Find the first four terms of the sequence given ai
31 and an+1
an
3.
Answer:
he arithmetic sequence ai is defined by the formula: a1= 2 ai= ai - 1 -3 find the sum of the first 335 terms in the sequence
Step-by-step explanation:
In an arithmetic sequence,
a_1=2a
1
=2
a_i=a_{i-1}-3a
i
=a
i−1
−3
To find:
The sum of the first 335 terms in the given sequence.
Solution:
The recursive formula of an arithmetic sequence is:
a_i=a_{i-1}+da
i
=a
i−1
+d ...(i)
Where, d is the common difference.
We have,
a_i=a_{i-1}-3a
i
=a
i−1
−3 ...(ii)
On comparing (i) and (ii), we get
d=-3d=−3
The sum of first i terms of an arithmetic sequence is:
S_i=\dfrac{i}{2}[2a+(i-1)d]S
i
=
2
i
[2a+(i−1)d]
Putting i=335,a=2,d=-3i=335,a=2,d=−3 , we get
S_{335}=\dfrac{335}{2}[2(2)+(335-1)(-3)]S
335
=
2
335
[2(2)+(335−1)(−3)]
S_{335}=\dfrac{335}{2}[4+(334)(-3)]S
335
=
2
335
[4+(334)(−3)]
S_{335}=\dfrac{335}{2}[4-1002]S
335
=
2
335
[4−1002]
S_{335}=\dfrac{335}{2}(-998)S
335
=
2
335
(−998)
On further simplification, we get
S_{335}=335\times (-499)S
335
=335×(−499)
S_{335}=-167165S
335
=−167165
Therefore, the sum of the first 335 terms in the given sequence is -167165.
Which choice is equivalent to the product below when x > 0?
Square root of 2/x time square root of x^2/8
Answer:
A.
[tex] \sqrt{x } \div 2[/tex]
is the answer
The choice which is equivalent to [tex]\sqrt{\frac{2}{x}}\cdot\sqrt{\frac{x^2}{8}}[/tex] is given by (A) [tex]\frac{\sqrt{x}}{2}[/tex].
What is expression?Expression is a mathematical term that involves variables, numbers and other mathematical quantities and operations or combinations of them.
The given expression is [tex]\sqrt{\frac{2}{x}}\cdot\sqrt{\frac{x^2}{8}}[/tex]
Calculating the expression we get,
[tex]\sqrt{\frac{2}{x}}\cdot\sqrt{\frac{x^2}{8}}=\sqrt{\frac{2}{x}\cdot\frac{x^2}{8}}=\sqrt{\frac{x}{4}}=\frac{\sqrt{x}}{2}[/tex]
So the expression equals to [tex]\frac{\sqrt{x}}{2}[/tex].
Hence the correct option is (A).
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Find the mean medan mode
and range for the following
numbers
3.125.8.6.6
I'm not sure if this is what you meant - 3.12.5.8.6.6, but I'm operating based on that
mean - 6.7
median - 6
mode - 6
range - 9
3.9015 to the nearest thousandth
Answer:
3.902.
Step-by-step explanation:
3. 9015:
The 10 thousandth digit is 5 so you round up the 1 to 2.
Plz answer it's important
Answer:
[tex]x_{M}[/tex] = - 1
Step-by-step explanation:
The coordinates of the midpoint are the average of the x and y coordinates of the endpoints , that is
[tex]x_{M}[/tex] = [tex]\frac{4-6}{2}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1
Is 9.5 an irrational number
Answer:
yes it is.....................
Step-by-step explanation:
9.5 = 19/2
So it is a rational number (and so is not irrational)
Need help ASAP please
Answer:
Terms for 4a^2-5a-3: 4a^2, -5a, -3
Terms for Equation 2 is correct.
Constants for 4a^2-5a-3: -3
Constants for Equation 2 is correct.
Coefficients for 4a^2-5a-3: 4, -5
Coefficients for Equation 2: 7, -3
Step-by-step explanation:
A new car sales person, sold an average of $46,975 per day for the first two days she worked. The next one days she worked, she sold an average of $45,765. How much did she sell on average per day over the entire time she worked?
Answer:
$46,571.67
Step-by-step explanation:
if your description is right and complete, she sold cars on the first 2 days as average for $46975.
and on the third day for $45765
to calculate the total average we need to know the total amount of sales and then divide it by the observation period length (3 days).
how do we get the total sales ?
we know the average of the first 2 days. we don't need to find the exact value for every day, but we know the exact value for these first 2 days : 2×46975 = $93950
as the average of these 2 days = (day1 + day2)/2
46975 = (day1 + day2)/2
day1 + day2 = 2×46975 = 93950
it is not important what two (day) numbers created 93950. we know that this was the total sum of the first two days. and that is enough.
so, we have in total
$93950 on the first 2 days
$45765 in the third day
-------------
$139715 for all 3 days
the average per day is then
139715 / 3 = $46,571.67
find the range of possible values for x
[tex]\\ \rm\longmapsto x-5=41[/tex]
[tex]\\ \rm\longmapsto x=41+5[/tex]
[tex]\\ \rm\longmapsto x=46[/tex]
Hence
[tex]\\ \rm\longmapsto 45<x<47[/tex]
Write 6.21 as a mixed number in simplest form.
Answer:
6.211=( 6.21×100) (1×100) =621100
Hope that helped you
Uma indústria produz mensalmente x lotes de um produto. O valor mensal resultante da venda deste produto é V(x) = 3x² + 400x e o custo mensal da produção é dado por C(x) = 5x² − 100x − 540. Sabendo que o lucro é obtido pela diferença entre o valor resultante das vendas e o custo da produção, calcule:
A) O número de lotes de produtos para maximizar o lucro?
B) Qual o lucro Mensal a indústria pode alcançar?
Answer:
The answer would be A
Step-by-step explanation:
can someone solve this for me and explain it please
Answer:
Answer is Triangle P'R'Q' is larger, explain how you know is steps
Step-by-step explanation:
So a Dilation is the expansion or shrinkage of an object. Because this is being dilated by 1.5 it is growing by 1.5
So triangle PRQ is the smaller version of P'R'Q' because
Line PR = 3.1
Line RQ = 3.9
Line QP = 5
Multiplying these by 1.5 you get
Line P'R' = 4.65
Line R'Q'= 5.85
Line Q'P' = 7.5
a number set consists of {4,5,6,7}。How many 2-digit combinations of numbers from the data set can be divided by 3?
Answer:
5
Step-by-step explanation:
This trick works with 3:
If the sum of the digits of a number is divisble by 3 then the number is divisble by 3.
44 is not divisble by 3 because 4+4=8 is not divisble by 3.
45 is divisble by 3 because 4+5=9 is divisble by 3.
46 is not divisble by 3 because 4+6=10 is not divisble by 3.
47 is not divisble by 3 because 4+7=11 is not divisble by 3.
54 is divisble by 3 because 5+4=9 is divisble by 3.
55 is not divisble by 3 because 5+5=10 is not divisble by 3.
56 is not divisble by 3 because 5+6=11 is not divisble by 3.
57 is divisble by 3 because 5+7=12 is divisble by 3.
64, 65,67 are not divisble by 3 because their digits' sums are 10,11, and 13 respectively. 66 is a winner because 6+6=12 is divisble by 3.
Finally 7...
74,76,77 are not divisble by 3 because their digits' sums are 11,13, and 14 respectively. 75 is divisble by 3 because 7+5=12 is divisble by 3.
The victors are
45
54
57
66
75
A recipe for fluffy slime calls for 3 3/4 cups of shaving
cream, 1/2 cup of glue, 1/2 teaspoon of baking soda
and 1 1/2 tablespoons of saline solution; this is
enough for 2 people. How much shaving cream
would you need if you were making enough slime
for ten people?
Answer:
75/4 cups (or 18-3/4 cups)
Step-by-step explanation:
2 people ---> requires 3 3/4 cups (or 15/4 cups) of shaving cream
10 people ----> requires 5 times the amount of shaving cream needed for 2 people
Hence shaving cream is needed for 10 people
= 5 x 3 3/4 cups
= 5 x 15/4 cups
= 75/4 cups (or 18-3/4 cups)
lemme know if it helped <3. and lemme me know if it's right :) .!
8a=4(a-9)
Show work I need help
Answer:
a = -9
Step-by-step explanation:
8a=4(a-9)
Divide each side by 4
8a/4=4(a-9)/4
2a = a-9
Subtract a from each side
2a-a = a-9-a
a = -9
Answer:
-9
Step-by-step explanation:
8a = 4(a-9)
Use the distributive property (Multiply 4 times a, and 4 times -9)
8a = 4a - 36
Bring the 4a to the other side
8a - 4a = -36
Add like terms
4a = -36
Divide both sides by 4 to get a by itself
a = -9
Match each value with its formula for ΔABC.
(choices are in 2nd pic)
Answer:
1- x b
2-sinc
3-sin b
4-sin a
5- x c
6- x a
Step-by-step explanation:
help me find the area pls
HELP HELP HURRYYY the product of two numbers is rational. The first number is 3 sqrt2. What is the possible value of the other number?
The possible value of the other number will be 7√32. The correct option is D.
What is a rational number?A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. For instance, every integer and 3/7 are rational numbers.
It is given that the first number is 3√2 the value of the second number will be:-
Rational number = 3√2 x 7√32
Rational number = 21√64
Rational number = 21√( 8 x 8 )
Rational number = 21 x 8
Rational number = 168
Therefore, the possible value of the other number will be 7√32. The correct option is D.
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Un parque tiene una piscina en forma circular de 22 yd de diámetro. Un sendero en forma anular rodea la piscina. El sendero mide 6 yd de ancho. El sendero necesita una nueva capa de revestimiento. Si un galón de revestimiento cubre 4 yd2 ¿cuantos galones de revestimiento se necesitan?
Answer:
La verdad Nose la respuesta espero que alguien te ayude
PLEASE HELP (GEO) Find X
Round to the nearest tenth.
20 ft
\22 ft
Y
X 18 ft
X= [?]
Law of Cosines: c2 = a2 + b2 - 2ab cos C
Answer:
70.5°
Step-by-step explanation:
cos x = (20²+18²-22²)/2(20)(18)
= (400+324-484)/720
= 240/720
= 1/3
so, X = arc cos ⅓ = 70.5°
HELP!! Will mark as brainliest!!!
In school, pupils study one language.
They choose either French, Spanish or Italian.
3/20 of the pupils study Italian and 5/8 of the pupils study French
What fraction of the pupils study Spanish?
Answer:
19/40
Step-by-step explanation:
mark meeeeeee
29 dekagrams equals 2900 what
Answer:
It equals 2900 decigrams
Step-by-step explanation:
29 dekagrams = 290 grams
290 grams = 2900 decigrams
Therefore, 29 dekagrams = 2900 decigrams
The equivalent weight in grams for a given weight in dekagrams is approximately 10 times the weight in dekagrams.
To find the equivalent weight in grams for a given weight in dekagrams, you can use the conversion factor that 1 dekagram (dag) is equal to 10 grams.
Given the information that 29 dekagrams equals 290 grams, you can set up a proportion:
[tex]\(\frac{29 \text{ dag}}{290 \text{ g}} = \frac{1 \text{ dag}}{x \text{ g}}\)[/tex]
Cross-multiplying:
[tex]\(29x = 290 \times 1\)[/tex]
Solving for x:
[tex]\(x = \frac{290}{29}\)\\\\\(x \approx 10\)[/tex]
Therefore, the equivalent weight in grams for a given weight in dekagrams is approximately 10 times the given weight in dekagrams.
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Complete Question:
If 29 dekagrams equals 290 grams, what is the equivalent weight in grams for a given weight in dekagrams?
If S is directly proportional to t squared and s= 8 when t= 4 find the value of s when t= 3
Answer:9/2
Step-by-step explanation:
Answer:
1.5
Step-by-step explanation:
k=8÷16=0.5
s=0.5×3=1.5
Which is the equation of the line that passes through (6, 2) and is perpendicular to a line with slope -1/3?
Answer:
(c) y = 3x - 16 or y - 2 = 3(x - 6)
Step-by-step explanation:
To be perpendicular, the slope must be the negative inverse of the other line,
so we know the slope must be -(-3/1) = 3
then the general point-slope form is
y = mx + b (m = slope and b = y-intercept) so
y = 3x + b (then use the point given (6,2) to find m)
2 = 3(6) + b
2 = 18 + b
2 - 18 = b
-16 = b
then
y = mx + b
y = 3x - 16
a+b in terms of a and evaluated these expressions when a = 3
Answer:
If a equals 3 then the answer should be 3b
Step-by-step explanation:
Answer:
a+b=a
or,3+b=3(a=3)
or,b=3-3
or,b=0
b=0 Ans
Which Experession Is Equivalent To 13-(21)
5.
A bank statement shows transactions of -$10.40 and $8.50.
A. Do these transactions represent deposits or withdrawals?
Plz help
A negative value is when money is taken out ( withdrawal). A positive value is when money is added to the account(deposit)
-10.40 is a withdrawal
8.50 is a deposit
Answer:
Hint :- Withdrawal is denoted as the -ve sign and deposit are denoted by the +ve sign. This is because if we deposit money then the money increase and if we withdraw then the money decreases.
-10.40
See there is a negative sign. This means it is a withdrawal
8.50
See there is a positive sign. This means it is a deposit
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
4x + 2y = -18
Answer:
Submit Answer
attestato
PLSSS HELP ASAP
Two cars leave towns 760 kilometers apart at the same time and travel toward each other. One car's rate is 20 kilometers per hour less than the other's. If they meet in 4 hours, what is the rate of the slower car?
Answer:
Let speed of slower car be xkm/h
Therefore rate of other car=x+20 km/h
After 4 hrs ,
Distance covered by Car A=4x
Distance covered by Car B=4x+80
4x+4x+80=760km
8x=680
x=45
The rate of the slower car=45km/h
Give the geometric representation of 2x+ 1= x-4 as an equation in (a) one variable (b) two variables
please help
Answer:
Step-by-step explanation:
2x+1=x-4
2x-x= -4-1
1x=-5
x=-5