Answer: A sequence is a enumerated collection of objects in which repetitions are allowed/order matters while a series is a infinite series. A series is definite if its based on the concept of sequences.
A series could be finite or infinite because its mainly often represented in compact form which is also known as a sigma notation(∑)to indicate the summation involved. infinite series is the sum of an infinite sequence.
Step-by-step explanation:
What is the solution set of the equation
3X=-6/1-X
for x # 1?
The solution set of the equation 3X=-6/1-X for x # 1 is {-2,1)
3x = -6/(1-x)
3x(1-x) = -6
3x – 3x2 = -6
Taking 3 as common from both sides
x –x2 = -2
x2 – x +2 =0
Using factorisation method we will get two factors
Factoring quadratics is a method of expressing the quadratic equation ax2 + bx + c = 0 as a product of its linear factors as (x - k)(x - h), where h, k are the roots of the quadratic equation ax2 + bx + c = 0. This method is also is called the method of factorization of quadratic equations. Factorization of quadratic equations can be done using different methods such as splitting the middle term, using the quadratic formula, completing the squares, etc.
( x – 2)(x+1)=0
So, x = 2 , -1
Now, when x ≠ 1
The solution of the equation will vary from {-2,1) .
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please help with this question, thank you!!
Answer:
[tex]-\sqrt{2}[/tex]
Step-by-step explanation:
Note that:
[tex]a^2-2ab+b^2=(a-b)^2 = 4ab \\ \\ a^2 + 2ab+b^2 = (a+b)^2 = 8ab \\ \\ \implies \frac{a+b}{a-b}=\frac{\sqrt{8ab}}{-\sqrt{4ab}}=-\sqrt{2}[/tex]
Answer:
[tex]\sf \dfrac{a+b}{a-b}= -\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sf a^2 + b^2 = 6ab \qquad where\:\:0 < a < b[/tex]
Basic formula:
[tex]\sf (a + b)^2 = a^2 +b^2 +2ab[/tex]
[tex]\sf (a - b)^2 = a^2 + b^2 -2ab[/tex]
solve for a + b
[tex]\sf \rightarrow a^2 + b^2 = 6ab[/tex]
[tex]\sf \rightarrow (a+b)^2-2ab = 6ab[/tex]
[tex]\sf \rightarrow (a+b)^2 = 6ab+2ab[/tex]
[tex]\sf \rightarrow (a+b)^2 = 8ab[/tex]
[tex]\sf \rightarrow a+b = \pm \sqrt{8ab}[/tex]
solve for a - b
[tex]\sf \rightarrow a^2 + b^2 = 6ab[/tex]
[tex]\sf \rightarrow (a-b)^2 + 2ab = 6ab[/tex]
[tex]\sf \rightarrow (a-b)^2 = 6ab-2ab[/tex]
[tex]\sf \rightarrow (a-b)^2 = 4ab[/tex]
[tex]\sf \rightarrow a-b = \pm \sqrt{4ab}[/tex]
Now solve for (a + b)/(a - b)
[tex]\sf \rightarrow \dfrac{a+b}{a-b}= \dfrac{\pm\sqrt{8ab} }{\pm\sqrt{4ab} }[/tex]
[tex]\sf \rightarrow \dfrac{a+b}{a-b}= \pm \sqrt\dfrac{8ab }{4ab}[/tex]
[tex]\sf \rightarrow \dfrac{a+b}{a-b}= \pm \sqrt{2}[/tex]
As, the value of b is greater than the value of a and both the values a and b are greater than 0. It turns the value of expression negative as the denominator will be always evaluated to negative integer and the numerator value always > 0. So, the answer will be negative, -√2.
[tex]\sf \rightarrow \dfrac{a+b}{a-b}= - \sqrt{2}[/tex]
find the LCM of 34,40,168
Answer:
14,280...............enjoy
A television cost $1,275. It is marked down 35%. What is the new cost of the television? Please answer this!!!
Answer:
$446.25
Step-by-step explanation:
1275 x 35% = 446.25
So, the television would be $446.25
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Hope this helps!
Have a great day and God bless! :)
The african bush elephant weights about 4.4 tons and 7.7 tons what are if least and greatest sight rounded to the nearest ton
The least ton is 4 ton and the greatest ton is 8 ton.
Given an approximation for the weight of African bush elephant.
If we take x as the weight of an African Bush elephant, then
4.4 < x < 7.7.
We are asked to find the least and greatest weights rounded to the nearest ton.
The least weight is 4.4. But when rounded to the nearest ton, we can consider the least weight at 4 tons.
Likewise, the greatest weight is 7.7 tons.
But the greatest weight rounded to the nearest ton = 8 tons
We rounded 4.4 to 4 because the decimal digit 4 is less than 5.
Also we rounded 7.7 to 8 because the decimal digit 7 is greater than 5.
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PUNTOS Write the equation of the line parallel to y = -1/3x + 4 and passing through the point (-6, -9). Be sure to write your answer in slope-intercept form(y=mx+b)
The slope intercept of the line is y = -1/3x -11
Slope-intercept is one of the special forms of line equation
The slope intercept of a line can be found by solving the slope-intercept equation of a line which is parallel to that line.
Slope-intercept equation is
y = mx + b
where m is the slope and b is the intercept.
The slope-intercept equation of the parallel line is
y = -1/3x + 4
The slope will be the same for both lines as they were parallel to each other.
Thus m = -1/3
The point in which the line passes is given as (-6,-9)
So with these data, We can find the intercept of the line
y = mx + b
where m = -1/3 and (x,y) is (-6,-9),Thus
-9 = -1/3(-6) +b
-9 = 6/3 +b
-9 = 2 + b
b = -9-2
b = -11
Thus the intercept of the line passing through the point (-6,-9) is -11
Thus, the slope-intercept equation of the line we need to find is
y = -1/3x -11
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
Step-by-step explanation:
"rise" is 10 units
"run" is 6 units
m = [tex]\frac{rise}{run}[/tex] = [tex]\frac{10}{6}[/tex] = [tex]\frac{5}{3}[/tex]
m = [tex]\frac{5}{3}[/tex]
Question 2(Multiple Choice Worth 2 points)
(01.03)
Solve for x, given the equation √x+9 -4 = 1.?
Answer:
x = 16
Step-by-step explanation:
Write the terminology for the power of a factored expression of a polynomial
function.
Answer:
a power function is a function with a single term that is the prudoct of a real number
A cereal box manufacturer changes the size of the box to increase the amount of cereal it contains. The expressions 16 + 6.6n and 14 + 7.1n, where n is the number of
box? smaller boxes, are both representative of the amount of cereal that the new larger box contains. How many smaller boxes equal the same amount of cereal in the larger
The larger box of cereal has as
(Type a whole number.)
boxes
Answer:
The answer should be 10.5 from what i have seen in the past
Step-by-step explanation:
Find the area of the triangle
Answer:
Step-by-step explanation: lengthxwidth
Question in photo. Too lazy to solve lol (I might mark u as brainliest if u answer)
Answer:
The first, third, and fourth.
Step-by-step explanation:
Those answers involve scaling the measurement up, which requires a positive power of 10. For scaling down, you'll need a negative power of 10, e.g., 2x10^-2=0.02.
use the space provided to create a list of important talent, skills and competencies a person will need to fill the position on (business functions on ) purchasing
There is space to identify the important talents, abilities, and competencies a person will need because every company aims to attain financial stability by streamlining its operations using resources.
A stable economy is what?Every firm strives to achieve financial stability by streamlining its operations with resources, thus there is room available to identify the critical talents, abilities, and competencies a person will require.
What is financial stability?"A state in which the financial system is not unstable" is the definition of financial stability. It may also refer to a state of stability among the three elements of the financial system, namely the infrastructure, markets, and institutions.The phrase "stability of financial institutions" refers to the degree to which each financial institution is sound enough to effectively perform the function of financial intermediation.Due to the advancement of financial deregulation, many nations around the world have experienced the benefits of rapid financial industry growth since the 1980s.
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What is the value of the expression -2/7 - 4/7
Answer: -6/7
Step-by-step explanation: combine like terms.
Same signs; add, different signs; subtract.
The graph of f(x) is increasing on
(-∞, 0) and decreasing on (0, +∞).
Which statement must be true?
A f(x) has a maximum at x = 0.
B f(x) has a minimum at x = 0.
The domain of f(x) is (0, +∞).
D The range of f(x) is (0, +∞).
Answer: c
Step-by-step explanation:
Simplify this expression.
9y + 3 - 4y + x +9
Answer: 5y + x + 12
Step-by-step explanation:
9y + 3 - 4y + x + 9
Group together 9y and -4y
5y + 3 + x +9
Group together 3 + 9
5y + 12 + x
Reorder the expression.
5y + x + 12
Ana compra en la tienda 15/20 gramos de jamon y 15/20 gramos de queso y quiere saber a cuanto equivale en decimales
15/20 gramos equivalen a 0 . 75 en forma decimal. Si se supone que las cantidades decimales deben sumarse, entonces 1 . 5
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Espero que esto te ayude.
Que tengas un buen día y que Dios te bendiga. :)
HELP.................................! !
Answer:
0.063
Step-by-step explanation:
Answer:
Your answer would be 0.063.
Step-by-step explanation:
0.504 divided by 8 = 0.063
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Hi again! :)
God bless! :)
Arianna and her friends are preparing for an epic snowball fight. They make 80
snowballs before Arianna's dad calls them in for lunch. After lunch, they make more
snowballs. In all, Arianna and her friends make 161 snowballs.
Which equation can you use to find the number of snowballs s Arianna and her
friends make after lunch?
Answer: 161-80=81
(or 161-x=y?)
Step-by-step explanation:
subtract the the amount of snowballs made before Adrianna's dad called them in for lunch from the total number of snowballs (161-80)
161-80=81
*the puzzle* n 48 abcd w 117 efgh a) professor x traveled 1500 miles to see jean grey. he read one book every 450 miles he traveled. how many books had he finished by the time he arrived? b) storm had $74 and withdrew some more money from her bank account. she bought a pair of slacks at $34, two shirts at $16 each and a pair of shoes at $24. after shopping, storm had $15 left. how much money did she withdraw from the bank? c) there are 12 pacific northwest geocachers in wolverine's living room. six of them are wearing socks, four of them are wearing shoes, while four people are wearing both socks and shoes. how many geocachers have nothing on their feet for their upcoming geo-excursion together? d) cyclops will buy a new pair of shoes in 1200 seconds. how many minutes must he wait before he can buy them? (second digit in the answer!) e) quicksilver collected 700 nickels in a jar. he went to the bank to cash them in. how much money did the bank give him? f) for breakfast, mystique bought a bagel for $1.55 and a glass of orange juice for $2.25. at lunch, mystique spent $6.25 on a sandwich and $0.55 on a carton of milk. how much more money did she spend on lunch than on breakfast? g) mirage had three pizzas. each pizza had eight slices. if mirage at 75% of the pizza slices, how many were left? h) iceman has a highlighter obsession. in his desk drawer, there are 19 yellow highlighters. there are 15 more blue highlighters than yellow, and there are 37 green highlighters total. how many more green highlighters than blue does he have?
He finished the number of books by the time he arrived = 3.3 books, b) she withdrew $15 from her bank account. c) 6 people have nothing on their feet.d) He must wait before he can buy the pair of shoes = 20 minutes. e) After dividing the bank gives him 700 nickels = $35. f) She spent more money on lunch than breakfast = $3. g) After eating the mirage slices left = 6 slices. h) He has more green highlighter than blue = 3
a) professor finished 3 books by the time he arrived.
Professor x traveled to see jean grey = 1500 miles
He read one book he traveled = 450 miles
So,
He finished books by the time he arrived by dividing both the numbers = 1500/450
He finished total books by the time he arrived = 3.3 books
b) Storm had money = $74
She bought a pair of slacks = $34
She bought two shirts = $16
She bought a pair of shoes = $24
After shopping she left with = $15
Storm expenses on the items = $34 + $16 + $24
= $74
So, after shopping she left with $15 so it is clear that she withdrew $15 from her bank account.
c) Pacific northwest geocachers in wolverine’s living room = 12
Wearing shoes = 4
Wearing socks = 6
Wearing both socks and shoes = 4
As we know 4people wearing both socks and shoes
So, 2 people are wearing only sock
And no people wearing only shoes = 4-4=0
So, in total 4+2+0= 6
Now, 12 people are there
So, 12-6=6
So, 6 people have nothing on their feet.
d) Cyclops waited 20 minutes
Cyclops will buy a new pair of shoes = 1200 seconds
Here, 60 minutes = 3600 seconds
Now, divide 1200 seconds by a minute (1 minute = 60 sec)
He must wait before he can buy the pair of shoes = 1200/60
He must wait before he can buy the pair of shoes = 20 minutes
e) Quicksilver collected nickels in a jar = 700
First, we have to calculate how many cents are there in 700 nickels by multiplying 700 * 5, and then dividing that result by 100 cents
=700 nickels x 5 cents
= 3,500 cents ( 100 cents = $1)
= 3,500 cents / 100 cents
The bank gives him 700 nickels = $35
f) For breakfast, Mystique bought a bagel = $1.55
A glass of orange juice = $2.25
At lunch,
On sandwich, she spent = $6.25
On a carton of milk, she spent = $0.55
Total spent on breakfast = $1.55+$2.25
= $3.80
Total spent on lunch = $6.25+$0.55
= $6.80
She spent more money on lunch than breakfast = $6.80-$3.80
She spent more money on lunch than breakfast = $3
g) Mirage had 3 pizzas
Each pizza had = 8 slices
So, After multiplying total number of slice we have of the pizza = 3*8
= 24 slices
He ate 75% of the pizza slices = 75/100 * 24
= ¾ * 24
After multiplying, he ate pizza slice = 3 * 6
= 18 slices
So, after eating by the mirage slices left = 24-18
= 6 slices
h) He has 3 more green highlighters than blue highlighters.
In the iceman desk drawer, the number of yellow highlighters are = 19
As given, there are 15 more blue highlighters than yellow in his desk drawer
Then,
the number of blue highlighters = 19+15
= 34
There are total numbers of green highlighters = 37
He has more green highlighters than blue highlighters = 37-34
= 3
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Write the polynomial -10xy5 + 2x³y² - 6x²y² in standard form.
Which of the following sentences is true? Use the number line to help you decide.
6.0 - 7.0
O 6.4 is greater than 6.6.
O 6.3 is less than 6.0.
O 6.4 is less than 6.2.
O 6.8 is greater than 6.6.
Answer: this may not be correct but I think that the answer is 6.8 being greater than 6.6 since it is more closer to 7.0.
Step-by-step explanation:
5. The distance between two lighthouses is 137 miles. There are approximately 8 kilometers
in 5 miles. Which measurement is closest to the number of kilometers between these
two lighthouses?
Measurement is closest to the number of kilometers between these
two lighthouses is 219.2 kilometers.
Assume the distance between two lighthouses is x kilometers in 137 miles.
It knows there are approximately 8 kilometer in 5 miles.
Since the number of kilometers per mile is same
So x:137=8:5
x/137=8/5
5x=1096
5x/5=1096/5
x=219.2
1 kilometer is equal to 0.621371 miles (often shortened to . 62). 1 mile is equal to 1.609344 kilometers. Thus, to convert kilometers to miles, simply multiply the number of kilometers by 0.62137.
The number of kilometers between these two lighthouses is 219.2.
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pls help u with these to
Answer:
5 acute
6 acute
3 obtuse
4 obtuse
Step-by-step explanation:
Hope this helps
5x+y
when x=6 and y=-2
Answer:
28
Step-by-step explanation:
5(6) + (-2) = 30 + (-2) = 30-2 = 28
Answer:
28
Step-by-step explanation:
x=5 y=2
5x + y
5(6) + (-2)
30 + (-2)
30 - 2
28
Use the distance formula to find the area of the square:
Answer:
10
Step-by-step explanation:
Distance formula:
d = √(x₂-x₁)²+(y₂-y₁)²
A (1,2) D (4,3)
d = √(4-1)²+(3-2)² = 3.16227766
All 4 sides of a square are equal lengths.
The equation for the area of a square:
A = a²
A = (3.16227766)² = 10
Under her cell phone plan, Hawa pays a flat cost of $51.50 per month and $3 per gigabyte. She wants to keep her bill at $64.10 per month. Write and solve an equation which can be used to determine gg, the number of gigabytes of data Hawa can use while staying within her budget.
If Hawa pays a flat cost of $51.50 per month and $3 per gigabyte and she wants to keep her bill at $64.10 per month. then the equation which can be used to determine gigabyte is 51.50+3x=64.10 and the number of gigabytes of data Hawa can be used is 4.2 gigabytes
Given,
The flat cost = $51.50 per month
The cost per gigabyte = $3
She wants to keep her bill = $64.10
Consider the number of gigabytes used as x
Then the equation is
51.50+3x=64.10
3x=12.6
x=4.2
Hence, if Hawa pays a flat cost of $51.50 per month and $3 per gigabyte and she wants to keep her bill at $64.10 per month. then the equation which can be used to determine gigabyte is 51.50+3x=64.10 and the number of gigabytes of data Hawa can be used is 4.2 gigabytes.
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dark city had a population of 350,000 in 1990, and has increased exponentially since then, to 475,000 in 2008. project the population in 2015.
The population of the dark city in 2015 will be 449,245.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The dark city had a population of 350,000 in 1990 and has increased exponentially since then, to 475,000 in 2008. Then the equation will be
350,000 = a(b) ...1
475,000 = a(b)¹⁸ ...2
From equations 1 and 2, then we have
475,000 / 350,000 = b¹⁷
b = 1.018
Then the value of the variable a will be
350,000 = 1.018a
a = 343768.87
Then the equation will be
y = 343,768.87 (1.018)ˣ
The population in 2015 will be
y = 343,768.87 (1.018)¹⁵
y = 343,768.87 x 1.3068
y = 449,245
The population of the dark city in 2015 will be 449,245.
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Why is the base of the triangle the same as the circumference
of the circle?
Answer: Because They are literally the same!
Step-by-step explanation:
So listen, The base of a cone is
1. Flat
2. Circle
3. no sides
And a circle has these characteristics too!
So here is your answer Brainliest and thanks + 5 STAR ⭐
The number line represents −412+314.
What is the sum?
Answer:
-98
Step-by-step explanation:
-412 + 314 = 314 -412
= -98
Tip:
Write the opposite symbol in the equation, then in the answer, write the opposite symbol
Just do 412 - 314
which is 98
opposite of 98 is -98
Answer is -98