Answers
[tex]a_n=3a_{n-1}-4[/tex]
Step-by-step explanation:Try the answers
You can try the answers to see what works. You can expect all of the choices to match the first two terms, so try some farther down. Let's see if we can get -25 from -7.
a) 3*(-7) -4 = -21 -4 = -25 . . . . this one works
b) -7 -2 = -9 . . . . ≠ -25
c) -3(-7) +2 = 21 +2 = 23 . . . . ≠ -25
d) -2(-7) +1 = 14 +1 = 15 . . . . ≠ -25
The formula that works is the first one.
_____
Derive it
All these formulas depend on the previous term only, so we can write equations that show the required relationships. Let the unknown coefficients in our recursion formula be p and q, as in ...
[tex]a_n=p\cdot a_{n-1}+q[/tex]
Then, to get the second term from the first, we have
... 1·p +q = -1
And to get the third term from the second, we have
... -1·p +q = -7
Subtracting the second equation from the first gives ...
... 2p = 6
... p = 3 . . . . . . . this is sufficient to identify the first answer as correct
We can find q from the first equation.
... q = -1 -p = -1 -3 = -4
So, our recursion relation is ...
[tex]a_n=3a_{n-1}-4[/tex]
Related Questions
Quadrilateral QRST has two pairs of congruentes sides, but it is not a parallelogram. What figure is it? What further condition would have to satisfy to be a parallelogram?
Answers
Answer:
The correct answer is: [C]:
________________________________________________
" {The figure is a kite. To be a parallelogram, it would have to have pairs of opposite congruent sides, not just congruent sides. } ."
________________________________________________
Step-by-step explanation:
________________________________________________
Note that "all" squares are "parallelograms" ; and that "all" rectangles are
"parallelograms" ;
yet: "Not All parallelograms" are "squares" or "rectangles".
________________________________________________
The question asks:
________________________________________________
"Quadrilateral QRST has two pairs of congruent sides, but it is not a parallelogram.
What figure is it?
What further condition would have to satisfy to be a parallelogram? " .
________________________________________________
So; we can rule out:
________________________________________________
"Answer choices:
[A]: "The figure is a square..." ;
________________________________________________
[B]: "The figure is a rectangle..." ; AND :
________________________________________________
[D]: "The figure is a square..." .
________________________________________________
We are left with:
________________________________________________
Answer choice: [C]:
________________________________________________
" { The figure is a kite. To be a parallelogram, it would have to have pairs of opposite congruent sides, not just congruent sides. } " .
________________________________________________________
Which of the following fractions are less than or equal to 0.66? Select all that apply.
D 9/14
C 33/50
A 3/7
B 4/9
Answers
All of them
Step-by-step explanation:A. 3/7 ≈ 0.43
B. 4/9 ≈ 0.44
C. 33/50 = 0.66
D. 9/14 ≈ 0.64
All of the above numbers are 0.66 or less.
the temperature in Tampa was 55°F at 5a.m . It rose 7°every hour for the next 2 hours and then rose 8° every hour for 3 hours after that. It then remained constant until 3p.m. what was the temperature at noon.
Answers
Answer:
93 °F
Step-by-step explanation:
At 7 am, the temperature was 55 °F + 2×7 °F = 69 °F.
At 10 am, the temperature was 69 °F + 3×8 °F = 93 °F.
Since the temperature was constant until 3 pm, it was 93 °F at noon.
f divided by 1/4 for f =2/9
Please help FAST
ASAP
Answers
[tex]f\div\dfrac{1}{4}=f\times\dfrac{4}{1}=4f\\\\f=\dfrac{2}{9}\to4f=4\times\dfrac{2}{9}=\boxed{\dfrac{8}{9}}[/tex]
At the produce counter, 71⁄5 pounds of seedless grapes cost $12.89. How much would 3 pounds cost?
A. $3.58
B. $5.16
C. $1.79
D. $5.37
Answers
Answer:
D. $5.37
Step-by-step explanation:
We need to figure out how much grapes cost per pound
Change the mixed number to an improper fraction
7 1/5 = (5*7+1) /5 = 36/5
$12.89 / 36/5
Copy dot flip
12.89 * 5/36 = 1.79 per lb
If we are purchasing 3 pounds, we will multiply by 3
3 lbs * $1.79 / lb = $5.37
the perimeter of a rectangle whose sides are lengths ( 4z + 3 ) units and ( 3z + 5 ) units
Answers
Answer:
14z + 16 is your perimeter
Step-by-step explanation:
To solve the perimeter, add all sides together. Note that in a rectangle, the opposite sides are congruent and parallel to each other.
Let Perimter = p
p = 2(4z + 3) + 2(3z + 5)
Simplify. Distribute the numbers.
2(4z + 3) = 8z + 6
2(3z + 5) = 6z + 10
Simplify. Combine like terms
p = 8z + 6 + 6z + 10
p = 14z + 16
14z + 16 is your perimeter
~
Evaluate the expression 8 to the second power + 3.8 - 10 * 2
Answers
Answer:
47.8
Step-by-step explanation:
8^2+3.8-10*2
64+3.8-20
47.8
PLEASE HELP, will give brainliest if you answer
consider the function represented by the equation 16b = 4r - 12. write the equation in function notation, where b is the independent variable. Must show work for full credit
Answers
b=1/4r-3/4
Step-by-step explanation:Divide everything by 16
Leave it a fraction
So ye...
a random generator is used to select an integer from 1 to 3 inclusive. What is the difference between the estimated probability that a 3 is generated and the actual probability that a 3 is generated?
1 2 3 3 3 2 2 1 1 1 2 3 1 1
A. 0.29
B. 0.33
C. 0.05
D. 0.04
Answers
Answer:
option no D
Step-by-step explanation:
AS it given that it is a random generator
so it will generate random integers between 1 and 3
so
possible sample space = {1,2,3}
Total no of out comes = 3
Estimated probability that 3 will occur will be obtained by dividing total no of outcomes with total no of possible events to occur
as the occurrence of event is only 1
so
Estimated probability = 1 /3 = 0.33333
Now
The experiment is performed
total outcomes = 14
Total no of like able events that 3 occurred = 4
Actual probability = 4 / 14
= 0.2857
Difference between actual and estimated probability is = 0.3333-0.2857
=0.0421
≅0.04
which is option D
Final answer:
The actual probability of a 3 being generated is 1/3, and the estimated probability from the given sequence is 4/14. The difference between the two probabilities is roughly 0.05, which corresponds to answer choice C.
Explanation:
The question refers to the probability of a random generator selecting the number 3 from a set of integers ranging from 1 to 3, where each number has an equal chance of being selected. The actual probability of the random generator selecting a 3 is 1/3, as there are three possible outcomes and each is equally likely. To find the estimated probability, we can look at the frequency of the number 3 in the provided set of generated numbers: (1 2 3 3 3 2 2 1 1 1 2 3 1 1). In this set, there are 4 occurrences of the number 3 out of 14 total numbers. Therefore, the estimated probability is 4/14 or approximately 0.2857. The difference between the estimated and actual probabilities is 0.3333 (actual) - 0.2857 (estimated) = 0.0476. When rounded to two decimal places, the difference is approximately 0.05. Thus, the correct answer to the question would be C. 0.05.
Select linear or nonlinear to correctly classify each function.
Answers
Answer:
okiii i got the answers right here i hope this helps!
Step-by-step explanation:
oki so for the first one liner
the second it non liner
third is also non liner
and the lasst one is liner
Pat bounces a basketball 25 times in 30 seconds. At that rate, approximately how many fimes will Pat bounces the ball in 150 seconds?
Answers
Answer:
125 times
Step-by-step explanation:
Set up the proportion
25 times/ 30 seconds = x / 150 seconds Multiply by 150
25 * 150 / 30 = x
3750 / 30 = x
x = 125
He will be able to bounce the ball 125 times
Answer:
The ball will bounce 125 times
Step-by-step explanation:
We can use ratio's to solve this problem. I will put how many times the basketball is bounced on top and how many seconds on the bottom.
25 times x times
------------- = ----------------
30 seconds 150 seconds
Using cross products
25 * 150 = 30 * x
Divide each side by 30
25*150/30 =30*x/30
25 * 5 = x
125 =x
find the value of x.
Answers
Answer:
71.79 degrees
Step-by-step explanation:
The cosine is (adjacent side to angle) / (hypotenuse)
so the cosine of x = 5/16
to get x you multiply cosine by its inverse
(cos^-1 x)(cos x) = (cos^-1 x)(5/16)
= 71.79 degrees
A punter kicks a football upward with an initial velocity of 48 feet per second. After how many seconds does the ball hit the ground? Use the formula h=rt−16t2, where h represents height in feet and r represents the initial velocity (rate) in feet per second.
A. 3
B. 6
C. 8
D. 12
Answers
A. 3
Step-by-step explanation:Fill in the given values in the formula (h=0, r=48) and solve for t.
... 0 = 48t -16t²
... 0 = 16t(3 -t)
This is true for t = 0 and for t = 3.
The ball will take 3 seconds to hit the ground.
Answer:
A.3
Step-by-step explanation:
once out of every two weeks of the year would be how may days through out the year
Answers
Answer:
26 most years; 27 some years
Step-by-step explanation:
1 day out of 14 is 1/14 of the number of days in a year.
The number of days in a year depends on the year or years you're talking about. In all cases, there are not an integer number of weeks in a year, so days are left over. 365/14 = 26 1/14.
For example, if you're concerned with every other Monday, most years, there will be 26 of them, but every few years there will be 27. Over a period of 800 years, there will be exactly 71 years with 27 days of interest instead of 26. 800 is not divisible by 71, so the spacing will be uneven.
A line has __________ dimension and is usually represented with two arrowheads.
one
two
three
Points that lie in the same plane are known as ___________ points.
collinear
coplanar
coordinate
Answers
1. A line has only a length dimension. It has no width or height. It is a one-dimensional object.
2. Points on the same line are collinear. On the same plane, they are called coplanar. Coordinates locate a point relative to some measurement reference.
Your class wants to know to most typical age of student in your class. It collects the ages of all students and the teacher. Which measures of central tendency would give you the best typical student age
Answers
Answer:
Median.
Step-by-step explanation:
Assuming the teacher is not of similar age to the students, their higher age would pull the mean higher than if the teacher were not included, where the median would not be pulled by this extreme value.
What is the solution to the system of equations?
x+y = 2
x -y =4
(__ , ____)
Answers
So with this system of equations, I will be using the elimination method. With the two equations, add them together and you will get:
[tex]2x=6[/tex]
Since the y-variable has been eliminated, we can solve for x. With this, divide both sides by 2:
[tex]x=3[/tex]
Now that we know the value of x, substitute it into either equation to solve for y:
[tex]3+y=2\\y=-1\\\\3-y=4\\-y=1\\y=-1[/tex]
Answer:In (x,y) form, your answer is (3,-1).
Answer:
x=3, y=-1
Step-by-step explanation:
x+y = 2
x -y =4
I will use elimination to eliminate the variable y. Add the two equations together.
x+y = 2
x -y =4
-------------
2x = 6
Divide each side by 2
2x/2 = 6/2
x = 3
But we still don't know y
x+y =2
Substitute x=3 into the equation
3+y =2
Subtract 3 from each side
3-3 +y =2-3
y =-1
What is the property of addition that is illustrated by the equation 0+34=34?
Answers
Answer:
Additive identity.
Step-by-step explanation:
The zero is the additive identity. It is so named because when you add 0 to anything, you leave the unchanged. To give you a better idea about what this is, the multiplication identity is 1
One times anything does not change anything's value. 1 * 33 = 33. 33 is left unchanged.
In kite JKLM , MJ=JK and ML=KL . Diagonals JL¯¯¯¯¯ and MK¯¯¯¯¯¯¯ intersect at point P, m∠MLK=48∘ , and m∠JKM=30∘ . What is m∠JML ?
Answers
Answer:
96°
Step-by-step explanation:
ΔKLM is isosceles, so base angle KML will be half the supplement of ∠MLK, or ...
.... ∠KML = (180° -48°)/2 = 66°
ΔKJM is also isosceles, so base angle JMK will be the same measure as ∠JKM, 30°.
∠JML = ∠JMK + ∠KML = 30° +66°
∠JML = 96°
PLZ HELP WILL MARK BRAINLEST SOLVE FOR X
Answers
[tex]\frac{x}{8} + 19 = 30[/tex] - subtract 19 from both sides
[tex]\frac{x}{8} = 11[/tex] - multiply both sides by 8
[tex]x = 88[/tex]
In this equation, x = 88.
Carter has balance of -2,096.37 on his bank loan.He makes a payment and subtracts $500 of his debt.Then he decides to make a monthly payment to subtract $250 of the debt each month.What is the least number of months that Carter needs to make the monthly payment to pay off the original debt? Explain your thinking
Answers
7 months
Step-by-step explanation:After Carter makes his $500 payment, the balance on the loan is -1596.37. We want to find the number of months (m) such that ...
... -1596.37 +250m ≥ 0
... m ≥ 1596.37/250 . . . . add 1596.37, divide by the coefficient of m
... m ≥ 6.4
The least number of months that is more than 6.4 is 7 months.
_____
Comment on this answer
Carter's loan balance may also be affected by interest charged on the loan amount. We don't expect those charges to be so high as to require an additional month's payment.
If f(x) is a third degree polynomial function and g(x) = f(–2x), which of the following is NOT true?
f(x) and g(x) have the same x-intercepts.
f(x) and g(x) have the same y-intercepts.
f(2) = g(–1)
f(x) and g(x) have the same number of zeros
Answers
Answer:
f(x) and g(x) have the same x-intercepts (is not true)
Step-by-step explanation:
g(x) is a reflection across the y-axis and a horizontal compression of f(x). In general those transformations will move the x-intercepts. (The y-intercept and the number of x-intercepts will remain unchanged.)
_____
Comment on the question/answer
f(x) = x^3 is a 3rd degree polynomial. When transformed to g(x) = -8x^2, its only x-intercept (x=0) remains the same. The answer above will not apply in any instance where the only x-intercept is on the line of reflection. (The question is flawed in that it does not make any exception for such functions.)
The fee for a balance transfer is 2% of the amount of the transfer. If b represents the amount of the balance transfer and ƒ represents the amount of the fee, which of the following equations represents the relationship between b and ƒ?
b = 0.2ƒ
ƒ = 0.02b
b = 0.2 + ƒ
ƒ = b + 2
Answers
Answer:
f=0.02b
Step-by-step explanation:
So we want to figure out the fee (f) therefore our answer will be in terms of f=(something). Now since the fee is 2% and 2% is decimals is 2÷100=0.02 then:
f=0.02b
Meaning that the fee is 2% of the balance (b).
Simplify (2p+3)2 - (2p-3)2 (Give proper detailed answer with all steps)
Answers
Answer:
[tex]24p[/tex]
Step-by-step explanation:
There's a very useful pattern in factoring and multiplying binomials called a difference of squares, and it looks like this:
[tex](x+y)(x-y)=x^2-y^2[/tex]
We can use this difference of squares to factor the expression we've been given, setting [tex]x=2p+3[/tex] and [tex]y=2p-3[/tex] to obtain the expression
[tex](2p+3)^2-(2p-3)^2=[(2p+3)+(2p-3)][(2p+3)-(2p-3)][/tex] (1)
tackling each of the multiplicands on the right:
[tex](2p+3)+(2p-3)=2p+2p+3-3=4p[/tex] (Left)
[tex](2p+3)-(2p-3)=2p-2p+3-(-3)=3+3=6[/tex] (Right)
This simplifies the expression on the right of (1) to [tex]4p\cdot6[/tex], or simply [tex]24p[/tex].
The ratio AB to CB is
Answers
Answer:
1/3
Step-by-step explanation:
The ratio of AB to CB
AB/CB
3/9
Simplifying by dividing the top and bottom by 3
1/3
(4x10^6) - (2x10^5)
Simplify!
Answers
3, 800, 000
When ( 4 × 10^6 ) - ( 2 × 10^5 ) is simplified, the answer is:
3, 800, 000.
STEP-BY-STEP EXPLANATION:
= ( 4 × 10^6 ) - ( 2 × 10^5 )
= ( 4 × 1, 000, 000 ) - ( 2 × 100, 000 )
= ( 4, 000, 000 ) - ( 200, 000 )
= 3, 800, 000
Trevon is making payments on a car that costs $26,555. He makes 36 equal payments. If he rounds the equal payments up to the nearest whole dollar, about how much will he overpay after 36 months? Show your work to justify your answer.
Answers
Answer:
$13
Step-by-step explanation:
$26,555 ÷ 36 = 737.6388889 ≈ $738 per month
36 × 738 = $26,568
= $13
Answer:
$13 will be overpaid after 36 months if payments are rounded of to nearest whole number dollar.
Step-by-step explanation:
We are given the following in the question:
Total cost of car = $26,555
Number of equal installments made = 36
Payment of 1 installment =
[tex]\displaystyle\frac{\text{Toatl cost}}{\text{Number of installments}} = \frac{26555}{36} = 737.6389\$[/tex]
Rounding of to nearest whole number, payment of one installment = $738
Value of 36 installments of $738 each =
[tex]36\times 738 = 26568\$[/tex]
Money overpaid after 6 months =
[tex]26568 - 26555 = 13\$[/tex]
Thus, $13 will be overpaid after 36 months if payments are rounded of to nearest whole number dollar.
30 ounces = how many pounds and ounces
Answers
Answer: " 1 lb , 14 oz. " .
_________________________________________________
Step-by-step explanation:
_________________________________________________
Note the exact conversion: " 16 oz. = 1 lb. " .
→ {that is: " 16 ounces = 1 pound " .}.
_________________________________________________
30 oz. * ( 1 lb / 16 oz). = [tex]\frac{30}{16}[/tex] lbs. ;
= (30/2) / (16/2) lbs.
= (15 / 8) lbs. ;
_________________________________________________
1
8 ┌ 15
- 8
7 ;
______________________
The answer is equal to: " 1 7/8 lbs. " .
→ (1 lb) + (7/8) (lb). ;
______________________
→ (7/8) lb. = how many "oz." ??
_______________________
Note the exact conversion: " 1 lb. = 16 oz. " .
_______________________
→ [tex]\frac{7 lb}{8}[/tex] * [tex]\frac{16 oz}{1 lb}[/tex] ;
= [tex]\frac{7}{8} * \frac{16}{1}[/tex] oz. ;
→ The "8" cancels to a "1" ; and the "16" cancels to a "2" ;
→ {since: " {16 ÷ 8 = 2 } " ;
and: {since: " {8 ÷ 8 = 1 } " .
_______________________________________________
→ So we can rewrite as:
_______________________________________________
→ [tex]\frac{7}{1} * \frac{2}{1}[/tex] oz. ;
= { 7 * 2 } oz. ;
= 14 oz.
_______________________________________________
→ So:
_______________________________________________
→ " 30 oz. " = " (1 lb) + (7/8) lb. " ;
= " 1 lb. + 14 oz. " ;
= " 1 lb , 14 oz. " .
_______________________________________________
→ The answer is: " 1 lb , 14 oz. " .
_______________________________________________
Let us check our answer:
→ Does: " 1 lb. + 14 oz. = ? 30 oz. ? " ;
_______________________________________________
Note the exact conversion: " 1 lb. = 16 oz. " .
_______________________________________________
→ Does: " 16 oz. + 14 oz. = ? 30 oz. ?? " ;
_______________________________________________
₁
16 oz
+ 14 oz
30 oz.
_______________________________________________
→ Does: " 30 oz. = ? 30 oz. ? " ??? ; → Yes!
_______________________________________________
Hope this helps!
Best wishes to you in your academic endeavors
— and within the "Brainly" community!
_______________________________________________
The frequency (F) and length (L) of a wave are related by the following formula: F x L = 3.0 x 1010. Consider that the wavelength of violet light is 1.3 x 10−8. What is the frequency of violet light?
Answers
Answer:
2.3 × 10^18
Step-by-step explanation:
Your formula tells you ...
... F × (1.3 × 10^-8) = 3.0 × 10^10
Dividing by the coefficient of F, you have ...
... F = 3.0/1.3 × 10^(10-(-8))
... F ≈ 2.3 × 10^18
Simplify t^12/t^6 help!
Answers
Answer:
t^6
Step-by-step explanation:
The simplified form is [tex]t^{6}[/tex].
What is simplification?Related to "simplification" troubles are a few "solving" issues. just as some expressions contain parentheticals and even nested grouping symbols, so also do a few equations. The simplification manner is equal, whether or not we are running with expressions (and for this reason best simplifying) or equations (so we're additionally fixing).
Like terms: terms which have equal variable elements (identical variable(s) and same exponent(s)). Whilst simplifying using addition and subtraction, you combine “like terms” through retaining the "like term" and including or subtracting the numerical coefficients.
[tex]t^{12}[/tex] divided by [tex]t^{6}[/tex]
[tex]=t^{12-6}\\ = t^{6}[/tex]
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