/3 is 6.666! therefore, the 1 cancels out and you get this number, which is the value of x.
now, for the second step, you would get 39.998, which is your overall answer! all you have to do is replace x with the answer from the previous step (6.666)
i hope this helped!!
Circle O shown below has a radius of 25 inches. To the nearest tenth of an inch,determine the length of the arc, x, subtended by an angle of 137°.
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
[tex]Length\text{ of Arc =}\frac{\theta}{360^0}\text{ x 2}\pi\text{ r}[/tex][tex]\begin{gathered} where\text{ }\theta\text{ = 137}^0 \\ radius\text{ = 25 inches} \end{gathered}[/tex][tex]Length\text{ of arc = }\frac{137^0}{360^0}\text{ x 2 x }\pi\text{ x 25}[/tex][tex]Length\text{ of arc =}\frac{137^0}{360^0}\text{ x }\frac{50\pi}{1}[/tex][tex]Length\text{ of Arc = }\frac{21,519.90968}{360}[/tex][tex]Length\text{ of Arc = 59.77752688 inches}[/tex][tex]Length\text{ of Arc }\approx\text{ 59. 8 inches \lparen to the nearest tenth \rparen}[/tex]Perform the indicated operations and write the result in
standard form.
6) 3√√-16 +2√√-64
A) -28i
C) -28
B) 281
D) 28
Answers
The standard form of the expression 3√-16 +2√-64 is 28i
The square root of minus one √(−1) is the "unit" Imaginary Number, the equivalent of 1 for Real Numbers. In mathematics the symbol for √(−1) is i for imaginary.
We need to write the expression is 3√-16 +2√-64 in standard form
The value of √-1 is i
3√-16 + 2 √-64
3√-1 √16 + 2√-1 √64
3 i 4 + 2 i 8
12 i + 16 i
= 28 i
Therefore, the standard form. of the expression 3√-16 +2√-64 is 28i
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<
An inequality is shown.
-2x+12<18
What is the solution to the inequality?
0x<3
x>3
Answers
Answer:
-3 < x
Step-by-step explanation:
first of all get the positive x on one side, so we have
12 < 18 + 2x ( positive x is easier to work with)
then, get only x on one side
-6 < 2x
simplify
-3 < x
HELP QUICK 30 POINTS!!!!
What equation is graphed in this figure?
A. y−4=−2/3(x+2)
B. y+2=−3/2(x−2)
C. y+1=−2/3(x−3)
D. y−3=3/2(x+1)
Answers
Answer:
B is correct. The slope is -3/2.
Answer:D
Step-by-step explanation:
Which of the following shows a graph of a tangent function in the form y = atan(bx − c) + d, such that b equals one half question markgraph of tangent function with one piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 2 times pi passing through the points negative 3 times pi over 2 comma negative 2 and negative pi comma negative 1 and negative pi over 2 comma 0 to the right asymptotic to the line x equals 0 and another piece that increases from the left in quadrant 4 asymptotic to the line x equals 0 passing through the points pi over 2 comma negative 2 and pi comma negative 1 and 3 times pi over 2 comma 0 to the right asymptotic to the line x equals 2 times pigraph of tangent function with one piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 2 times pi passing through the points negative pi comma negative 2 and 0 comma negative 1 and pi comma 0 to the right asymptotic to the line x equals 2 times pigraph of tangent function with one piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 2 times pi passing through the points negative 3 times pi over 2 comma 1 to the right asymptotic to the line x equals negative pi and another piece that increases from the left in quadrant 3 asymptotic to the line x equals negative pi passing through the point negative pi over 2 comma 1 to the right asymptotic to the line x equals 0 and continuing periodicallygraph of tangent function with one piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 7 times pi over 4 passing through the point negative 3 times pi over 2 comma negative 1 to the right asymptotic to the line x equals negative 5 times pi over 4 and another piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 5 times pi over 4 passing through the point negative pi comma negative 1 to the right asymptotic to the line x equals negative 3 times pi over 4 and continuing periodically
Answers
In general, given
[tex]y=a*tan(bx-c)+d[/tex]b is related to the period of the function, such that, in the case of the tangent function,
[tex]period=\frac{\pi}{b}[/tex]Remember that the period of tan(x) is equal to pi.
Therefore, in our case,
[tex]\begin{gathered} b=\frac{1}{2} \\ \Rightarrow period=\frac{\pi}{\frac{1}{2}}=2\pi \end{gathered}[/tex]The period of the function is 2pi, which means that it repeats every 2pi units.
Thus, the answer is the first graph, the one shown below.Dada a função y= -3x²+5x+2
Answers
Answer:
y= -4x+2
Step-by-step explanation:
y= -3x²+5x+2
y= -9x+5x+2
y= -4x+2
How many times larger is 6 × 108 than 3 × 10-4?
Answers
Answer:
About 24.9 or 25 (if rounded to the nearest whole number or tenth).
Attendance at october fest was 15% more than last year. this year's attendance was 1785 people. find the number of people who attended the festival last year. rounded to the nearest person
Answers
Using the concept of equations, 1552 people attended the festival last year.
What are algebraic equations?Two algebraic expressions are combined to create an algebraic equation using the equals (=) sign. Algebraic equations are also known as polynomial equations since they contain polynomials on both sides of the equal sign. An algebraic equation consists of variables, coefficients, constants, and algebraic operations including addition, subtraction, multiplication, division, and exponentiation.
An integer or set of integers that satisfy the condition in the equation are the roots or solutions of an algebraic equation.
Let the number of people who attended the festival last year =x
Then, we can write an equation as
1785=1.15 × x
x = 1785/1.15
=1552 people
So, last year's attendance = 1552
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number 8 State how you know each pair of triangles are congruent
Answers
trianglesPairs of congruent triangles
Triangles A is congruent since UV = WX
Triangle Δ KLJ = Δ MNO and are congruents
Triangle Δ UGI ≠ Δ MNO ≠ ΔKLJ is congruent