Answer:
A whole number first term to render as fifth term a value larger than 10000, should be at least 121
Step-by-step explanation:
The formula is given as recursive since it involves the previous number of the sequence, and defined as:
[tex]a_n=a_{n-1}*3+6[/tex]
we also know that the first term is 4
Then in this case, the first five terms are:
[tex]a_1=4\\a_2=4*3+6=18\\a_3=18*3+6=60\\a_4=60*3+6=186\\a_5=186*3+6=564\\[/tex]
So if we want to find the first term in the case that the fifth one is greater than 10,000 using this recursive formula, now we have to start backwards, and say that the fifth term is "> 10000" and what the fourth one is.
Notice that if you have this definition for the nth term, we can obtain from it, what the previous term is to find the general rule:
[tex]a_n=a_{n-1}*3+6\\a_n-6=a_{n-1}*3\\\frac{a_n-6}{3} = a_{n-1}\\a_{n-1}=\frac{a_n}{3} -2[/tex]
So the rule is to subtract 6 from he term, and divide the subtraction by 3. Then working backwards:
[tex]a_5>10000\\\frac{a_5}{3} -2>\frac{10000}{3} -2\\a_4>=\frac{10000}{3} -2\\\frac{a_4}{3} -2>\frac{\frac{10000}{3}-2}{3}-2 =\frac{10000}{9}-\frac{8}{3} \\a_3>\frac{10000}{9}-\frac{8}{3} \\\frac{a_3}{3} -2>\frac{\frac{10000}{9}-\frac{8}{3} }{3} -2=\frac{10000}{27} -\frac{8}{9} -2=\frac{10000}{27} -\frac{26}{9}\\a_2=\frac{10000}{27} -\frac{26}{9}\\\frac{a_2}{3} -2>\frac{\frac{10000}{27} -\frac{26}{9}}{3} -2=\frac{10000}{81} -\frac{80}{27} \\a_1>\frac{10000}{81} -\frac{80}{27}\approx 120.49[/tex]
therefore, the starting first term should be at least about 121 to give a fifth term larger than 10,000
Find the value of x. Give reasons to justify your solution. C ∈ AE
Answer:
x = 11º
Step-by-step explanation:
1. Notice Parallel Lines
2. Understand Angle Relationships When Parallel Lines Are Present (e.g., alternate interior/exterior)
3. ∠CAB ≅ ∠DCA ∴ m∠CAB = 33º
4. Use exterior angle theorem: the sum of non-adjacent angles of the same triangle which the exterior angle is drawn is equal to the measure of that angle.
5. Therefore write and solve the equation 2x + 33º (sum of non-adjacent interior angles) = 5x (exterior angle).
2x + 33 = 5x (C.L.T or Combine Like Terms)3x = 33 (inverse operations; divide by 3)x = 11º (remember to apply units)Answer:
11 degrees
Step-by-step explanation:
Ur welcome
a bike store marks up the wholesale cost of all bikes by 30%. Calvin wants to buy a bike that has a price tag of $125. What was the wholesale price of this bike
Answer:
$162.50
Step-by-step explanation:
Answer:
87.5
You need to take 30 percent from 125 and subtract it to get the wholesale price
Twice the sum of two numbers is 72 if one number is 20 then the other number is_______
Answer:
16
Step-by-step explanation:
If you add 16 to 20 then you get 36. twice of 36 is 72
Can anyone help please! Thanks!
Let f(x) = x2 and g(x) = x - 3.
Evaluate (gºf)(-2).
A. -20
B. 20
C. 7
D. 1
Answer:
D. 1
Step-by-step explanation:
Step 1: Find g of f(x)
g(f(x)) = (x²) - 3
Step 2: Plug in -2 as x
g(f(x))(-2) = (-2)² - 3
g(f(x))(-2) = 4 - 3
g(f(x))(-2) = 1
Mr. Avogadro started with 5.14x1022 atoms of Pa-234. Ten days later Mr. Avogadro calculated the original sample had only 6.43 X 1021 atoms of Pa-234. What s the half life of Pa-234?
Answer:
The half life of Pa-234 is approximately 0.0701656609 days
Step-by-step explanation:
The formula for half life is calculated as:
t½ = t.In(2)/In(No/Nt)
Where:
t½ = Half life of the substance in days
t = Time elapsed in days
No = Beginning amount
Nt = End Amount
In the question,
t = Time elapsed = 10 days
No = Beginning amount = 5.14 × 10²²
Nt = End Amount = 6.43 × 10²¹
t½ = t.In(2)/In(No/Nt)
t½ = 10.In(2)/In(5.14 × 10²²/6.43 × 10²¹)
t½ = 6.9314718056/98.78723754
t½ = 0.0701656609 days
The half life of Pa-234 is approximately 0.0701656609 days
what is 0.73 as a decimal
Answer:
0.73
Step-by-step explanation:
The decimal 0.73 is already in decimal form.
Answer:
73/100
Step-by-step explanation:
I put it down as 100
So 73/100 is the answer
URGENT Please help!!!!! Time I have: 5 minutes There are 101 candies in a pile. Two boys take turns taking candies from the pile. They are allowed to take 1 to 9 candies in one move. The player who cannot make a move, loses. Which player is the winner, the first or the second? Assume both players choose the best strategy.
these tables of values represent continuous functions. for which function will the y-value be the greatest for very large values of x
Answer:
Option A.
Step-by-step explanation:
We need to find a table for which the y-value will be the greatest for very large values of x.
From the given table it is clear that the largest value of x in all tables is 5.
In table A, y=64 at x=5.
In table B, y=32 at x=5.
In table C, y=40 at x=5.
In table D, y=13 at x=5.
It is clear that 64 is the greatest value among 64, 32, 40 and 13.
It means table in option A represents the function for which the y-value will be the greatest for very large values of x.
Therefore, the correct option is A.
Answer:
Option A
Step-by-step explanation:
Took the quiz
Which form of a quadratic function is easiest to use when finding the maximum or minimum value of the function?
Answer:
ax² + bx + c
Step-by-step explanation:
The form of a quadratic equation that is easy to use when finding the maximum or minimum value of the function is ax² + bx + c.
Suppose a quadratic function:
f(x) = 2x² - 8x + 9
Use ( -b/2a , f(-b/2a) ).
-b/2a
a = 2
b = -8
-(-8)/2(2)
8/4
= 2
f(2) = 2(2)² - 8(2) + 9
f(2) = 2(4) - 8(2) + 9
f(2) = 8 - 16 + 9
f(2) = 1
The minimum value of this quadratic function is (2, 1).
It represents a minimum value because a > 0.
Answer:
Vertex form
Step-by-step explanation:
There are several forms of the quadratic equation
Standard form: y = ax^2 + bx + c which is useful for the quadratic equation and the axis of symmetry
Factored form: y = (ax - c)(bx - d) which will give us the zeros
and
Vertex form: y = a(x - h)2 + k where ( h,k) is the vertex
The maximum and minimum would be the value of k
It would be maximum when a >0 and minimum when a<0
Find the area of the right triangle. If necessary, round to the nearest tenth.
A right triangle with side 9 meters and hypotenuse of 18 meters.
a.
15.6 m
b.
70.2 m
c.
42.6 m
d.
243 m
Answer:
b
Step-by-step explanation:
Let's find the area of the adjacent side.
Applying Pythagoras' Theorem,
(adjacent side)²= 18² -9²
adjacent side[tex] = \sqrt{243} [/tex]
adjacent side= 15.588 m (5 s.f.)
Area of triangle= ½ ×base ×height
Area of traingle
[tex] = \frac{1}{2} \times15.588 \times 9 \\ = 70.1m \: (nearest \: tenth)[/tex]
The nearest answer is B.
*If you rounded of to the nearest tenth for the adjacent side first then use the formula for area of traingle, the result would be exactly 70.2 m.
Answer:
The answer above me is correct
Step-by-step explanation:
Solve the compound inequality.
5 < 2x - 1 < 9
Show work
Answer:
3 < x < 5Step-by-step explanation:
5 < 2x - 1 < 9
Add 1 to both sides
That's
5 + 1 < 2x - 1 + 1 < 9 + 1
6 < 2x < 10
Divide all sides by 2
That's
6/2 < 2x/2 < 10/2
We have the final answer as
3 < x < 5Hope this helps you
5t - 30t + 50 =0 pls help!!!
Answer:
t= 2
Step-by-step explanation:
5t - 30t + 50 =0
-50 -50
5t - 30t =-50
-25t = -50
÷-25 ÷-25
t= 2
Answer:
t = 2
Step-by-step explanation:
5t - 30t + 50 = 0
-25t = -50
t = -50/-25
t = 2
3
What is the y-coordinate of the point that divides the
directed line segment from J to k into a ratio of 5:1?
2
AK (7.2)
1
y =
m
m+
-)(x2 - wa) + v
2 3 4 5 6 7 8 9 10 11 x
-11
-2
-3
-4
-5
-8
0-5
0 0
O 6
ibd
-10
J (1,-10)
Answer:
0
Step-by-step explanation:
Given the points J (1,-10) and K (7, 2)
From the section formula
[tex](x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)[/tex]
The y-coordinates of the point that divides the directed line segment from J to K into a ratio of 5:1 is obtained using the formula:
[tex]y=\dfrac{my_2+ny_1}{m+n}\\m=5, n=1, y_1=-10, y_2=2\\Therefore:\\y=\dfrac{5*2+1*-10}{5+1}\\=\dfrac{10-10}{6}\\=0[/tex]
The y-coordinates of the point that divides the directed line segment from J to K into a ratio of 5:1 is 0.
The y coordinate of the point that divides J to K in the ratio 5 : 1 is 0.
DistanceIf a point O(x, y) divides the line segment AB with end points A(x₁, y₁) and B(x₂, y₂) in the ratio n:m, the coordinate of O is:
[tex]x=\frac{n}{n+m} (x_2-x_1)+x_1\\\\y=\frac{n}{n+m} (y_2-y_1)+y_1[/tex]
Let O(x, y) represent the point dividing J to K in the ratio 5 : 1. K(7,2) and J(1, -10)Hence:
[tex]y=\frac{5}{5+1}(2-(-10)) + (-10)=0[/tex]
The y coordinate of the point that divides J to K in the ratio 5 : 1 is 0.
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In a class of c children,2/5 are boys What fraction are girls?
Hello! :)
________ ☆ ☆______________________
Answer:
3/5
Step-by-step explanation:
Here is the work:
You only have to subtract and you will get your answer.
5/5-2/5=3/5
We know 1 whole equals to 5/5, and there is 2/5 boys
So there will be 3/5 girls
Hope this helps! :)
_________ ☆ ☆________________________
By, BrainlyMember ^-^
✨ Good luck! ✨
Answer: 3/5c
Step-by-step explanation:
2/5 is 40%. 100-40=60. Thus, 60% of c, or 3/5c are girls.
Hope it helps <3
put the following values in ascending order 4 2/7, 31/7, 3 5/7, 29/7, 27/7, the above are fractions you will get brainliest
Answer:
2/7 , 5/7 , 3 , 27/7 , 4 , 29/7 , 31/7
Step-by-step explanation:
2/7= 0.3
5/7= 0.7
3
27/7= 3.9
4
29/7= 4.1
31/7= 4.4
please mark me brainliest
Step-by-step explanation:
you first change the mixed fractions to improper fractions
it now becomes 4 2/7 = 30/7 and 3 5/7 = 26/7
then you find the least common multiple of the denominators of the fractions
which is 7. because they all have a common denominator
Then, you divide 7 with the denominators, the answer you get multiply with the numerators
i.e 30/7 ÷ 7 = 1, 1 × 30 = 30
26/7 ÷7=1,1×26=26
31/7÷7=1, 1×31=31
29/7÷7=1,1×29=29
27/7÷7=1,1×27=27
from the answers above you arrange them in ascending order (least to highest)
i.e 26/7 27/7, 29/7,30/7,31/7
A factory can work its employees no more than 5 days a week, and no less than 2 days per
week. Create an inequality to represent the range of days an employee can work. Solve the
inequality to determine the range in hours. Show all of your work and explain each of your
steps. Explain your answer.
Answer: 2 <= X <= 5
Step-by-step explanation:
Answer: 2 <= X <= 5
Step-by-step explanation:
Given that a factory can work its employees no more than 5 days a week, that is, less than or equal to 5 days.
And no less than 2 days per week. That is, greater than or equal to 2 days.
Let X be the number of days employee can work. Then, according to the first statement, X <= 5 and according to the second statement, X >= 2
An inequality to represent the range of days an employee can work will be
2 <= X <= 5
Therefore, an employee can work for 2 days, 3 days, 4 days and 5 days
Which table represents the function y = -2x + 4?
Answer:
Table 2.
Step-by-step explanation:
Input x as 0, the output y should be 4.
y = -2(0) + 4
y = 0 + 4
y = 4
Input x as 1, the output y should be 2.
y = -2(1) + 4
y = -2 + 4
y = 2
Input x as 2, the output y should be 0.
y = -2(2) + 4
y = -4 + 4
y = 0
Help pls!!1!___________
Answer:
1.08*10^11
Step-by-step explanation:
how many more it means you need to subtract :
in year 1965 : 7.2*10^10
in 1995 :1.8*10^11
(1.8*10^11)-(7.2*10^10)
18*10^10-(7.2*10^10)=
10.8*10^10 or 1.08*10^11
Please help i will mark brainliest!
Answer:
A. and C. are true i think :/
Step-by-step explanation:
im not 100% sure though but again, good lucks!
BRAINLIEST!!!! Suppose 40 bikes stand near a playground. Some of them are bicycles, some of them are tricycles, and two of them have four wheels. John counts all the wheels and gets 100, in total. How many tricycles are there?
Answer:
16 tricycles
Step-by-step explanation:
First, let's make a chart:
Bicycles- x bicycles and 2x wheels
tricycles- y tricycles and 3x wheels
Four wheeled vehicles- 2 bikes (given), 8 wheels
Since the total amout of bikes is 40, that means that x+y+8=40
You can simplify that to x+y=38.
now, we're going to form another equations dealing with the number of wheels.
Since we know that four wheeled vehicles already have only 8 wheels, then that means 2x+3y=92
Solve the system of equations:
2x+3y=92
x+y=38
y will be 16
An equation is formed of two equal expressions. There are a total of 16 tricycles.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the total number of bicycles be represented by x, while the total number of tricycles is represented by y.
The total number of vehicles is 40. Therefore, we can write the equation as,
x + y + 2= 40
x + y = 38
Solving the equation for x,
x = 38-y
Also, given that the total number of wheels is 100, also, the number of four-wheelers is 2. Therefore, the total number of wheels can be written as,
2x + 3y + 2(4) = 100
2x+ 3y = 92
Substitute the value of x from the above equation,
2(38 - y) + 3y = 92
76 - 2y + 3y = 92
y = 16
Hence, there are a total of 16 tricycles.
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Need help solving algebraic expression 3H+20+H=180
Answer:
H=40
Step-by-step explanation:
3H+20+H=180
4H +20 = 180
4H = 180 - 20
4H = 160
H = 160/4
H = 40
I solved it Step-by-step hoping this helps u to understand it.. Good Luck
How many different 2-digit numbers are there with the following property: it is even and its digits are distinct?
Answer:
There are 41 different 2-digit numbers with the following properties in the question
Step-by-step explanation:
This may not be easy, but I counted them all:
10
12
14
16
18
20
24
26
28
30
32
34
36
38
40
42
46
48
50
52
54
56
58
60
62
64
68
70
72
74
76
78
80
82
84
86
90
92
94
96
98
I counted them. There were 41 numbers.
In conclusion, there are 41 2-digit numbers with the following properties: it is an even number and its digits are distinct.
A student was given the following diagram and asked to prove that ac=xc. What would be the reason for the second step in the proof?
Answer:
Reflexive property
Step-by-step explanation:
Please answer this question now
Answer:
The midpoint is (2.5, 3.5)
Step-by-step explanation:
The midpoint is the average of the coordinates
x = (x1+x2)/2 and y =(y1+y2)/2
x = (2+3)/2 = 5/2 = 2.5
y = (3+4)/2 = 7/2 = 3.5
The midpoint is (2.5, 3.5)
Answer:
(2.5, 3.5)
Step-by-step explanation:
The midpoint is found by taking the average of the x-coordinates and the average of the y-coordinates.
Here, the average of the x-coordinates is (2 + 3)/2 = 5/2 = 2.5.
The average of the x-coordinates is (3 + 4)/2 = 7/2 = 3.5.
The answer is thus (2.5, 3.5).
~ an aesthetics lover
Find the value of x.
Answer:
x = √21.
Step-by-step explanation:
Triangles ADB and BCD are similar.
So their corresponding sides are in the same ratio:
x / 7 = 3 / x
x^2 = 21
x = √21.
PLS ANSWER I WILL MARK U AS THE BRAINLIEST!!! Correct 36.2598 to
a) decimal place.
b) To the nearest hundredth.
c) to nearest 0.001
d) to the nearest whole number
The question is incomplete.
Complete Question
Correct 36.2598 to
a) to one decimal place.
b) To the nearest hundredth.
c) to nearest 0.001
d) to the nearest whole number
Answer:
a) to one decimal place = 36.3
b) To the nearest hundredth= 36.26
c) to nearest 0.001 = 36.260
d) to the nearest whole number = 36
Step-by-step explanation:
From the question, we are to round up 36.2598 to the following:
a) to one decimal place.
Rounding up 36.2598 to one decimal place means we are looking at the first number after the decimal which is 2. The number after it is 5, so we are adding one to 2. Hence,
36.2598 to one decimal place = 36.3
b) To the nearest hundredth:
Rounding up 36.2598 to the nearest hundredth means we are rounding up to 2 decimal places. This means we are looking at the second number after the decimal which is 5. The number after it is 9, which is higher than 5 so we are adding one to 5. Therefore,
36.2598 to the nearest hundredth = 36.26.
c) to nearest 0.001
Rounding up 36.2598 to the nearest 0.001 means we are rounding up to the nearest thousandth which is 3 decimal places.
This means we are looking at the third number after the decimal which is 9. The number after it is 8, which is higher than 5 so we are adding one to 9.
Therefore,
36.2598 to the nearest 0.001 = 36.260
d) to the nearest whole number
Rounding up 36.2598 to the nearest whole number means we are rounding up the number before the decimal place. That number is 6. We look at the first digit after the decimal, it is less than 5, 6 remains unchanged, if it is 5 and above, we add one to 6.
For our question, the number after the decimal is 2, it is less than 5 so 6 remains unchanged.
36.2598 to the nearest whole number = 36.
What is the completely simplified equivalent of 2 over 5+i? the 'i' is 1! thx for the help!
Answer:
1/3 ≅ .33333
Step-by-step explanation:
If 'i' is 1, then 5+i is 6. 2 over 6 is 1 over 3. (2/6 = 1/3) 1 over 3 is also .3333... forever repeating.
Hope this helps!
Another math question I couldn't figure out.
(I did actually figure out an answer for this one, but it's definitely wrong.)
Each year the value of a bank account increases by 3% because of interest.
If £700 is paid into the account and no money is paid in or taken out, how much will be in the account after 3 years?
I believe the answer is 764.90. 3% of 700 is 21, then add that to 700- have three percent of that- add it to the 721, find 3% of that, then three percent of that then add that to 700 :)
Of the following statements, which one or ones describe actions helpful to your credit score?
I. Quickly paying off debts
II. Having recent debts
III. Having long-standing lines of credit
a. I only
b. II and III
C. I and III
d. III only
Please select the best answer from the choices provided
A
B
Answer:
I’m going to say C in order to improve you have to pay off debts
Step-by-step explanation:
The Credit Score helps us to
Quickly paying off debts and Having long-standing lines of credit.
What is Credit Score?Based on information from your credit reports, a credit score predicts your credit behavior, such as how likely you are to repay a loan on time.
This is determined by the total amount you owe, the variety and quantity of accounts you have, and the ratio of your debt to your available credit.
Given:
As, Smaller amounts may boost your credit score if you make on-time payments, but larger balances and maxed-out credit cards will lower it.
So, Credit Score usually used to pay the debts.
But the debts are bad for credit.
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