Problem example: For the given sequence: -2,2,6,10,14,18
Write a recursive formula to find the nth term: a = an-1+4
Write a explicit formula to find the nth term: a = -2 + 4(n-1)
What is the 64th term in the sequence?
Answer:
250
Step-by-step explanation:
You can take the explicit formula and simply substitute the n value with 64:
-2 + 4 * (64 - 1)
-2 + 4 * (63)
-2 + 252
250
expand and simplify (3x-2)2
Answer:
9x² - 12x + 4
Step-by-step explanation:
(3x - 2)² = (3x - 2)(3x - 2)
Each term in the second factor is multiplied by each term in the first factor , that is
3x(3x - 2) - 2(3x - 2) ← distribute both parenthesis
= 9x² - 6x - 6x + 4 ← collect like terms
= 9x² - 12x + 4
solve the equation 5/x+3 + 4/x+2 = 2
Answer:
5 + 4 = 9
x × x = X2
3 + 2 = 5
9/x + 5 = 2
Answer:
5/x+3+4/x+2=2
=9/x+5=2
9/x=-3
Multiply both sides by x
9= -3x
Divide by -3
Answer x= -3
Hope this helps
Anna ate 1/5 of her candy bar. What decimal represents the amount she ate?
Answer:
.25
Step-by-step explanation:
What is the slope of the line between the points ( 2 , 7 ) and ( 7 , 1 )?
Answer:
slope = - [tex]\frac{6}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 7 ) and (x₂, y₂ ) = (7, 1 )
m = [tex]\frac{1-7}{7-2}[/tex] = [tex]\frac{-6}{5}[/tex] = - [tex]\frac{6}{5}[/tex]
Hello there! :)
To find the slope of the line when we are given 2 points, we use the following formula:
m=[tex]\frac{y2-y1}{x2-x1}[/tex]
m=[tex]\frac{1-7}{7-2} \\\frac{-6}{5}[/tex]
So the slope is -6/5. Hope this helps!
~Just a cheerful gal
#CarryOnLearning
[tex]MysteriousNature :)[/tex]
The union of { 1, 2, 3, 4, 5, 6 } and { 4, 5, 6, 7, 8, 9, 10} is ( 4, 5, 6 }. True or false?
Answer:
Below:
Step-by-step explanation:-
The answer is in the comment!! someone answered your question!!
Answer:
false this is because the answer would contain all the values in both sets
1 32 multiplied by 0.32 when rounded to the nearest hundredths
Answer:
42.20
Step-by-step explanation:
132 ×0.32
=42.24
rounded off it give 42.20
On a coordinate grid, point L is at (−4, 4) and point S is at (8, 4). The distance (in units) between points L and S is ______. Input only whole numbers, such as 2.
Answer:
12 this is da a answer
12 twelve
1) Company A charges $55 per hour and a service charge of $250 and Company B charges $60
per hour and a service charge of $225. At what time are they equal?
Answer:
5 hours
Step-by-step explanation:
PLEASE HELP! Economics
100 francs = 50 dollars
Exchange rate = 50/100
= 1/2
= 0.50 dollars per franc (C)
Note :-
It's dollars per franc because here the dollar has more value.
______
RainbowSalt2222 ☔
Answer:
Im pretty sure it is c
Step-by-step explanation:
no link no bot right answer
Can someone help me please I’ve been stuck for a week :(
Answer:
8/25.
Step-by-step explanation:
As a fraction it is 32/100 but simplified is 8/25 :)
What is a common denominator for 1 3/4 and 1 4/5
Answer:
20
Step-by-step explanation:
A common denominator is a number that is a multiple of both denominators.
To find it just write the multiplication table of the numbers and find a number that appears in both of them.
In this case, we have 4 and 5:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40
5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Since it only asks for a common denominator, it can be 20, 40, 60, 80... Although it's usually smarter to pick the lower number.
[tex]1\dfrac 34 =1+ \dfrac 34 =\dfrac 74 = \dfrac{35}{20}\\\\\\1\dfrac 45 = 1+ \dfrac 45 = \dfrac 95 =\dfrac{36}{20}\\\\\text{The answer is 20}[/tex]
Apply the distribute property, substitute the given numerical value given:
9(-3r -11), r=10
Answer:
-369
Step-by-step explanation:
Replace r with 10.
9(-3(10)-10))
9(-30-11)
9*-30+9*-11
-270+ -99
-369
Hope this helped. :)
Is ( - 1, 2) a solution of the system y > x and x + y > 0?
O No, because ( - 1, 2) is a solution to only one of these inequalities.
O Yes, because ( – 1, 2) is a solution to both inequalities.
O Yes, because ( - 1, 2) is the point of intersection of the two boundary lines of this system.
No, because ( – 1, 2) is not a solution to either inequality.
Answer:
Yes, because (-1,2) is a solution to both inequalities
Step-by-step explanation:
2>-1 so the first inequality is correct
-1+2>0 so the second inequality is correct
You exchange 50 AED, and receive 12 Euro. How many Euros would you receive for 1 AED? Please explain step by step on how you solved the problem. (Using equations like multiplication, devision, adding, subtracting.)
Answer:
Step-by-step explanation:
if 50 AED= 12 Euro
for 1 AED ? Euro
50AED/1AED= 12Euro/x
cross multiplication:
50*x=12*1
50*x=12
x=12/50
x=0.24 Euro
so for 1AED you will get 0.26 Euro
Write the ratio as a ratio of whole numbers using fractional notation.
45 days to 24 days
The ratio of 45 days to 24 days can be written in fractional form as
(Type the ratio as a simplified fraction.)
Answer:
15:8=15/8
Step-by-step explanation:
45:24=45/24
15/8=15:8
In the diagram, <4 and <5 are what type of angles?
A. corresponding angles
B. Alternate interior angles
C. Alternate exterior angles
D. Consecutive interior angles
Answer:
B. Alternate interior angles
Step-by-step explanation:
Differential Equation
1. The given equation is probably supposed to read
y'' - 2y' - 3y = 64x exp(-x)
First consider the homogeneous equation,
y'' - 2y' - 3y = 0
which has characteristic equation
r² - 2r - 3 = (r - 3) (r + 1) = 0
with roots r = 3 and r = -1. Then the characteristic solution is
[tex]y = C_1 e^{3x} + C_2 e^{-x}[/tex]
and we let y₁ = exp(3x) and y₂ = exp(-x), our fundamental solutions.
Now we use variation of parameters, which gives a particular solution of the form
[tex]y_p = u_1y_1 + u_2y_2[/tex]
where
[tex]\displaystyle u_1 = -\int \frac{64xe^{-x}y_2}{W(y_1,y_2)} \, dx[/tex]
[tex]\displaystyle u_2 = \int \frac{64xe^{-x}y_1}{W(y_1,y_2)} \, dx[/tex]
and W(y₁, y₂) is the Wronskian determinant of the two fundamental solutions. This is
[tex]W(y_1,y_2) = \begin{vmatrix}e^{3x} & e^{-x} \\ (e^{3x})' & (e^{-x})'\end{vmatrix} = \begin{vmatrix}e^{3x} & e^{-x} \\ 3e^{3x} & -e^{-x}\end{vmatrix} = -e^{2x} - 3e^{2x} = -4e^{2x}[/tex]
Then we find
[tex]\displaystyle u_1 = -\int \frac{64xe^{-x} \cdot e^{-x}}{-4e^{2x}} \, dx = 16 \int xe^{-4x} \, dx = -(4x + 1) e^{-4x}[/tex]
[tex]\displaystyle u_2 = \int \frac{64xe^{-x} \cdot e^{3x}}{-4e^{2x}} \, dx = -16 \int x \, dx = -8x^2[/tex]
so it follows that the particular solution is
[tex]y_p = -(4x+1)e^{-4x} \cdot e^{3x} - 8x^2\cdot e^{-x} = -(8x^2+4x+1)e^{-x}[/tex]
and so the general solution is
[tex]\boxed{y(x) = C_1 e^{3x} + C_2e^{-x} - (8x^2+4x+1) e^{-x}}[/tex]
2. I'll again assume there's typo in the equation, and that it should read
y''' - 6y'' + 11y' - 6y = 2x exp(-x)
Again, we consider the homogeneous equation,
y''' - 6y'' + 11y' - 6y = 0
and observe that the characteristic polynomial,
r³ - 6r² + 11r - 6
has coefficients that sum to 1 - 6 + 11 - 6 = 0, which immediately tells us that r = 1 is a root. Polynomial division and subsequent factoring yields
r³ - 6r² + 11r - 6 = (r - 1) (r² - 5r + 6) = (r - 1) (r - 2) (r - 3)
and from this we see the characteristic solution is
[tex]y_c = C_1 e^x + C_2 e^{2x} + C_3 e^{3x}[/tex]
For the particular solution, I'll use undetermined coefficients. We look for a solution of the form
[tex]y_p = (ax+b)e^{-x}[/tex]
whose first three derivatives are
[tex]{y_p}' = ae^{-x} - (ax+b)e^{-x} = (-ax+a-b)e^{-x}[/tex]
[tex]{y_p}'' = -ae^{-x} - (-ax+a-b)e^{-x} = (ax-2a+b)e^{-x}[/tex]
[tex]{y_p}''' = ae^{-x} - (ax-2a+b)e^{-x} = (-ax+3a-b)e^{-x}[/tex]
Substituting these into the equation gives
[tex](-ax+3a-b)e^{-x} - 6(ax-2a+b)e^{-x} + 11(-ax+a-b)e^{-x} - 6(ax+b)e^{-x} = 2xe^{-x}[/tex]
[tex](-ax+3a-b) - 6(ax-2a+b) + 11(-ax+a-b) - 6(ax+b) = 2x[/tex]
[tex]-24ax+26a-24b = 2x[/tex]
It follows that -24a = 2 and 26a - 24b = 0, so that a = -1/12 = -12/144 and b = -13/144, so the particular solution is
[tex]y_p = -\dfrac{12x+13}{144}e^{-x}[/tex]
and the general solution is
[tex]\boxed{y = C_1 e^x + C_2 e^{2x} + C_3 e^{3x} - \dfrac{12x+13}{144} e^{-x}}[/tex]
6. Johanna buys a shirt for s dollars to sell in her clothing
store. She
increases the price by 7.5% Write an
expression to represent the new price of the shirt.
Answer: 1.075s
Step-by-step explanation:
s*175/100=1.075s
Which situation involves permutations? A. choosing 5 people out of 15 to participate in a survey B. choosing 3 flavors of ice cream out of 15 for an ice-cream sundae C. choosing a dozen flowers out of 30 to create a bouquet D. choosing first second-, and third-place winners in a cooking contest
9514 1404 393
Answer:
D. choosing first second-, and third-place winners in a cooking contest
Step-by-step explanation:
Permutations are involved when order matters. The order of people surveyed, sundae flavors, and flowers are irrelevant. The order of first-second-third is entirely relevant.
Cooking contest winners involve permutations.
Select all the correct answers.
Which statements are true about function g?
Answer:
i need the question
Step-by-step explanation:
-
Find the equation of the line that
is parallel to y = 2x – 7 and
contains the point (-3,6).
Step-by-step explanation:
The first step is to Know the condition for two lines be parallel is that have the same slope, and this form the slope given is 2, therefore the new function has its slope too
2) with the slope and the two points givens, you can find the equation
Y-Y1 = m( X-X1) , Y-6 = 2[(X-(-3)] ⇒Y-6 = 2X+6 ⇒Y = 2X+12, AND THIS IS THE EQUATION PARALLEL TO THE LINE Y = 2X-7
-2.875 greater than or less than -2 7/8
Answer:
They are both the same.
Step-by-step explanation:
-2.875
7/8 = 0.875 thus -2 7/8 is equal to -2.875
Find the product. Simplify your answer.
(m+2)(3m+2)
there you go the answer is in the picture
A package contains 12 ounces of cereal .If you use 1 portion of this cereal which is 1 1/3 how much would be left in the cereal box?
To answer this question, you would need to divide the total amount of cereal in the box by the serving size.
This would be 12 2/3 divided by 1 1/3.
We can write each mixed number as an improper fraction first before we divide:12 2/3 = 38/3 and 1 1/3 = 4/3
Now divide 38/3 by 4/3. Recall that dividing by a fraction is accomplished by multiplying by the reciprocal of the divisor: 38/3 * 3/4 = 114/12 = 38/4 OR 19/2
Also, 19/2 is equivalent to 9 and 1/2. There would be 9 and 1/2 servings in the box of cereal.
Hope this helps
45 cows can graze a field in 13 days. How many cows will graze the same field in 9 days
Answer:
65 cows
Step-by-step explanation:
Inverse rule of three
[tex]45-------13\\x -------- 9[/tex]
[tex]x=\frac{(45)(13)}{9}=585/9=65[/tex]
Hope this helps
A committee is formed consisting of one representative from each of the 4 departments (CS-IS-IT-SW) in the computer science college, where the representative from a department is either the president or one of the two representatives from that department. How many ways are there to form this committee?
Step-by-step explanation:
each department has 3 options for their representative.
and each of these options can be associated with the 3 options of the next department. and so on.
so, we have
3×3×3×3 = 3⁴ = 81
possibilities to firm that committee overall.
Which is greater, -6.4 or -6.5? please explain !!
Answer:
-6.4 is GREATER.
The number closest to 0 is greater.
2(x + 1) - 3x
howwwwwww
Answer:
a = -x + 2
Step-by-step explanation:
First, you must distribute to get 2x + 2 and adding in the -3x it equals 2x + 2 - 3x = a
Combine the like terms to get -x + 2 = a
Since there is 2 variables then the answer will stay a = -x + 2 because x or a must be substituted in order to find the other variable
