The recursive formula to describe a sequence is shown below.
PART A:
State the first four terms of this sequence.
PART B:
Can this sequence be represented using an explicit geometric formula? Justify your answer.
Answers
The first four terms of the sequence are 3, 7, 15, and 31. This sequence is represented using an explicit geometric formula.
What is the recursive rule?A rule is defined such that its definition includes itself.
Example:
F(x) = F(x-1) + c
is one such recursive rule.
PART A:
State the first four terms of this sequence.
[tex]a_1 = 3\\\\a_n = 1+ 2a_{n-1}[/tex]
[tex]a_2 = 1+ 2a_{2-1}\\\\a_2 = 1+ 2a_{1}\\\\a_2 = 7\\\\a_3 = 1+ 2a_{2}\\\\a_3 = 15\\\\a_4 = 1+ 2a_{3}\\\\a_4 = 31\\[/tex]
PART B:
This sequence is represented using an explicit geometric formula.
Learn more about the recursive rule and explicit rule here:
https://brainly.com/question/12620593
#SPJ2
Related Questions
A bungee jumper leaps off a cliff 122 meters from the ground. Her cord, when fully stretched, is 72 meters long, and it takes 6 seconds after the jump for it to extend fully. The distance between e jumper and the ground as a function of time can be modeled as a quadratic function. Which equation represents her distance from the ground as a function of time?
Answers
Answer:
Answer is B.
Step-by-step explanation:
You can solve this by recognizing the vertex and the y-intercept of the quadratic equation based on the information provided.
The vertex occurs 6 seconds into the jump, when the cord is fully stretched to 72m, before it starts to contract again. This is when the jumper is closest to the ground, 122-72 = 50m above the ground. Notice the jumper never reaches the ground because the cord is only 72m long - it can't make it the full 122m - so there will not be an x-intercept (or t-intercept in this case). Anyway - the vertex is (6,50) using this information.
The y-intercept is the point at which t=0, the beginning of the jump. At the beginning of the jump, the jump is still on top of the cliff, 122m up. So the coordinates of the y-intercept are (0,122).
Now plug these values into the vertex form of the quadratic formula and solve for a:
[tex]f(t) = a(t-h)^2+k\\122=a(0-6)^2+50\\72 = 36a\\a=2[/tex]
This means our general equation (in vertex form) for this scenario is:
[tex]f(t)=2(t-6)^2+50[/tex]
Our answer options are in standard form, so just expand the vertex form of the equation to finish:
[tex]f(t)=2(t-6)^2+50\\f(t)=2(t^2-12t+36)+50\\f(t)=2t^2-24t+72+50\\f(t)=2t^2-24t+122[/tex]
find atleast 3 solutions for the following linear equation in two variables:2x + 3y = 4
Answers
First solution :
Say, x = 0
→ 2x + 3y = 4
→ 2(0) + 3y = 4
→ 0 + 3y = 4
→ 3y = 4
→ y = 4/3
x = 0, y = 4/3Second solution :
Say, x = 1
→ 2x + 3y = 4
→ 2(1) + 3y = 4
→ 2 + 3y = 4
→ 3y = 4 - 2
→ 3y = 2
→ y = 2/3
x = 1, y = 2/3Third solution :
Say, x = 2
→ 2x + 3y = 4
→ 2(2) + 3y = 4
→ 4 + 3y = 4
→ 3y = 4 - 4
→ 3y = 0
→ y = 0 ÷ 3
→ y = 0
x = 2, y = 012 points!! Please help out if you can! Means so much!!
Answers
Answer:
(2w+2)(w+8) ≤ 100
Step-by-step explanation:
due in 20 mins help pls
Answers
Step-by-step explanation:
[tex] {13}^{2} = {6.5}^{2} + {x}^{2} \\ {x}^{2} = 126.75 \\ x = 11.2[/tex]
Answer:
11.3 cm
Step-by-step explanation:
since this is an equilateral triangle it's every sides are equal
side length (a) = 13 cm
formula to calculate the height of equilateral triangle is
h = [tex]a *\frac{\sqrt{3} }{2}[/tex]
=[tex]13 * \frac{\sqrt{3} }{2}[/tex]
=[tex]\frac{13\sqrt{3} }{2}[/tex]
=11.25
=11.3
answer choices:
a. 122
b. 102
c. 138
d. 85
Answers
Answer:
option b
Step-by-step explanation:
The sum of the interior angles of a quadrilateral is 360°.
That is,
120 + y + 85 + 53 = 360
y = 360 - 120 - 85 - 53
y = 102
Answer:
Option B is correct
Step-by-step explanation:
Hint :
Sum of angles in quadrilateral = 360°
Simplify :
[tex] {y}^{o} + {120}^{o} + {85}^{o} + {53}^{o} = {360}^{o} \\ {y}^{o} + {258}^{o} = {360}^{o} \\ {y}^{o} = {360}^{o} - {258}^{o} \\ {y}^{o} = {102}^{o} [/tex]
Hope it is helpful...Doughnuts are sold in bags and cartons
A bag holds four doughnuts and a carton holds ten doughnuts
Tom buys B bags of doughnuts and C cartons of doughnuts
He buys a total T doughnuts
Writs down a formula for T in terms of B and C
Answers
Answer:
Doughnuts are sold in bags and cartons
A bag holds four doughnuts and a carton holds ten doughnuts
Tom buys B bags of doughnuts and C cartons of doughnuts
He buys a total T doughnuts
Writs down a formula for T in terms of B and C
Step-by-step explanation:
Doughnuts are sold in bags and cartons
A bag holds four doughnuts and a carton holds ten doughnuts
Tom buys B bags of doughnuts and C cartons of doughnuts
He buys a total T doughnuts
Writs down a formula for T in terms of B and C
y = 4x – 18
y = -5x +9
Answers
Answer:
(3, -6)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y)Terms/CoefficientsSolving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 4x - 18
y = -5x + 9
Step 2: Solve for x
Substitution
Substitute in y [2nd Equation]: 4x - 18 = -5x + 9[Addition Property of Equality] Add 5x on both sides: 9x - 18 = 9[Addition Property of Equality] Add 18 on both sides: 9x = 27[Division Property of Equality] Divide 9 on both sides: x = 3Step 3: Solve for y
Substitute in x [1st Equation]: y = 4(3) - 18Multiply: y = 12 - 18Subtract: y = -6Answer:
x=3
y = -6
Step-by-step explanation:
y = 4x – 18
y = -5x +9
Set the two equations equal
4x – 18 = -5x +9
Add 5x to each side
4x – 18 +5x= -5x+5x +9
9x -18 = 9
Add 18 to each side
9x -18 +18 = 9+18
9x =27
Divide by 8
9x/9 = 27/9
x = 3
Now find y
y = 4x-18
y = 4*3 -18
y =12-18
y = -6
Which point is located on the x-axis?
D
4
А
3
BE
2+
1
C
-4 -3 -2 -1
-1
1
2
3
4 X
-2+
-3+
4
Answers
Answer:
point C ad B located on the x axis
express your answer as a polynomial in a standard form.
Answers
Which class is better, math or science (in your opinion)
comment/answer your fav i need this for a survey
Answers
Answer:
Science is more interesting for me than math and fun!
Step-by-step explanation:
Answer:
Math is more fun for me because you get to learn more stuff in it. Plus, math can help you in everyday stuff like for example cooking.
Step-by-step explanation:
Everyone agrees that learning math can be difficult, but some people believe math is important and some people believe math is not important. Math is important for three reasons: math is everywhere, children need math, and God created math.
The first reason math is important is math is everywhere. Math is used in everyday life; it is useful, but it is more than just useful. Math is there to help us, to keep us well ordered, to help us learn new things, and to help us teach new things. Students will become adults who will use math in their jobs. All kinds of careers use math; for example, musicians, accountants, fashion designers, and mothers use math. However, math is not only used for things you do. It also brings order to everything around you; the world is organized essentially because it was made with math.
The second reason math is important is children need math. Now, as we all know, children are as chaotic as a volcanic eruption, but children, as they grow, need to learn patience. Patience is precisely what math teaches us. It also teaches us curiosity; for example, why is this rule used here? Why would that number be negative? Why is that equation set up like that? These are questions they will learn to ask if they are taught math. The parents’ job is to help their children grow up to become good people who are patient and wise, who want to learn even more about anything and everything. Their future depends on what they have learned and if they have learned mathematics, then they will be able to do many different things—maybe even anything—when they are adults.
The third reason math is important is God created it. This is a reason most adults use to convince their children that math is not boring and unimportant, so it may seem unoriginal. I believe, however, it is something that needs to be stated. God created the universe as well as math. The universe is full of math and it is orderly because of math. The sun is a certain distance from the earth; everything is organized in such a way that no matter what has happened we have always been safe. We need math. From this, you should be able to see how much we really do use and need math. We would not be able to process or even do everyday things without it. Math, in addition to these things, helps us to know God. God gave us math to live well and to serve Him. With everything we learn using math in science, we learn more about the world, which can help draw us closer to God.
Some people say math is unimportant because you don’t need math other than basic math principles—you can live without more complicated math. They say, if you need it, then simply use a calculator and leave the more complicated math to people who like math, the mathematicians. This, however, is not correct; you need math and could not live well without math, even including more complicated math concepts. God made us with a sense of curiosity so we can learn, do, and think about all sorts of things. Math is that thing that connects everything together, everything people love to do: music, cooking, painting, and everything else. Math is important.
Math is important because math is everywhere, children need math, and God created math. This matters to me and other children because math determines our future and how we choose to live.
Dr. Kang, a cognitive psychologist, conducts an experiment examining the effect of emotion on memory. He provides lists of 15 words to two groups of participants at his university. He puts the names of all the participants in a hat. The first 20 names he assigns to Group A and the last 20 he assigns to Group B. Group A is given a list of words that are very emotional in content (e.g., passion, murder). Group B is given a list of words that are neutral in content (e.g., houseplant, desk). He then measures how many words each group is able to remember after being distracted for 5 minutes by watching a video about the history of the university. He finds that Group A remembers 15% more words than Group B. Use the scenario to answer the following questions (A though C).
A. What is the dependent variable? [1 pt]
B. What is the independent variable? [1 pt]
C. Can Dr. Kang make a causal claim that "emotion enhances memory"? Why or why not?
Answers
Answer:
21
Step-by-step explanation:
best pickup line: Even if earth didn't have gravity i would still fall for you.
Select the two values of x that are roots of this equation. x2 + 3x - 3 = 0
A. X- 2
B. X = -3 +721 2
C. x. -3-1
D. x. -3-17
Answers
Answer:
B and D
Step-by-step explanation:
Put these numbers in order from least to greatest.
3/4,0.6, and 0.7
Answers
Answer:
O.6, 0.7, 3/4 (0.75)
Find the equation for the line that passes through the point (−3,−3), and that is perpendicular to the line with the equation x=4.
Answers
Answer:
y = - 3
Step-by-step explanation:
x = 4 is a vertical line parallel to the y- axis
A line perpendicular to it will be a horizontal line parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates of the points the line passes through.
The line passes through (- 3, - 3) with y- coordinate - 3 , then
y = - 3 ← equation of perpendicular line
ANSWER IS C
Which number line represents the solution to 2.5 – 1.2x < 6.5 – 3.2x?
1.) A number line from negative 5 to 5 in increments of 1. An open circle is at 4 and a bold line starts at 4 and is pointing to the left.
2.) A number line from negative 5 to 5 in increments of 1. An open circle is at 4 and a bold line starts at 4 and is pointing to the right.
3.) A number line from negative 5 to 5 in increments of 1. An open circle is at 2 and a bold line starts at 4 and is pointing to the left.
4.) A number line from negative 5 to 5 in increments of 1. An open circle is at 2 and a bold line starts at 4 and is pointing to the right.
Answers
Answer:
x <2
Step-by-step explanation:
2.5 – 1.2x < 6.5 – 3.2x
Add 3.2x to each side
2.5 – 1.2x+3.2x < 6.5 – 3.2x+3.2x
2.5 +2x < 6.5
Subtract 2.5 from each side
2.5+2x-2.5<6.5-2.5
2x<4
Divide by 2
2x/2 < 4/2
x <2
Question 5 of 10
In the diagram below, 30 is parallel to XY. What is the value of x?
769
Answers
Answer:
D
Step-by-step explanation:
a and 76° are corresponding angles and are congruent , then
x = 76° → D
m∠DEF = __because they are_________
Answers
Answer:
m∠GDE
alternate interior angles
If the first three Fibonacci numbers are given as x, = 1, X2 = 1 and x3 = 2,
what is the value of n for which X, + Xp = 55?
Answers
Answer:
n=8
Step-by-step explanation:
Which value of “x” would satisfy the following equation 24x - 18 - 8x - 30 = 96?
Answers
Answer:
x = 9
Step-by-step explanation:
24x - 18 - 8x - 30 = 96
add or subtract like terms
16x - 48 = 96
shift - 48 to right hand side . when it goes to other side minus changes to plus
16x = 96 + 48
16x = 144
x = 144/16
x = 9
to prove that the value of x satisfy the given equation or not.
to prove that the value of x is 9 substitute 9 inplace of x and if it gives 96 then it satisfy
24x - 18 - 8x - 30 = 96
24*9 - 18 - 8*9 - 30 = 96
216 - 18 - 72 - 30 = 96
216 - 120 = 96
96 = 96
since both sides is equal to 96 it can be concluded that the value of x is 9.
Which value of “x” would satisfy the following equation 24x - 18 - 8x - 30 = 96?
AnswerX = 9Step by Step Explanation24x - 18 - 8x - 30 = 96
First let's just add/subract the following terms.
16x - 48 = 96
Second.. shift the 48 to the right side. after that change the minus sign into plus sign.
16x = 48 + 96
16x = 44
x = 144/16
x = 9
Explanation:
So we just prove that the value of x satisfy the equation true or not.To prove that the value of x is 9.. we just substitute the 9 in place of x and if it was 96 the result of the equation the problem must be true.So we begin to solve it!
24x - 18 - 8x - 30 = 96
24*9 - 18 - 8*9 - 30 = 96
216 - 18 - 72 - 30 = 96
216 - 120 = 96
Since that all both sides are equal to 96 it can be concluded that the value of x is 9.
#LearnwithBrainly
rewrite the following linear equation in general form
Answers
Given:
The linear equation is:
[tex]y+6=-\dfrac{5}{2}(x+4)[/tex]
To find:
The general form of the given linear equation.
Solution:
The general form of a line is equation is:
[tex]Ax+By=C[/tex]
We have,
[tex]y+6=-\dfrac{5}{2}(x+4)[/tex]
Multiply both sides by 2.
[tex]2(y+6)=-5(x+4)[/tex]
[tex]2(y)+2(6)=-5(x)-5(4)[/tex]
[tex]2y+12=-5x-20[/tex]
Isolating variable terms, we get
[tex]2y+5x=-20-12[/tex]
[tex]5x+2y=-32[/tex]
Therefore, the general form of the given linear equation is [tex]5x+2y=-32[/tex].
Can someone tell me… Given the right triangle ABC, what is the value of tan(A)?
A. 5/13
B. 12/13
C. 12/5
D. 13/12
Answers
Answer:
C
Step-by-step explanation:
tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{24}{10}[/tex] = [tex]\frac{12}{5}[/tex] → C
Select the choice that follows the correct sequence of steps in solving this inequality.
-1/2y - 1 < or equal to 3
Answers
Answer:
what are the choices?? if you don't mind me asking
At a carnival, single rides cost $2 each, and all day ride passes cost $15. The total revenue for the day was $2,960.
Which equation can be used to represent x, the number of single ride passes sold and y, the number of all day ride
passes sold?
O 2x + 15y = 2,960
O 12x + 5y = 2,960
O 15x + 2y = 2,960
O 17x + 15y = 2,960
Answers
Answer:
2x+15y=2960
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Please answer i will give brainliest
Answers
Answer:
sorry bro......sis
Step-by-step explanation:
don,t know its answer
Degree= radian x 57.3 = 5π/9 x 57.3 = 100.007 degree
I hope that helps and wish you the best !!
FIRST ANSWER GETS BRAINLIEST !!!!
16.
What is the solution of the equation 56 = 2.8y ?
a. y = 156.8
b. y = 58.8
c. y = 2
d. y = 20
Answers
Answer:
When you solve for y, you get y = 20.
Step-by-step explanation:
You isolate the variable by dividing each side of the equation by the number with the variable, therefore getting 20.
[tex]\longrightarrow{\green{d.\:y\:=\:20}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
➝[tex]\:56 = 2.8y[/tex]
➝[tex]\:y = \frac{56}{2.8} [/tex]
➝[tex]\:y = 20[/tex]
Therefore, the value of [tex]y[/tex] is 20.
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
➝[tex]\:56 = 2.8y[/tex]
➝[tex]\:56 = 2.8 \times 20[/tex]
➝[tex]\:56 = 56[/tex]
➝[tex]\:L.H.S.=R. H. S[/tex]
Hence verified.
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Translate to the correct equation: The sum of 24 and three times a number is 57 *
Translate into an inequality: Six less than double a number is less than 18.
Answers
Answer:
EQUATION: 24 + 3X = 27. INEQUALITY: 2X - 6 < 18.
Step-by-step explanation:
For the equation:
"A number" means that we do not know what the number is yet. So it is a variable. I chose the variable, "X."
"The SUM of 24 AND" means we are adding 24 to something. So what we have so far is "24 + ..."
"3 times a number" means we are multiplying 3 by the unknown variable X. So 3X. What we have so far is "24 + 3X..."
"is 57" means that everything we've just stated equals 57.
Our entire equation is: 24 + 3x = 27.
For the inequality:
Inequalities mean that two expressions are NOT equal to each other.
"6 less than" means that we subtract 6. So we have,"6 - ..." so far.
"Double a number" means 2 times a number, which we are saying is X. So "2X."
" is less than 18" means that everything we just said is less than the value of 18.
So the whole inequality is: 2X - 6 < 18.
how to solve mix surds 8√2+2√8
Answers
Answer:
[tex] { \tt{8 \sqrt{2} + 2 \sqrt{8} }}[/tex]
separate the biggest root ( √8 ):
[tex]{ \tt{ = 8 \sqrt{2} + 2 \sqrt{4 \times 2} }} \\ = { \tt{ 8 \sqrt{2} + (2 \times 2) \sqrt{2} }} \\ = { \tt{8 \sqrt{2} + 4 \sqrt{2} }}[/tex]
factorise √2 out:
[tex] = { \tt{(8 + 4) \sqrt{2} }} \\ \\ = { \bf{12 \sqrt{2} }}[/tex]
Consider the polygon shown. Determine the value of y.
67
75
Answers
Answer:
70 degrees
Step-by-step explanation:
It's a right angle and have angles. The polygon is 5 sides. It's 540 degrees.
It's complementary.
Step-by-step explanation:
i don't know but i think it 157 because:
180-67=113
113-90=23 x
180-23-75=82 y
hope u can understand this
Find the distance between the pair of points given on the graph.
Answers
Answer:
√74
Step-by-step explanation:
49 + 25
if brainly deletes this answer, i swear this community is going down in the dumps
Answer:
[tex]\sqrt{74}[/tex] = 8.6
Step-by-step explanation:
use distance formula
points are (4,2) and (-3,-3)
d= [tex]\sqrt{(x_{2}-x_{1) ^{2} + (y_{2} -y_{1} )^{2} }[/tex]
substitute points into formula
help please asap just the answers
a = 2 ; b = −1 and c = −3
Answers
Answer:
-5/ 3
Step-by-step explanation:
solving 2a - b
= (2 × 2) - (-1)
= 4 + 1
= 5
solving (2a - b)/ c
= 5/ (-3)
= -5/ 3
that is the third option
[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]
[tex] \huge\underline{\sf{\red{Problem:}}}[/tex]
6.) Detemine the value of [tex] \sf{(2a - b) \div c.}[/tex]
[tex] \huge\underline{\sf{\red{Given:}}}[/tex]
[tex]\quad\quad\quad\quad\sf{a = 2}[/tex]
[tex]\quad\quad\quad\quad\sf{b = - 1}[/tex]
[tex]\quad\quad\quad\quad\sf{c = - 3}[/tex]
[tex] \huge\underline{\sf{\red{Solution:}}}[/tex]
[tex]\quad\quad\quad\quad\sf{⟶(2a- b)÷c}[/tex]
[tex]\quad \quad \quad \quad \sf{⟶(2(2)-(-1))÷(-3)}[/tex]
[tex]\quad \quad \quad \quad \sf{⟶(4-(-1))÷(-3)}[/tex]
[tex]\quad \quad \quad \quad \sf{⟶4+1÷(-3)}[/tex]
[tex]\quad \quad \quad \quad ⟶ \boxed{ \sf{ - \frac{5}{3} }}[/tex]
[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]
[tex]\huge\quad\quad\underline{ \boxed{ \sf{ \red{ - \frac{5}{3} }}}}[/tex]
[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]
#CarryOnLearning
[tex]\sf{\red{✍︎ C.Rose❀}}[/tex]