• {4, 7, 12, 19, … }
has 1st differences
7 - 4 = 3
12 - 7 = 5
19 - 12 = 7
and 2nd differences
5 - 3 = 2
7 - 5 = 2
• {-1, 2, 7, 14, …}
1st differences:
2 - (-1) = 3
7 - 2 = 5
14 - 7 = 7
2nd differences:
5 - 3 = 2
7 - 5 = 2
• {-2, -8, -18, -32, …}
1st differences:
-8 - (-2) = -6
-18 - (-8) = -10
-32 - (-18) = -14
2nd differences:
-10 - (-6) = -4
-14 - (-10) = -4
Answer:
Hello,
Step-by-step explanation:
I am going to explain the method with the 1th:
[tex]\begin{array}{ccccc}n & u_n&u_{n+1}-u_{n}&u_{n+2}-2u_{n+1}+u_{n}&v_{n}\\1&4&&6\\2&7&3&9\\3&12&5&2&14\\4&19&7&2&21\\...&&&\\\end{array}\\\boxed{u_{n+2}=2u_{n+1}-u_{n}+2}\\[/tex]
[tex]Let\ say\\v_{n}=u_{n}+2\\v_{n+2}=u_{n+2}+2=(2u_{n+1}-u_{n}+2)+2=2(v_{n+1}-2)-(v{n}-2)+4\\v_{n+2}=2v_{n+1}-v{n}+2\ (1)\\v_{n+3}=2v_{n+2}-v{n+1}+2\ (2)\\(2)-(1)==> \boxed{v_{n+3}=3v_{n+2}-3v_{n+1}+v_n}\\[/tex]
[tex]Caracteristic\ equation:\\P(r)=r^3-3r^2+3r-1=0\\P(r)=(r-1)^3\\v_n=\alpha+\beta*n+\gamma*n^2\\v_1=6 ==> \alpha+\beta*1+\gamma*1=6\\u_2=9 ==> \alpha+\beta*2+\gamma*4=9\\u_3=14 ==> \alpha+\beta*3+\gamma*9=14\\[/tex]
[tex]\begin{bmatrix}1&1&1\\1&2&4\\1&3&9\end{bmatrix}*\begin{bmatrix}\alpha\\\beta\\\gamma\end{bmatrix}=\begin{bmatrix}6\\9\\14 \end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\1&2&4&9\\1&3&9&14\end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\0&2&3&3\\0&2&8&8\end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\0&1&3&3\\0&1&4&4\end{bmatrix}\\\\[/tex]
[tex]\begin{bmatrix}1&1&1&6\\0&1&3&3\\0&0&1&1\end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\0&1&0&0\\0&0&1&1\end{bmatrix}\\\\\\\begin{bmatrix}1&0&0&5\\0&1&0&0\\0&0&1&1\end{bmatrix}\\[/tex]
[tex]\alpha=5\\\beta=0\\\gamma=1\\\boxed{v_n=5+0*n+1*n^2}\\\boxed{u_n=5+0*n+1*n^2-2}\\\begin{array}{ccccc}n & u_n\\1&5+1-2=4\\2&5+4-2=7\\3&5+9-2=12\\4&5+16-2=19\\...&...\\\end{array}\\[/tex]
2/4.7+2/7.10+2/10.13+2/13.16+.....+2/49.52
tính giá trị biểu thức
It looks like you're trying to evaluate the sum,
[tex]\displaystyle \frac2{4\times7} + \frac2{7\times10} + \frac2{10\times13}+\cdots+\frac2{49\times52}[/tex]
which can be written as
[tex]\displaystyle \sum_{n=1}^{16} \frac2{(3n+1)(3n+4)}[/tex]
Split up the summand into partial fractions:
[tex]\displaystyle \frac2{(3n+1)(3n+4)} = \frac a{3n+1} + \frac b{3n+4} \\\\ \implies 2 = a(3n+4)+b(3n+1) \\\\ \implies 2 = (3a+3b)n+4a+b[/tex]
so that
3a + 3b = 0, or a = -b
4a + b = 2
Solve for a and b :
4a + (-a) = 3a = 2 ==> a = 2/3 ==> b = -2/3
So the sum is
[tex]\displaystyle \frac23 \sum_{n=1}^{16} \left(\frac1{3n+1} - \frac1{3n+4}\right)[/tex]
Write out the first terms and observe that several terms cancel with each other:
2/3 (1/4 - 1/7)
+ 2/3 (1/7 - 1/10)
+ 2/3 (1/10 - 1/13)
+ …
+ 2/3 (1/43 - 1/46)
+ 2/3 (1/46 - 1/49)
+ 2/3 (1/49 - 1/52)
So the sum collapses and simplifies to
[tex]\displaystyle \sum_{n=1}^{16} \frac2{(3n+1)(3n+4)} = \frac23 \left(\frac14 - \frac1{52}\right) = \boxed{\frac2{13}}[/tex]
Answer please. Will give brainly thingy.
(if correct and I will click check answer.)
Answer: A.
Step-by-step explanation:
1/4 is not in fact a natural number, it's a rational number, a ratio.
The sum of 30 terms of series in A.P, whose last term is 98, is 1635. Find the first term and the common difference.
Let a(n) denote the n-th term in the sequence. Because the terms are in arithmetic progression, there is a fixed number d that separates consecutive terms, so that starting with a(1) = a, the next few terms are
a(2) = a(1) + d = a + d
a(3) = a(2) + d = a + 2d
a(4) = a(3) + d = a + 3d
and so on, up to
a(n) = a + (n - 1) d
We're given that the 30th term is 98, so
a(30) = a + 29d = 98
The sum of the first 30 terms is 1635, so that
[tex]\displaystyle \sum_{n=1}^{30}a(n) = \sum_{n=1}^{30}(a+(n-1)d) \\\\ 1635 = a\sum_{n=1}^{30}1 + d\sum_{n=1}^{30}(n-1) \\\\ 1635 = 30a + d\sum_{n=0}^{29}n \\\\ 1635 = 30a + d\sum_{n=1}^{29}n \\\\ 1635 = 30a + \frac{d\times29\times30}2[/tex]
so that
30a + 435d = 1635
Solve the equations in boldface for a and d. I'll eliminate a and solve for d first.
-30 (a + 29d) + (30a + 435d) = -30 (98) + 1635
-30a - 870d + 30a + 435d = -2940 + 1635
-435d = -1305
d = 3
Then
a + 29 (3) = 98
a + 87 = 98
a = 11
Bob has twice as many marbles as Alice. Alice has twice as many marbles as Ted. Ted has one-quarter of the number of marbles that Carol has. If Bob has x marbles, how many marbles does Carol have?
E. x/8
F. x/4
G. x
H. 4x
Answer:
,X/8 F CJFVYVEM SORY
Step-by-step explanation:
DUNIA BERDITI TAHUN TOGTV
whats does it me study the exercises in which both addends are negative.what do you notice about the sum
Answer:
Jsjiaghajqkkooo898iiwiqiooopwpppwopfokejejieieieieiie
A car left Sydney at 9 am and arrived in
Melbourne at 6 pm. The distance travelled
was 711 km. Find the car's average speed.
km/h
Answer:
average speed = distance/ time
711/9
79km/h
Which question can be answered using the expression 1/3 ÷ 3/4 ?
Answer:
0.4444444
Step-by-step explanation:
yes
work out the values of a and b in the identity 5(7x + 8) + 3(2x + b) = ax+ 13
will give brainiest!!!
Answer:
a=41 b=-9
Step-by-step explanation:
By expanding the brackets on the left hand side of the equation you get,35x + 40 + 6x + 3b and by simplifying you get 41x + 40 + 3b.by comparing the x and constant terms on either side you find that a = 41, and3b + 40 = 13, rearranging b = -9.
Answer from Gauth math
Answer:
Hello,
Step-by-step explanation:
We are going to use identification of terms.
[tex]5(7x+8)+3(2x+b)=ax+13\\\\35x+40+6x+3b=ax+13\\\\41x+40+3b=ax+13\\\\\\\Longrightarrow \left\{\begin{array}{ccc}a&=&41\\3b+40&=&13\\\end{array}\right.\\\\\\\Longrightarrow \left\{\begin{array}{ccc}a&=&41\\b&=&-9\\\end{array}\right.\\\\[/tex]
Produced by myself
If the range of the function f(x) =5x + 8 is 18, find its domain.
Step-by-step explanation:
f(X) = 5x+18= 18
so,
18 = 5x+18
18-18 = 5x
X= 0
so domain of the function is 0
Each month a manufacturing plant makes 14500 light bulbs. last month, a random sample of 200 bulbs found that 2.5% were defective. Estimate the number of defective bulbs that were produced last month.
PLEASE HELP ASAP I WILL GIVE BRAINLIEST
Answer:
363
Step-by-step explanation:
Of 2.5% of 200 is 5 so we can scale that up to 14500 we get 362.5 and then we round it up to 363.
Two sides of a triangle are 12 and 18 cm. Complete the inequality to show the possible lengths of the third side.
Let a = 12 and b = 18 be the two given sides
Let c be the unknown third side
Due a modified form of the triangle inequality theorem, we know that,
b-a < c < b+a
18-12 < c < 18+12
6 < c < 30 which is the final answer
This says c is between 6 and 30, but cannot equal either endpoint.
find the slope and y intercept
Answer:
slope = -1
y intercept (0,-2)
Step-by-step explanation:
We can use the two points to find the slope
(-4,2) and (1,-3)
m = ( y2-y1)/(x2-x1)
= (-3 -2)/(1 - -4)
= -5 /(1+4)
= -5/5
- 1
The y intercept is where it crosses the y axis
y intercept is (0,-2)
After substituting, what is the first step when evaluating x + 3 x minus 4.2 when x = 5?
Multiply 3 by 5
Add 5 and 3
Subtract 4.2 from 5
Add 3 and 4.2
Answer:
Multiply 3 by 5
Step-by-step explanation:
the P and M in PEMDAS because there’s multiplication inside the parentheses
5 + 3(5) - 4.2
When the movies is half over , popcorn sells for half price. Full price popcorn is $3.50 and drinks are $1.35 . Determine the cost for purchasing 3 orders of popcorn and 3 drinks when the movie is half over
Answer:
The total price is $9.30
Step-by-step explanation:
Price of the orders of popcorn= $5.25
Price of the drinks= $4.05
PLZ HELP ASAP ITS KHAN WILL GIVE 5 STARS AND HEART AND 10 POINTS AND BRAINLIST
Answer:
14.4
Step-by-step explanation:
Cross multiply.
5x = 8 * 9
5x = 72
x = 14.4
Answer:
x= 14.4
Step-by-step explanation:
1. cross multiply
5*x and 8*9
5x=72
2. divide 72 by 5
x= 14.4
Someone explain what this means ?
Answer:
20 P 9 means selecting 9 objects (order matters) out of 20 objects.
So in this case, the eight choice of a line up of 9 has 13 options.
For example, think about it this way. The first choice has 20 options, 2nd has 19, and so on...
So the answer is 13
Let me know if this helps!
What is the most dangerous country
Answer:
Iceland
Step-by-step explanation:
what is the the value of ∣9∣
Hey there! I'm happy to help!
This symbol is an absolute value symbol. It means that we are looking for that number's distance from 0. There is no such thing as a negative distance; the distances are all positive, so both ∣9∣ and ∣-9∣ have a value of 9.
Have a wonderful day and keep on learning! :D
(x-5)(3x-8)=(4-3x)(6-x)+13
Answer:
x = 3
Step-by-step explanation:
Use FOIL method
(x - 5)(3x - 8) = x*3x + x*(-8) + (-5)*(3x) + (-5)*(-8)
= 3x² - 8x - 15x + 40 {Combine like terms}
= 3x² - 23x + 40
(4 - 3x)( 6 - x) = 4*6 + 4 *(-x) + (-3x)*6 + (-3x)*(-x)
= 24 - 4x - 18x + 3x² {Combine like terms}
= 3x² - 22x + 24
(x - 5)(3x - 8) = (4 - 3x)( 6 - x) + 13
3x² - 23x + 40 = 3x² -22x + 24 + 13
3x² - 23x + 40 - 3x² + 22x - 24 - 13 = 0
3x² - 3x² - 23x + 22x + 40 - 24 - 13 = 0 {Combine like terms}
0 - x = 0
-x +3= 0
3 = x
x =3
If you help me, you will get this cookie
Answer:
B. 7y - 15
Step-by-step explanation:
Simplifying
10y + -3(y + 5) = 0
Reorder the terms:
10y + -3(5 + y) = 0
10y + (5 * -3 + y * -3) = 0
10y + (-15 + -3y) = 0
Reorder the terms:
-15 + 10y + -3y = 0
Combine like terms: 10y + -3y = 7y
-15 + 7y = 0
Solving
-15 + 7y = 0
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '15' to each side of the equation.
-15 + 15 + 7y = 0 + 15
Combine like terms: -15 + 15 = 0
0 + 7y = 0 + 15
7y = 0 + 15
Combine like terms: 0 + 15 = 15
7y = 15
Divide each side by '7'.
y = 2.142857143
Simplifying
y = 2.142857143
Answer:
b. 7y-15
Step-by-step explanation:
First, write out the expression
1. [tex]10y-3(y+5)[/tex]
To simplify the expression distribute the -3 to the terms within the paratheses.
2. [tex]10y-3y-15[/tex]
Then, combine like terms to simplify further. Since 10y and -3y are like terms they can be subtracted
3. [tex]7y-15[/tex]
This means that B is the correct answer.
Help? Please! I need hElppz
Answer:
-29Step-by-step explanation:
- 22 - □ = 7
=> - 22 - 7 = □
=> - 29 = □
=> □ = - 29 (Ans)
If you know the answer please help me
Answer:
2/7
Step-by-step explanation:
This is basically asking how many 7/10 's fit in 1/5. Or 1/5 divided by 7/10.
1/5 divided by 7/10 is the same as 1/5 times the reciprocal, 10/7. Therefore it is 1/5*10/7, or 10/35.
That simplifies to 2/7.
I need help with all 4
For # 31 - 34, solve the equation for the unknown variable.
Pls pls pls help me
Answer:
48
Step-by-step explanation:
AC = 10
DC² = 10² - 6² = 64
DC = 8
[tex]A_{ABCD}[/tex] = 6 × 8 = 48
Find tan a Picture included
Answer:
5/12
Step-by-step explanation:
We know its a right angled triangle because of phythogorean theorem,
h^2=p^2+b^2
Take angle A as reference,
13^2=12^2+5^2
or,169=144+25
169=169
Now,
We know,
Tanx=p/b
As we took angle A as reference,
p=5
b=12
h=13
Put that in tanx=p/b
We get,
tanx=p/b=5/12
Answer:
Step-by-step explanation:
[tex]tan \ A = \frac{opposite \ side}{adjacent \ side}\\\\tan \ A = \frac{5}{12}[/tex]
(81/16)1/4 +(81/16)0
Answer:
should be 0.28125
Step-by-step explanation:
In which of the following expressions is the coefficient of term "x" 1?
2x^2+x−9
2 x squared plus x minus 9
x^2+2x+7
x squared plus 2 x plus 7
3x^2−x−5
3 x squared minus x minus 5
2x^2−3x+1
Using the coefficient concept, it is found that the expression in which the coefficient of the term x is 1 is:
[tex]2x^2 + x - 9[/tex]
-----------------------------------------
In a polynomial, the terms that multiply the x variables are called coefficients.
For example, take a standard quadratic equation: [tex]ax^2 + bx + c[/tex]
The coefficient of x² is a.The coefficient of x is b.The coefficient of [tex]\mathbf{x^0}[/tex] is c.-----------------------------------------
In this problem, we want an expression in which the term "x" is multiplied by 1, and the desired expression is:
[tex]2x^2 + x - 9[/tex]
A similar problem is given by https://brainly.com/question/15446728
Evaluate the expression shown below and write your answer as a fraction in simplest form(1/10-2/3) ÷ 0.5
Answer:
[tex]\frac{-17}{15}[/tex]
Step-by-step explanation:
When solving this problem you must follow PEMDAS, so parentheses should go first. To solve 1/10 - 2/3, first, find the common denominator. In this case, that is 30. Then, subtract, [tex]\frac{3}{30} - \frac{20}{30}[/tex]. This equals -17/30. Finally, divide by 0.5. To do this remember that dividing by half is the same as multiplying by 2. Doing [tex]\frac{-17}{30} *2[/tex] equals [tex]\frac{-17}{15}[/tex].
Which ratio represents $20 for every 4 cups of lemonade sold?
4/1 or 4,
1/5,
5/1 or 5
Answer:
5/1 or 5
Step-by-step explanation:
4 cup of lemonade is $20
then,
1 cup of lemonade is 20 ÷4 =5
Please help I don’t understand math
Answer:
x = 12
Step-by-step explanation:
The sum of the two smaller angles is 140
80+5x = 140
Subtract 80 from each side
80+5x-80 =140-80
5x = 60
Divide each side by 5
5x/5 = 60/5
x = 12
