This proves that the sum of 1/2n(n+1) + 1/2(n+1)(n+2) is always a square number.
What is square number?When a number is multiplied by itself, the result is a square number. As an illustration, 25 is a square number as it is composed of 5 groups of 5, or 5 x 5. A square number, sometimes 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 as it equals 32 and is represented by the symbols 3.
Here,
Find the sum:
=1/2n(n+1) + 1/2(n+1)(n+2)
=1/2(n² + n) + 1/2(n² + 3n + 2)
=1/2(n² + n + n² + 3n + 2)
=1/2(2n² + 4n + 2)
=n² + 2n + 1
=(n + 1)²
This demonstrates that 1/2n(n+1) + 1/2(n+1)(n+2) is always a square number when added together.
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Divide. If there is a remainder, include it as a simplified fraction.
(-24a³ + 16a²) ÷ 4a
Answer: -6a^2+4a
Step-by-step explanation: simplify
Megan opens a savings account which gives compound interest of 2.5% per
year. She puts £2000 into it.
a) How much money will Megan have in the account after 7 years?
b) How much interest will Megan have earned from this account after 7 years?
Give your answers in pounds (£) to the nearest 1p.
Using compound interest, it is found that:
a) The amount of money that she will have is of £2377.
b) The interest she will have earned is of £377.
What is compound interest?The balance of an investment of P in compound interest after t years is modeled as follows:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which the remaining parameters are:
r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The values of these parameters in this problem are given as follows:
P = 2000, r = 0.025, n = 1, t = 7.
Hence the balance of the account after 7 years will be of:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(7) = 2000\left(1 + \frac{0.025}{1}\right)^{7}[/tex]
A(7) = 2377.
The interest earned is calculated as the final balance subtracted by the principal, hence:
I(7) = A(7) - P
I(7) = 2377 - 2000
I(7) = 377.
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What is the simplified form of this expression? (x+y)(x³y-3)
The simplified form of this expression is x^4y-3x+y^2x^3-3y
From the question, we have
(x+y)(x^3 y-3)
= xx^3 y-x⋅3+yx^3 y-y⋅3
=x^4y-3x+y^(1+1) x^3-3y
=x^4y-3x+y^2 x^3-3y
The simplified form of this expression is x^4y-3x+y^2 x^3-3y
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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The table shows the high temperature on the moon during the day and the overnight low temp.
time of day | temperature
day | 253
night | -387
what is the range between the moons minimum temp in degrees fahrenheit?
The range between the moon's minimum and maximum temperature in degrees Fahrenheit is 640°F
From the question, we have
Time of Day Temperature
Day 253°F
Night -387°F
the moon's minimum temperature = -387°F
and maximum temperature = 253°F
range = 253 - (-387) = 640°F
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
Complete question:
The table shows the high temperature on the moon during the day and the overnight low temperature.
Time of Day Temperature
Day 253°F
Night –387°F
What is the range between the moon's minimum and maximum temperature in degrees Fahrenheit?
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..........................................
Answer:
.....................................
Step-by-step explanation:
f(x) = 2x² + 7x + 18
Find f(-4)
Answer:
f(- 4) = 22
Step-by-step explanation:
substitute x = = - 4 into f(x)
f(- 4) = 2(- 4)² + 7(- 4) + 18 = 2(16) - 28 + 18 = 32 - 10 = 22
Spiral Review A room is 15 feet long and 12 feet wide. A scale drawing of the room is 10 inches by 8 inches. What is the scale of inc
in the drawing to inches in the actual room?
Enter the correct answer in the box.
The scale of increase in the drawing to inches in the actual room is 18
A room is 15 feet long and 12 feet wide. A scale drawing of the room is 10 inches by 8 inches
1 feet = 12 inches
Initially the room's length = 15 feet = 15 x 12 = 180 inches
On scale drawing the length = 10 inches
Let the scale of inc in the drawing to inches in the actual room be k
10 x k = 180
k = 180 / 10 = 18
Initially the room's width = 12 feet = 12 x 12 =144 inches
On scale drawing the width = 8inches
8 x k = 144
k = 18
Therefore, the scale of inc in the drawing to inches in the actual room is 18
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.
Find the value of the variable(s) in each figure.
(9x+12)3x(4y-10)13x
For the given figure, the value of the variable x is 14° and the value of the variable y is 37°.
Variable:
Variable is known as an alphabet which is used to represent the unknown number.
Given,
Here we have the figure with the expressions
(9x + 12)°
3x°
(4y - 10)°
Now, we have to find the value of the variables x and y.
Here we know that the "If two lines which are parallel are intersected by a transversal then the pair of interior angles on the same side of the transversal are supplementary."
So, here we have write the given values as,
=> (9x + 12)° + 3x° = 180°
=> (12x + 12)° = 180°
=> 12x° = 168°
=> x = 14°
Similarly, the value of y s calculated as,
=> (4y - 10)° + 3x° = 180°
We know the value of x, then the value of y is,
=> (4y - 10)° + 3(14)° = 180°
=> 4y - 10 + 42 = 180°
=> 4y = 148
=> y = 37°
Therefore, the value of the variable x is 14° and the value of the variable y is 37°.
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Kelsey buys several pairs of uniform pants for $17.95 each, and a sweater for $24.
Jeana shops at a different store and buys several pairs of uniform pants for $18.95 each, plus a sweater for $18.
They set up the situation with the equation below, where x is the number of pairs of pants.
Is there a situation in which they pay the same amount for their purchases?
Select all the statements that correctly represent this situation.
17.95x + 24 = 18.95x + 18
OA
OB
There are no solutions to the equation.
There is one solution to the equation.
Review Progress
Type here to search
O
E
Q
What type of solution is this?
There is one solution to the equation.
What is solution of the equation?
An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Given: Kelsey buys several pairs of uniform pants for $17.95 each, and a sweater for $24.
Jeana shops at a different store and buys several pairs of uniform pants for $18.95 each, plus a sweater for $18.
The equation represents the situation is,
17.95x + 24 = 18.95x + 18
Subtract 18 from both sides,
17.75x + 24 - 18 = 18.95x + 18 - 18
17.95x + 6 = 18.95x
18.95x - 17.95x = 6
x = 6
Therefore, there is one solution to the equation.
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Line 1: 4x + 2y = 12
Line 2: 3x - 6y =18
State the slope of each line, then determine if the lines are parallel, perpendicular, or neither.
slope of line 1 =
slope of line 2 =
Are the lines parallel, perpendicular, or neither?
Answer:
lines are perpendicular
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
line 1
4x + 2y = 12 ( subtract 4x from both sides )
2y = - 4x + 12 ( divide through by 2 )
y = - 2x + 6 ← in slope- intercept form
slope of line 1 = - 2
line 2
3x - 6y = 18 ( subtract 3x from both sides )
- 6y = - 3x + 18 ( divide through by - 6 )
y = [tex]\frac{1}{2}[/tex] x - 3 ← in slope- intercept form
slope of line 2 = [tex]\frac{1}{2}[/tex]
• Parallel lines have equal slopes
Clearly the lines are not parallel
• the product of the slopes of perpendicular lines = - 1
- 2 × [tex]\frac{1}{2}[/tex] = - 1
then Line 1 and Line 2 are perpendicular to each other
Suppose adam wants to have $750,000 in his ira at the end of 30 years. He decides to invest in an annuity paying 6% interest, compounded annually. What does he have to contribute each year to reach this goal? enter your answer, rounded to the nearest cent. Omit the dollar sign and the comma.
Each year Adam have to contribute $9486.68 to reach his goal of $750000 .
In the question ,
it is given that ,
Adam wants to have $75000 at the end of 30 years .
So ,the future value (FV) = 75000
the interest rate compounded annually = 6%
So , i = 6% = 0.06
given n = 30 , where n is the number of periods in which payments will be made .
we know , that the formula to calculate the Future value of the Annuity is
[tex]FV=PMT\times(\frac{(1+i)^{n}-1) }{i} )[/tex]
where ,
FV = Future Value
PMT = Periodic Payment
i = interest rate
n [tex]=[/tex] number of periods in which payments will be made .
Substituting the values in the formula ,
we get ,
75000 = PMT×((1+0.06)³⁰-1)/0.06)
75000×0.06 = PMT×(1+0.06)³⁰-1)
PMT = 45000/(1+0.06)³⁰-1)
PMT = 9486.6836
PMT ≈ 9486.68
Therefore , Each year Adam have to contribute $9486.68 to reach his goal of $750000 .
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to learn about the tv viewing habits of all the children attending oakbridge school, professor hull randomly selected and interviewed 50 of the school students. in this instance, all the children attending the school are considered to be a(n) population. representative sample. independent variable. control condition.
Answer:
representative sample
Step-by-step explanation:
ik things
Which of the following is equivalent to the expression below?
ln(e^4)
The equivalent expression is;
⇒ ln (e⁴) = 4
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 expression is,
⇒ ln (e⁴)
Now,
Since, We know that;
ln (eˣ) = x
So, We can apply the above rule, we get;
⇒ ln (e⁴) = 4
Thus, The equivalent expression is;
⇒ ln (e⁴) = 4
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If a population of 1000 people were to increase by 5% every year, what would the
population be in 20 years?
Population in 20 years is 2654 .So option(2) is correct
A percentage is a percentage of something expressed as a number between 0 and 100 rather than as a fraction. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.
Given that a population of 1000 people were to increase by 5% every year
We have to determine the population be in 20 years
P = 1000
R = 5
T = 20
Population in 20 years = P[(1+(r/100)]t
= 1000[1 + 5/20]20
= 1000(21/20)20
= 1000 x 2.6538
= 2653
Therefore population in 20 years is 2654
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2.5 > -8 + v Solve the inequality for v.
Simplify your answer as much as possible.
Answer: 10.5 > v
Step-by-step explanation:
Add both sides by 8 to isolate the right side to just v. You would get 10.5 > v as a result.
find the exact value of the fallowing ,give your answers as factions ;
a)3^-2
b)4^-3
c)2^-6
A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
3² = 3 X 3 = 9
4³ = 4 x 4 x 4 = 64
[tex]2^{6}[/tex] = 2 x 2 x 2 x 2 x 2 x 2 = 64
The exact value in fractions are:
a) 1/9
b) 1/64
c) 1/64
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
[tex]3^{-2}[/tex]
= 1/3²
3² = 3 X 3 = 9
= 1/9
[tex]4^{-3}[/tex]
= 1/4³
4³ = 4 x 4 x 4 = 64
= 1/64
[tex]2^{-6}[/tex]
= 1/[tex]2^{6}[/tex]
[tex]2^{6}[/tex] = 2 x 2 x 2 x 2 x 2 x 2 = 64
= 1/64
Thus.,
The exact value in fractions are:
a) 1/9
b) 1/64
c) 1/64
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Please help
1. what is 1+1=
2. 2+_=22
3. 10,999,999 divided by 2 (round it in the nearest whole number)
Answer:1. 2
2. 20
3. 5499999.5 or5500000
Step-by-step explanation:
Answer:
1. 2
2. 20
3. 5,499,999.5 = 5,500,000
A fruit company needs to mail an order of 8,927 watermelons. If each crate can hold 79 watermelons, how many crates will the company need?
i suck at division.
Answer:
113 crates
Step-by-step explanation:
hope it helped :)
Find the length of the third side. If necessary, write in simplest radical form
Answer:
5
Step-by-step explanation:
By the Pythagorean Theorem:
[tex] {x}^{2} + {10}^{2} = {(5 \sqrt{5} )}^{2} [/tex]
[tex] {x}^{2} + 100 = 125[/tex]
[tex] {x}^{2} = 25[/tex]
[tex]x = 5[/tex]
A new soup recipe contains 33\%33%33, percent less sodium per serving than the old soup recipe. The old soup recipe contained xxx milligrams of sodium per serving.
Which of the following expressions could represent the amount of sodium per serving, in milligrams, in the new soup recipe?
The expression that could represent the amount of sodium per serving, in milligrams, in the new soup recipe would be = (1 - 33/100)X but when simplified it can be represented with 0.67x.
What is sodium?Sodium is defined as an element that is made up of 11 electrons revolving round it's atomic orbit. It serves as the major component of common salt found in food products.
From the question;
The new soup recipe = - 33% = - 33/100
The old soup recipe = X milligrams.
Since the new recipe is 33/100 less than the old soup recipe.
The new soup recipe would be = (1 - 33/100)X
When further simplified;
= 1 - 33/100
= 100-33/100
= 67/100
= 0.67x
Therefore, the new soup recipe can be represented with the above derived expressions such as (1 - 33/100)X and 0.67x when simplified.
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For a concert event there are 30 reserved seat tickets and 20 general admission tickets. There are 1,900 reserved seats available, and fire regulations limit the number of paid ticket holders to 2,800. The promoter must take in at least 63,000 in ticket sales?
The system of inequalities is as follows:
30x + 20y ≥ 63,000
x ≤ 1900
x + y ≤ 2800
What is inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality'.
Given that, for a concert event, there are 30 reserved seat tickets and 20 general admission tickets. There are 1,900 reserved seats available, and fire regulations limit the number of paid ticket holders to 2,800.
The system of inequalities can be explained as follows:
30x + 20y ≥ 63,000 → Indicating a take in of at least $63,000 in ticket sales.
x ≤ 1900 → Indicating that 500 reserved seats are available.
x + y ≤ 2800 → Indicating limits of the paid ticket holders to 2800.
x ≥ 0 → Indicating ticket x must be equal or greater than 0.
y ≥ 0 → Indicating ticket y must be equal or greater than 0.
Hence, The system of inequalities is as follows:
30x + 20y ≥ 63,000
x ≤ 1900
x + y ≤ 2800
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17. how many cards must be drawn from a standard 52-card deck to guarantee 2 cards of the same suit?
If you want to guarantee that two cards are from the same suit, you need only draw five cards (since there is no way you can draw five cards without at least two of them being the same suit)
What is probability ?Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.
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The following equation can be used to determine c, the cost of a taxicab ride of m miles.
c = 3.5m + 3
What will happen to the cost of the taxicab ride if the distance increases by 2 miles?
A. The cost will go up by $2.00
B. The cost will go up by $3.50
C. The cost will go up by $6.50
D. The cost will go up by $7.00
Graph the points of the given function with the x-values x=−2 , x = 2, and x = 7. f(x)=−3x+2−−−−√
By evaluating the linear function we will get the 3 points:
A. (-2, 8)
B. (2, -4)
C. (7, -19)
You can see the graph on the image at the end.
How to graph the points?Well, the first thing we need to do is get these points, to do so, we need to evaluate the linear function in the given values.
We have f(x) = -3x + 2
if x = 2
f(2) = -3*2 + 2 = -4
if x = -2
f(-2) = -3*-2 + 2 = 8
if x = 7
f(7) = -3*7 + 2 = -19
So we have the points (-2, 8), (2, -4), and (7, -19)
The graph of these 3 points can be seen in the image below.
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Simplify 5(2x-3)-2(3x-8)
Answer: 4x+1
Step-by-step explanation:
1. 5(2x-3)-2(3x-8)
2. 10x-15-2(3x-8)
3. 10x-15-6x+16
4. 10x+1-6x
5. 4x+1
Answer:
4x+1
Step-by-step explanation:
First you have to expand it like 10x-15-2(3x-8) Basically multiplying 5 with 2x and -3.
Then take -2 multiply with 3x and -8 which will make it 10x-15-6x+16
Now Put together the like terms 10x-6x -15+16
Which makes it 4x+1
Hope it helped! I am a student too.
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Carmen worked for 13 hours each day for 5 days. Then the next day she worked 6 hours. How many hours did Carmen work in
all?
71 Hours
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What does the data above tell you about the difference in haircut costs between women and men? You may want to discuss similarities or differences in the shape, center, and spread of the data. Explain your reasoning and give mathematical evidence to support any claim that you make.
The difference shows that woman on average pays higher than men.
What is mean/ average?
Mean is that the average of the given ranges and is calculated by dividing the add of given numbers by the whole number of numbers.
Main body:
The wider range in prices may be due to the higher number of observation.
females have a bigger spread and overall higher cost. 50% of females spend between $20-$75 on a haircut, while 50% of men only spend between $9.25-$20. The median for Female is also significantly higher.
The mean is higher due to the high max valves that are bringing the mean up.
Hence from observing we can say that woman on average pays higher than men.
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Ken and hamid run around a track
it take ken 80 econd to complete a lap. It take hamid 60 econd to complete a lap
ken and hamid tart running at the ame time from the tart line
how many lap will they each have run when they next meet on the tart line?
Ken will run 3 laps and Hamid will run 4 laps in 80 and 60 seconds.
To find this, we first find the number of seconds that will have passed when they meet again. We use the LCM, or least common multiple, for this. First we find the prime factorization of each number:
LCM of 80 and 60 = 2X2X5X4X3
= 4X5X4X3
= 240
Now, divide the respective seconds from the total 240, we get
for Ken, 240÷ 80 = 3 laps
For Hamid, 240÷ 60 = 4 laps
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Which of the following is an example of a linear function in two variables?
a. 13 - √x = y
b. 3.1y - 6 = 7x
c. 3x + 4y = 11z + 1
d. 10 - xy = 4
The option that is an example of a linear function in two variables is b. 3.1y - 6 = 7x
What is a linear function?Linear functions have a straight line as their graph. The following is the form of a linear function. y = f(x) + a+bx There is one independent variable and one dependent variable in a linear function.
A straight line on the coordinate plane is represented by a linear function. For example, y = 3x - 2 denotes a straight line on a coordinate system.
Linear equations are classified into three types: point-slope, standard, and slope-intercept.
In this case, we can see that the variables are x and y. Therefore, the correct option is B.
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Which ordered pair in the form (x, y) is a solution of this equation? x+6y=9 (4.1) (2,1) (12,2) (-3,2)
