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Related Questions
The sum of the first 10 terms of a linear sequence is 5 and the sumof the next 10 terms is 215. Find the sequence.
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Answer:
The first term of the sequence is -8.95 with a common difference of 2.1.
The sequence is:
-8.95, -6.85, -4.75, -2.65...
Step-by-step explanation:
We are given that the sum of the first ten terms of a linear sequence is 5, and the sum of the next ten terms is 215.
And we want to find the sequence.
Recall that the sum of an A.P. is given by:
S = k / 2 ( a + xk)
Where a is the first term, k is the number of terms, and x_k is the last term.
We can represent our term values with the direct formula:
Xn = a + d (n-1)
Where the first term, x₁ = a.
The sum of the first ten terms is 5. Hence, S = 5, k = 10, a = x₁ and x_k = x₁₀:
(5) = 10/2 (a+xk)
5 = 5(a+(a+9d))
2a + 9d = 1
The sum of the next ten terms (that is, from x₁₁ to x₂₀) is 215. Hence, S = 215 when k = 10, a = x₁₁, and x_k = x₂₀:
(215) = (10)/2 (a + xk)
215 = 5((a+d(11-1))+(a+d(20-1)))
2a + 29d = 43
This yields a system of equations:
[tex]\left \{ {{2a+9d=1} \atop {2a+29d=43}} \right.[/tex]
Solve:
(2a + 9d) + (-2a - 29d) = (1) + (-43)
-20d = -42
d = 2.1
Consequently:
a = 1/2(1-9d)
= 1/2(1-9(2.1))
= -8.95
In conclusion, the first term of the sequence is -8.95 with a common difference of 2.1.
The sequence is:
-8.95, -6.85, -4.75, -2.65...
C=pi/2 what is the area?
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Answer:
A=1
Step-by-step explanation:
The formula to find the area of a circle is πr^2, meaning that you divide the diameter in half which is 1. So 1^1 is one. The area would be one.
Hope this helps :)
The area would be one, is, A=1.
What is area of circle?The area of a circle is π multiplied by the square of the radius. The area of a circle, (A) when the radius 'r' is given is πr2. π is approximately 3.142
here, we have,
C=pi/2
The formula to find the area of a circle is πr^2,
meaning that you divide the diameter in half which is 1.
So 1^1 is one.
The area would be one.
To learn more on area of circle click:
brainly.com/question/22964077
#SPJ2
Olivia has blue, pink and orange counters in a bag.
The ratio of blue to pink to orange counters is 4:5:2
(a) What fraction of the counters are blue?
(b) What fraction of the counters are orange?
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Answer:
A. 4/11
B. 2/11
Step-by-step explanation:
Use the given values to find the fractions (4+5+2=11)
Plant A Plant B WeeksHeight (inches) WeeksHeight (inches) 06 04 28 27 Part A To graph the two linear relationships, you need to know which variable is the independent variable, x, and which is the dependent variable, y. Of the two variables, weeks and height, which is the independent variable and which is the dependent? Explain your answer.
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Answer:
Weeks is the independent variable and height is the dependent variable.
Step-by-step explanation:
The height of the plant depends on the weeks the plant has been growing. So the height is the dependent variable. Because the number of weeks doesn't depend on anything, the number of weeks is an independent variable.
HELP PLEASE ASAP WILL GIVE BRAINLIEST
Farmer Hopt started with some alabers on her farm. She had 90 alabers after 5 months. After 16 months, she had 167 alabers. Assume a constant rate of change.
Write an equation in slope-intercept form for total alabers, y, after x months.
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Answer:
[tex]y= 11x+35[/tex]
Step-by-step explanation:
Let's find the slope first. It took hopt 11 months (from 5 to 16) to grow 77 trees. It means that each month he grew [tex]\frac{77}{11} = 7[/tex] trees.
At this point you can use the point-slope form and re-write the equation or, let's think about it. It's a direct proportion. If at month 5 she has 90 trees, one month earlier she had 11 less. two month earlier, 22 less. 5 month earlier, or at x = 0 (ie, our intercept!) she had 55 less trees, or 90-55 = 35 trees
The equation is then [tex]y= 11x+35[/tex]
Mai skated x miles, and Clare skated farther than that. Write an expression for the distance Clare skated. Write an equation to represent the relationship between the distance Mai skated (x) and the distance Clare skated (y).
Whats the answer?
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Answer:
X over y or x/y since y is claire and she skated more
Step-by-step explanation:
Pls brainliest
Is this a function? I don’t think it is but I’m not sure.
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Answer:
no
Step-by-step explanation:
Pleaaaaaaaaaaaaaaaaaaaaaaase help me
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Answer:
It would be the first one
Step-by-step explanation:
Start at 0 and the end shows 2.5
WATER The workers at the plant drink 38 gallons of water per day. Write an equation to find the number of gallons g the workers drink in any number of days d?
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Hope this helps
Enter an expression equivalent to (x^4 y^3 y)^2 in the form x^m y^n
Answers
Answer:
Step-by-step explanation:
GEOMETRY PROOFS!
Given: AB ≅ DB; AC ≅ DC
Prove: ABC ≅ DBC
refer to attachments
WILL GIVE BRAINLIEST! PLS HELP!
Answers
Given that
In ∆ ABD , AB = BD------(1)
=> Angle B = Angle D
Since the angles opposite to equal sides are equal.
=> Angle A = Angle D
and
BC bisects Angle B
=> Angle BCA = Angle CDB ----(2)
And
BC = BC (Reflexive Property) -----(3)
From Eqⁿ(1),(2)&(3) we have
BA = BD
< ABC = BCD
BC = BC ( Common Side)
Therefore, ∆ ABC =~ ∆ DBC
by SAS property
Hence, proved.
Additional comment:
The angles opposite to equal sides are equal.In two triangles , the two sides and the included angle of the first triangle are equal to the corresponding two sides and the included angle in the second triangle then they are congruent and this property is called Side-Angle-Side (SAS) Property.CPCT - Corresponding parts in the Congruent triangles are equal.Angle bisector divides the angle into two equal parts.The sum of two adajacent angles is 180° they are called Linear Pair.also read similar questions:Given: AD perpendicullar DB, DB perpendicullar BC, AB = CD Prove: AB||DC..
https://brainly.com/question/20369276?referrer
given: AB ≈ DC ; AC ≈ DB PROVE: ABC ≈ DCB THE DIAGRAM SHOWS A 2 COLUM PROOF. ORDER THE REASONS SHOWN IN THE LIST TO MATCH THE STATEMENTS ......
https://brainly.com/question/22172471?referrer
Type the missing digit down below
63,927,_76 is divisible by 8.
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Answer:
4
Step-by-step explanation:
Answer:
63,927,476 is divisible by 8.
What is a trend line in math.
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Answer:
Determining if a set of points exhibits a positive trend, a negative trend, or no trend at all.
A trend line, often referred to as a line of best fit, is a line that is used to represent the behavior of a set of data to determine if there is a certain pattern.
What fraction of an hour is 15 minutes?
Give your answer in its simplest form.
Answers
Answer:
1/4
Step-by-step explanation:
15/60 = 1/4
Hello there! :)
15 minutes is 1/4 of an hour.
An hour is 60 minutes:
[tex]\frac{}{60}[/tex]
We have 15 minutes:
[tex]\frac{15}{60}[/tex]
Reduce your answer by dividing 15 and 60 by 15:
[tex]\frac{1}{4}[/tex]
Hope this helps!
~Just a determined gal
#CarryOnLearning
Please mark brainliest!!
[tex]Mysterious Nature[/tex]
find the sum of the first 8 terms of the geometric sequence 2,4,8,16,..
(with solution)
PA HELP PO THANKYOUU
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Answer:
I think the common difference is 2. The formula to create the sequence is n (number) is multiplied by 2.
1 x 2 = 2
2 x 2 = 4
4 x 2 = 8
8 x 2 = 16
16 x 2 = 32
32 x 2 = 64
64 x 2 = 128
128 x 2 = 256
256 is the 8th term of the sequence. Since your question says that we should look for the sum, add the number of the sequence I guess.
2 + 4 +8 + 16 + 32 + 64 + 128 + 256 = 510
If Lucy runs 1 mile in 6
minutes, how many miles
will she run in 23 minutes?
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hi guys pls answer this we will pass the tomorrow
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Answer:
1. 25/24
2. 7/6
3. 4/3
4. 6/8 or 3/4
5. 5/4
1. 1
2. 1/4
3. 2/10 or 1/5
4. 7/3
5. 13/6
Solve. −6.6x=−4 What is the solution to the equation? Enter your answer as a simplified fraction in the box. x =
Answers
Answer:
20/33
Step-by-step explanation:
i took the test
Answer:
x = 20/33
Step-by-step explanation:
−6.6x = −4
Divide both sides by -6.6
x = -4/(-6.6)
x = 40/66
x = 20/33
Answer: x = 20/33
If y + 6 = 45, then y = 39
Answers
Answer:
True!
Step-by-step explanation:
5. How is each centimeter on a ruler further divided?
tenths
fourths
sixteenths
O eighths.
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In an attempt to predict a single response variable y, three models are estimated. The standard error of the estimate for Model 1 equals 10, for Model 2 equals 100, and for Model 3 equals 1000. According to the standard error of the estimate, which model provides the best fit
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How do you know it is positive or negative in exponents.
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use synthetic division to evaluate f(x)=x^3-6x+1 for x=6. f(6)=____
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Given: x=6
By substituting value of x as 6 in the given expression, we get:
[tex]f(6) = {x}^{3} - 6x + 1[/tex]
[tex]→f(6) = {6}^{3} + (6 \times 6) - 1[/tex]
[tex]→f(6) = 216 - 36 + 1[/tex]
Now, using integer sign property,
[tex]→f(6) = 216 - 35[/tex]
[tex]→f(6) = 181[/tex]
Therefore, f(6)=181
Dan and Paul share some money in the ratio 13:5.
Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1.
How much did Paul originally have?
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Answer:
Dan had $104
Paul had $40
Step-by-step explanation:
13x-32=5x+32
8x=64
x=8
8*5=40
13*8=104
BOWLING A bowling alley charges a flat fee to rent shoes. There is an additional fee for each game played. The function y=2.5x+3
represents the cost y of bowling x games. Interpret the parameters of the function.
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URGENTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT
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Answer:
I don't think soo that it make a function
So the answer is A
What is the scale factor from ABC to XYZ?
A 1/5
B 1/6
C 5
D 6
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Answer:
Is 6
Step-by-step explanation:
5X6=30
3X6=18
4X6=24
As water evaporates from a bucket, its weight changes at a rate of -11/4 ounces per day.
what's the answer?
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Answer:
the five differences are 24.88
Find the value of the variable(s) in each figure explain your reasoning.
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Answer:
...............................
Patrick makes chocolate chip cookies. The recipe calls for 1 3/4 cups of flour. If Patrick triples the recipe, how much flour will he need?
A. 3 9/12 cups
B. 4 1/4 cups
C. 3 3/4 cups
D. 5 1/4 cups
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Answer: 21/4 or 5 1/4
Step-by-step explanation: sorry for the 21/4 if this is wroNG IM SOOO SORRy if it is..