Question 2 of 5
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each explicit formula to its corresponding recursive formula,
Answers
Given:
The different recursive formulae.
To find:
The explicit formulae for the given recursive formulae.
Solution:
The recursive formula of an arithmetic sequence is [tex]f(n)=f(n-1)+d, f(1)=a,n\geq 2[/tex] and the explicit formula is [tex]f(n)=a+(n-1)d[/tex], where a is the first term and d is the common difference.
The recursive formula of a geometric sequence is [tex]f(n)=rf(n-1), f(1)=a,n\geq 2[/tex] and the explicit formula is [tex]f(n)=ar^{n-1}[/tex], where a is the first term and r is the common ratio.
The first recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=f(n-1)+5[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:
[tex]f(n)=5+(n-1)(5)[/tex]
[tex]f(n)=5+5(n-1)[/tex]
Therefore, the correct option is A, i.e., [tex]f(n)=5+5(n-1)[/tex].
The second recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=3f(n-1)[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:
[tex]f(n)=5(3)^{n-1}[/tex]
Therefore, the correct option is F, i.e., [tex]f(n)=5(3)^{n-1}[/tex].
The third recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=f(n-1)+3[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of an arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:
[tex]f(n)=5+(n-1)(3)[/tex]
[tex]f(n)=5+3(n-1)[/tex]
Therefore, the correct option is D, i.e., [tex]f(n)=5+3(n-1)[/tex].
Answer:
From Edmentum :)
Related Questions
Geometry, please answer question ASAP
Answers
9514 1404 393
Answer:
D. 5.4
Step-by-step explanation:
The point U divides segment SP into the ratio 1 : 2. So, segment SU is 1/2 the length of segment UP.
SU = UP/2 = 3.6/2 = 1.8
The length of PS is ...
PS = PU +US = 3.6 +1.8
PS = 5.4
__
Additional comment
If you were asked to find the value of x, you would discover x=1. That is not what you're asked here.
I need help I don't understand it.
Answers
These angles are corresponding angles, and we know that corresponding angles are equal when a transversal intersects two parallel lines.
So,
8x - 12 = 6x + 8
=> 8x - 6x = 8 + 12
=> 2x = 20
=> x = 20/2
=> x = 10
So, the value of x is 10.
please mark this answer as brainlist
how to change mixed fraction into improper fraction and improper to proper fraction easy way
Answers
Answer with Step-by-step explanation:
To change the mixed fraction into improper fraction you multiply the denominator with the whole and add to numerator.
For example: 4 1/5 = (5*4)+1/5=21/5
To change improper into proper mixed fraction,
Divide the numerator by denominator and write the remainder on numerator
For example: 7/2= 3 1/2
I need help ASAP please
Answers
Answer:
it's the third one.
Step-by-step explanation:
It should be a bold/filled circle on the line instead of an empty one.
can anyone help me please ?
Answers
Basically, everything except choice A.
=========================================================
Explanation:
All exponential functions can be written into the form y = a*b^x
The b term determines if we have growth or decay.
If 0 < b < 1, then we have decay. If b > 1, then we have growth.
------------
For choice A, we have b = 1.7 which satisfies b > 1. This represents growth. So we cross choice A off the list.
Choice B looks almost identical since it appears b = 1.7 here as well, but note the negative exponent. It might help to rewrite choice B into y = 3( 1.7^(-2) )^x and note how b = (1.7)^(-2) = 0.346 approximately. This represents decay.
Choice C has b = 1/3 = 0.33 approximately which is also decay.
Finally, choice D has b = 2^(-1) = 1/(2^1) = 1/2 = 0.5 which is also decay.
Choices B through D have b values such that 0 < b < 1.
------------
Check out the graph below. It visually confirms the answers mentioned earlier. A growth function goes uphill as we move to the right, while a decay function moves downhill while moving to the right.
I used GeoGebra to make the graph.
[tex]\sqrt[3]{x+1} =2x+2[/tex]
Answers
A number added by 7 is the same as that
number times four minus eleven.
Translate into an equation
Answers
Answer:
[tex]x+7=4x-11[/tex]
Step-by-step explanation:
Hi there!
Let [tex]x[/tex] represent "the number".
A number added by 7 is the same as that number times four minus eleven.
A number added by 7 ⇒ [tex]x+7[/tex]
Is the same as ⇒ [tex]x+7=[/tex]
The number times four ⇒ [tex]x+7=4x[/tex]
Minus eleven ⇒ [tex]x+7=4x-11[/tex]
I hope this helps!
On a recent math test. Samantha scored 3 points for each of the 18 multiple choice que non se
answered correctly and 5 points for each of the 6 short response questions she answered correctly
She scored an additional 4 points for the bonus question. Write an expression for her total score on
the test and then find her score.
Answers
The required expression will therefore be:
(3×18) + (5×6) + 4
Her total score is 88points :
From the question given, we are told that Samantha scored 3 points for each of 18multiple questions his means that the total points made here is expressed as:
(3 × 18) ...1
If she got 5 points for each of the 6 short responsmultiple choice questione questions she answered
correctly, the total point made will be expressed as;
(5×6) ... 2
Total score for an additional 4 points for the bonus question will be "4"
Expression for her total score will be the sum of all the expression above as thus:
(3×18) + (5×6) + 4
Taking the sum, her score will be:
= (3×18) + (5×6) + 4
= 54 + 30 + 4
= 84 + 4
= 88 points
The required expression will therefore be:
(3×18) + (5×6) + 4
Her total score is 88points
Learn more about sum here: brainly.com/question/16397188
Fill in the table to explore the graph.
Miles Walked by Alonso
" Time (hours) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Miles Walked
6
V
16
12
Miles
8
4
X
1
4
3
Time (hours)
time
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Answer:
Step-by-step explanation:
so you have divide ok by my and divide 5x1
Math nation section 2
Answers
Send the question?
Must click thanks and mark brainliest
Please help! Geometry 9th grade
Answers
Answer:
69.3
Step-by-step explanation:
if you put it into 2D, you get a right triangle with leg lengths 62 (vertical height) and 31 (1/2 the base's length). Using Pythagorean's Theorem you get sqrt((62^2)+(31^2))= 69.318. Rounding to the nearest tenth you get 69.3
Question Two please help
Answers
Answer:
The similarity statement is RTS and ACB. Other options are correct
how much cost Rs 1136 when it is 10% discount and 13% vat is added then find out the discount and Vat amount
Answers
Answer:
Rs 1155.3
Step-by-step explanation:
1136 * .1 = 113.6
1136 - 113.6 = 1022.4
1022.4 * 1.13 = 1155.3
. If a = 120°, find the measure of angles b, c and d.
Explain your reasoning.
Answers
a full circle has a total of 360°, ∡d and ∡c are vertical angles, namely two angles across from each other at a junction, and therefore ∡d = ∡c.
∡a + ∡b is 120° + 120° thus 240°, since a circle has a total of 360°, 360 - 240 = 120, so the other two angles pick up that slack and divide it among each other evenly, 120/2 = 60, so ∡d = ∡c = 60°.
Brainliest if you help me ….
Answers
If A=(prime number less than 10)list the element of set A and find n(A)
Answers
N(A) =4
( sorry I need the points)
11) MZHGF = 16x + 4, m EGF = 110°,
and MZHGE = 3x + 11. Find x.
G
H
F
E
Answers
=======================================================
Explanation:
The smaller angles HGE and EGF combine to form the largest angle HGF.
This is an example of the angle addition postulate.
(angle HGE) + (angle EGF) = angle HGF
(3x+11) + (110) = 16x+4
3x+121 = 16x+4
121-4 = 16x-3x
117 = 13x
13x = 117
x = 117/13
x = 9 which is the final answer
We can stop here.
--------------------
Extra info (optional section)
Use this x value to find each angle shown below
angle HGE = 3x+11 = 3*9+11 = 27+11 = 38 degreesangle HGF = 16x+4 = 16*9+4 = 144+4 = 148 degreesThen notice how,
(angle HGE)+(angle EGF) = 38+110 = 148
which is exactly the measure of angle HGF
This confirms that the equation
(angle HGE) + (angle EGF) = angle HGF
is true for that x value of x = 9. Therefore, the answer is confirmed.
9514 1404 393
Answer:
11) x = 9°
13) x = -12°
Step-by-step explanation:
11) ∠HGE +∠EGF = ∠HGF
(3x +11) +(110°) = (16x +4)
117° = 13x . . . . . . . . . . . . . . . subtract 3x+4, collect terms
9° = x . . . . . . . . . . . . divide by 13
__
13) ∠BCF +∠FCD = ∠BCD
(x +78) +(x +41) = 95°
2x = -24°
x = -12°
Pls help in this maths problem
Answers
Answer:
SORRY I don't know second number . I did only first .
Seventy-two books were to be divided up among 18 children. Which of the following
expressions is equivalent to this fraction?
a. 8/3 divided by 6/9
b. 8/3 times 2/3
c. 2/9 divided by 8/9
d. 2 times 8/2
Answers
Answer:
a
Step-by-step explanation:
cause if 72 book were divided by 18 kids they would hav all gotten 4 books each
so a is the answer cause it gives youthe answer 4
Answer: a. 8/3 divided by 6/9
Step-by-step explanation: I got this question on my test
How do I do question 2?
Answers
Answer:
518
Step-by-step explanation:
solution:
=8^2^×1^+1+6^2^×1^-1
=8^3+6^1
=8^3+6
=8×8×8+6
=512+6
=518
Find the distance between the two points.
(5,5)
(2.2)
✓ [?]
Enter the number that
goes beneath the
radical symbol.
Answers
Answer:
[tex]{18}[/tex]
Step-by-step explanation:
[tex] \sqrt{(2 - 5) {}^{2} + ( 2 - 5) {}^{2} } [/tex]
[tex] = \sqrt{( - 3) {}^{2} + ( - 3) {}^{2} } [/tex]
[tex] = \sqrt{9 + 9} [/tex]
[tex] = \sqrt{18}[/tex]
Answered by GAUTHMATH
Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
A. 11.7
B. 11.9
C. 11.4
D. 14.4
Answers
Answer:
Option A, 11.7
Step-by-step explanation:
To find height,
tan 68 = 26/h
h = 26/tan(68)
to find x
tan(42) = h/x
x = h/tan(42)
x = 11.7 (rounded to the nearest tenth)
Answered by GAUTHMATH
Find slopes of the given points .
[tex]\Large\star\tt {(5,6)\atop (3,-2)}[/tex]
[tex]\Large\star\tt {(-3,4)\atop (4,-7)}[/tex]
Spam free answers required .
Well explained answer will be marked as brainliest .
Answers
Answer:
Use the slope formula:
m = (y₂ - y₁)/(x₂ - x₁)The first one:
m = (-2 - 6)/(3 - 5) = -8/-2 = 4The second one:
m = (-7 - 4)/(4 - (-3)) = -11/7Answer:
Step-by-step explanation:
1) (x₁,y₁) = (5 , 6) & (x₂,y₂) = (3 , -2)
[tex]Slope = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{-2-6}{3-5}\\\\=\dfrac{-8}{-2}\\\\=4[/tex]
2) (x₁,y₁) = (-3, 4) & (x₂,y₂) = (4 , -7)
[tex]Slope= \dfrac{-7-4}{4-[-3]}\\[/tex]
[tex]= \dfrac{-11}{4+3}\\\\=\dfrac{-11}{7}[/tex]
need help with this!!!
Answers
Answer:
I say the fourth one just because
HELPP!!
What is the approximate sum of this series?
Answers
Answer:
The answer of this question is 134.83
What is the range of the function y = x² + 1?
Answers
Answer
[ 1 by 2, -1 by 2 ]
Step-by-step explanation:
https://haygot.s3.amazonaws.com/questions/1118559_1200733_ans_2ec06a240d2240e49dc1c9fda7b41ef5.jpeg
Answer:
range { 1, ∞ }
Step-by-step explanation:
y = x² + 1
is a parabola with its vertex at (0, 1)
The range is { 1, ∞ }
The product of two numbers is 10000.If one number is 16 times the other numbers ,find the two numbers.
Answers
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
➯Question:The product of two numbers is 10000. If one number is 16 times the other numbers ,find the two numbers.Answer:Both numbers are 25 and 400.Step By Step Explanation:Given that:The product of two numbers is 10000.One number is 16 times the other number.To Find:Both numbers?Solution:Let us consider that one number be n, in question it is stated that other number is 16 times the first number. Therefore, other number is 16n.According to the Question :[tex]\sf↦ Product ~of ~numbers = 10000\\\\↦ n × 16n = 10000\\\\↦ 16n² = 10000\\\\↦ n² = \sf \dfrac{10000}{16}\\\\↦ \sf n = \sqrt{\dfrac{10000}{16}}\\\\↦ \sf n = \sqrt{\dfrac{100\:\times\:100}{4\:\times\:4}}\\\\↦ \sf n = {\cancel{\dfrac{100}{4}}}\\\\➦\pmb{\underline{\boxed{\sf{\pink{n = 25}}}}}[/tex]
Hence,1st number = n = 252nd number = 16n = 16 × 25 = 400∴ Hence, both numbers are 25 and 400.▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
Answer:
(25, 400) or (-25, - 400)Step-by-step explanation:
Let the numbers be x and y.
We have:
y = 16xxy = 10000Substitute y and solve for x:
x(16x) = 1000016x² = 10000x² = 10000/16x² = 625x = √625x = ± 25Then y is:
y = ± 25*16 = ± 400The numbers are:
25 and 400 or -25 and - 400Ashish is 175 cm tall his sister Annu is 8% shorter than him what is Annu's height
pls help
Answers
Answer:
8% out of 175 = ( 8 ÷ 100 ) × 175 = 14
175 cm - 14 = 161 cm
...............
2 cm = 7.5 m in the drawing the mall is 8.6 cm tall how tall is the actual mall
Answers
Step-by-step explanation:
here's the answer to your question
HELP RIGHT AWAY!!!PLEASE EXPLAIN HOW TO SOLVE THE PROBLEM
Answers
Answer:
264
Step-by-step explanation:
Volume = Area of cross section x height
Area of cross section = 1/2 bh
1/2 (8x6) = 24
24 x 11 = 264 yd^3
