PLEASE HELP
7.02
1. Determine whether the sequence converges or diverges. If it converges, give the limit.
60, 10, five divided by three , five divided by eighteen , ...
A) Converges; 72
B) Converges; 0
C) Diverges
D) Converges; -15540
2. Find an explicit rule for the nth term of the sequence.
1, 3, 9, 27, ...
A) an = 1 • 3n + 1
B) an = 3 • 1n - 1
C) an = 1 • 3n - 1
D) an = 1 • 3n
3. Find an explicit rule for the nth term of the sequence.
-5, -25, -125, -625, ...
A) an = -5 • 5n
B) an = 5 • -5n + 1
C) an = 5 • -5n
D) an = -5 • 5n - 1
4. Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.
A) an = 2 • 3n - 1
B) an = 2 • (-3)n - 1
C) an = 2 • 3n
D) an = 2 • (-3)n + 1
5. A certain radioactive isotope has a half-life of 11 days. If one is to make a table showing the half-life decay of a sample of this isotope from 32 grams to 1 gram; list the time (in days, starting with t = 0) in the first column and the mass remaining (in grams) in the second column, which type of sequence is used in the first column and which type of sequence is used in the second column?
Answers
2. C
5.
TABLE
0 32
5 16
10 8
15 4
20 2
after 25 days ----> from 32g to 1g
first column: increments of +5; arithmetic sequence
second clmn: x5 ; geometric sequence
Answers:
1-A, 2-C, 3- D, 4- B.
Related Questions
Use the quadratic function to predict f(x) if x equals 2. f(x) = −3x2 + 180x − 285
Answers
For this case, the first thing to do is replace the value of x = 2 in the given function to know the result.
We have to replace:
f (2) = -3 * (2) ^ 2 + 180 * (2) - 285
f (2) = 63
Answer:
the value of pa for x = 2 is:
f (2) = 63
Suppose that x and y vary inversely and x = 1 when y = 12. Write a function that models the inverse variation. Graph the function and find y when x = 20.
Write a function that models the inverse variation.
Answers
y = k / x
We observe that we must find the value of k.
For this, we use the following fact:
"x = 1 when y = 12"
Substituting we have:
12 = k / 1
Therefore k = 12
Thus, the equation is:
y = 12 / x
For x = 20 we have:
y = 12/20
y = 6/10
y = 3/5
y = 0.6
Answer:
when x = 20, and is:
y = 0.6
See attached graph.
The diameter of your bicycle wheel is 25 inches. How far will you move in two turns of your wheel? Use 3.14 for π.
A) about 39 inches
B) about 78 inches
C) about 157 inches
D) about 314 inches
Answers
[tex]circumference \: = 2\pi \: r [/tex]
diameter = 25 inches
radius = 25/2
= 12.5 inches
= 2(3.14)(12.5)
= 78.5 inches ( for a turn )
Two turns = 78.5 inches X 2
= 157 inches
C.
Answer: D) About 314 inches
Step-by-step explanation:
Since, the radius of the wheel = 25 inches
Also, the angle in one turns of the wheel [tex]= 2\pi[/tex]
⇒ The angle in 2 turn of the wheel [tex]= 4\pi[/tex]
Hence, the distance it will cover in two turns
[tex]= 4\pi\times 25[/tex] ( Arc length = central angle × radius)
[tex]= 4\times 3.14\times 25[/tex]
[tex]=314.159265\approx 314\text{ inches}[/tex]
⇒ Fourth option is correct.
Mary leaves her house to take a walk. The graph shows the distance, d, in feet from her house that Mary is at any given time, t, in minutes. How many minutes has Mary walked when she reaches the farthest point from her house
Answers
However, I will tell you how to solve it and you can apply on the graph you have.
Now, we are given that:
x-axis represents the distance in ft
y-axis represents the time in minutes
To get the time that she has walked when she reaches the farthest point from her house, all you have to do is:
1- go to the greatest point on the x-axis. This point would be representing the farthest distance.
2- get the value of the y corresponding to the x-point you got in step one. This would be the time walked when she reaches the farthest point which is the value you are looking for.
Hope this helps :)
The next term of the arithmetic sequence 39,60,81,102,123.....is
Answers
so the next number is 123 +21 = 144
Samantha has 3 times as many baseball cards as mark. mark has 12 baseball cards. write an equation that shows how many cards samantha has.
Answers
hope this helped :)
A transformation T: (x, y) (x - 5, y + 3).
The image of A(2, -1) is
(3, 2)
(-3, 2)
(-3, -2)
Answers
Answer:
i can confirm the above awnser is correct
How do you represent 4/7 + 3/14 on a number line?
Please Help Asap!!
Answers
Josie had a choice of 3 breads, 4 choices of meat, and 4 choices of cheeses to make a sandwich.
How many different sandwiches can she make?
24
36
48
60
Answers
she can make 48 different sandwiches
Answer:
The answer is 48
Step-by-step explanation:
For every different sandwich, she needs to choose one breat, one meat and one cheese.
For each choice of bread, there are 4 choices of meat and 4 choices of cheese. Also, for each meat, there are four choices of cheese. It means that for each bread there are 4(choices of meat)*4(choices of cheeses) = 16 possible combinations.
There are also 3 choices of breads. For each bread, there are 16 possible combinations. So, in all, there are 3*16 = 48 possible combinations.
create the equation of a quadratic function with a vertex of (5,6) and a y-intercept of -69
Answers
[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \boxed{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k})\\\\ -------------------------------\\\\ vertex~(5,6)\quad \begin{cases} x=5\\ y=6 \end{cases}\implies y=a(x-5)^2+6 \\\\\\ \textit{we also know that } \begin{cases} x=0\\ y=-69 \end{cases}\implies -69=a(0-5)^2+6 \\\\\\ -75=25a\implies \cfrac{-75}{25}=a\implies a=-3 \\\\\\ therefore\qquad \boxed{y=-3(x-5)^2+6}[/tex]
Which of the following is not a method used to prove triangles congruent?
A) AAS Theorem
B) SSA Postulate
C) SAS Postulate
D) ASA Postulate
Answers
Answer:
B) SSA Postulate
Step-by-step explanation:
Two triangles are congruent if they are of the same shape and size.
Two triangles can be proved congruent by AAS ,SAS ,ASA ,SSS ,HL postulates.
Two triangles are congruent if two angles and one side of both the triangles are congruent that is AAS and ASA postulates.(option A and D)
The triangles can be congruent by SAS that is if two sides and included angle of two triangles are congruent then the triangles are congruent .(Optionc)
Option B that is SSA is not a congruence postulate.
The windows of a downtown office building are arranged so that each floor has six fewer windows than the floor below it. If the ground floor has 52 windows, how many total windows are on the first eight floors?
Answers
windows on first floor = 52
windows on 8th floor (52 - 6 * 7) = 10
average windows = (52 + 10)/2 = 62/2 = 31
8 floors * 31 average windows = 248.
Answer:
There are 248 windows on the first eight floors.
Step-by-step explanation:
As given:
The ground floor has 52 windows.
This question is based on arithmetic sequence:
a1 = 52
d = - 6 (each floor has six fewer windows than the floor below it)
[tex]a_n=a1+(n-1)d[/tex]
[tex]a_8 =a1+7d[/tex]
=> [tex]52+[7 \times (-6)][/tex]
=> [tex]52-42 =10[/tex]
We know:
[tex]S_n= n/2 \times (a1 +a _n)[/tex]
[tex]S_8 =8/2 \times(52+10)[/tex]
= 248
Therefore, there are 248 windows on the first eight floors.
Orlando bought a new couch for 2,736, using the furniture store's finance plan. He will pay $114 a month for 24 months. Which equation can Orlando use to find out how much money he still owes after each month of the plan?
Answers
y: debts after each month
y = $2736 - $114 * x
I hope this is self-explanatory.
Answer:
[tex]y = 2736 - 114x[/tex]
Step-by-step explanation:
It is given that the cost of the couch was $2,736. Orlando bought that couch using furniture store's finance plan. The plan says that he is supposed to pay $114 per month for a period of 24 months.
we are asked to determine the equation which can determine the total amount still due on orlando after x number of months.
Let the total number of month we are calculating = x
Payment per month = $114
Hence payment made in x months = $114x
Hence payment still owned by Orlando = $2736-$114x
Above equation gives us the dues on Orlando
A jug of juice has 7 cups of pineapple juice and 3 cups of orange juice. write the ratio of number of cups of pineapple juice to total number of cups of juice *
Answers
Each summer Primo Pizza and Pizza Supreme compete to see who has the larger summer profit. Let f ( x ) f(x) represent Primo Pizza's profit x x days after June 1. Let g ( x ) g(x) represent Pizza Supreme's profit x x days after June 1. Suppose Primo Pizza's profit each day is two times as large as the profit of Pizza Supreme. Express the function f f in terms of the function g
g.
Answers
f (x) = Primo Pizza's profit
g (x) = Pizza Supreme's profit.
According to the statement we have:
"Primo Pizza's profit each day is two times as large as the profit of Pizza Supreme"
Therefore, we can write one function in terms of the other in the following way:
f (x) = 2g (x)
Answer:
the function f in terms of the function g is:
f (x) = 2g (x)
The profit of Primo Pizza is twice the profit of Pizza Supreme each day. Therefore, if g(x) represents the profit of Pizza Supreme x days after June 1, then f(x), representing Primo Pizza's profit, is given by f(x) = 2g(x). This means if Pizza Supreme's profit on a particular day is $500, Primo Pizza's profit on the same day is $1000.
Explanation:In this problem, we are given that the profit of Primo Pizza (represented by the function f(x)) is two times larger than the profit of Pizza Supreme (represented by the function g(x)). This relationship between the two profits can be expressed as f(x) = 2 * g(x). So, if you know the profit of Pizza Supreme on a particular day (g(x)), you can determine the profit of Primo Pizza on that day by doubling the profit of Pizza Supreme.
For instance, if Pizza Supreme's profit 10 days after June 1st is $500 (so, g(10) = $500), then Primo Pizza's profit on the same day would be f(10) = 2 * g(10) = 2 * $500 = $1000. Thus, Primo Pizza is making twice the profit of Pizza Supreme each day.
Learn more about Functions here:https://brainly.com/question/30721594
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The area of a parallelogram is 400m2 the base is 25m find the length of the height
Answers
The radius of a circle is 10 feet. What is the angle measure of an arc 4 feet long?
Answers
Hope this helps u
I WILL GIVE 40 POINTS FOR EACH QUESTION REALLY NEED HELP THERE ANOTHER POST FOR THE OTHER QUESTION IT WILL BE ANOTHER 40 AS WELL AND MARKED AS BRAIN~LEST AND STAR RATEING
Answers
The fourth page is The last option
The fifth page maybe the last one (im not sure)
Answer:The first page is S^2
The fourth page is The last option
The fifth page maybe the last one
Step-by-step explanation:
The surface area of a box is 160. the length of the box is twice its width as well as 4 less than its height. how many units are in the height of the box? (the surface area of a box is the sum of the areas of all 6 of its rectangular faces.) aops
Answers
Length = 2n
Height = 2n + 4
2 (n x 2n) = 4n^2
2 (n x (2n + 4)) = 4n^2 + 8n
2 (2n x (2n + 4)) = 8n^2 + 16n
4n^2 + 4n^2 + 8n + 8n^2 + 16n = 160
16n^2 + 24n = 160
(Divide everything by 8)
2n^2 + 3n = 20
2n^2 + 3n - 20 = 0
(2n - 5)(n + 4) = 0
n = 2.5 Or n = -4
However n can not be less than 0
So n = 2.5
Height =2n +4
=2(2.5) +4
=5+4
=9
Final Answer:
The height of the box is 9 units.
Explanation:
Let's denote the width of the box as w, the length as l, and the height as h. According to the problem, we have the following relationships:
l = 2w (the length is twice the width) and
l = h - 4 (the length is also 4 less than the height).
The surface area SA of a rectangular box is calculated by the formula:
SA = 2lw + 2lh + 2wh.
Given that the surface area is 160, we set up our equation:
160 = 2lw + 2lh + 2wh.
Now let's substitute the relations l = 2w and l = h - 4 into the surface area equation:
Since l = 2w, 160 = 2(2w)w + 2(2w)h + 2wh.
Simplifying the equation, we have:
160 = 4w² + 4wh + 2wh
160 = 4w² + 6wh
Now we use the fact that l = h - 4 to substitute for h:
h = l + 4
h = 2w + 4
Now substitute h back into the surface area equation:
160 = 4w² + 6w(2w + 4) ,
Expand the terms:
160 = 4w² + 12w^2 + 24w,
Combine like terms:
160 = 16w² + 24w
Now, we must solve for w. Let's move all terms to one side to solve the quadratic equation:
16w² + 24w - 160 = 0
Divide all terms by 8 to simplify:
2w² + 3w - 20 = 0
We can now attempt to factor the quadratic equation:
(2w - 5)(w + 4) = 0
This gives us two solutions:
2w - 5 = 0 or w + 4 = 0
Solving the first equation for w:
2w = 5,[tex]\( w = \frac{5}{2} \)[/tex]
w = 5/2
We can disregard the second solution w + 4 = 0 for w, as it gives us a negative width, which isn't possible for a box.
Now that we have w, we can find h.
Using our earlier substitute for h:
h = 2w + 4 ,
[tex]h = 2 \cdot \frac{5}{2} + 4[/tex] ,
h = 5 + 4 ,
h = 9 .
Thus, the height of the box is 9 units.
Patrick is constructing the circumscribed circle for △RST.
Which construction could be his first step?
Construct the perpendicular bisector of ST¯¯¯¯¯ .
Construct the angle bisector of ∠T .
Construct a copy of ∠S that is adjacent to ∠R .
Construct the angle bisector of ∠R .
Answers
Construct the perpendicular bisector of ST¯¯¯¯¯ .
Hope this helps !
Photon
A cylinder shaped drum is used to store used motor oil. The drum has a height of 3 ft and a radius of 1.5 ft. How many cubic feet of oil does the drum hold? Use 3.14 to approximate pi. Enter your answer as a decimal rounded to the nearest hundredth in the box.
Answers
To do this we need to calculate the volume of the cylinder shaped drum.The volume (V) of the cylinder with height h and radius r is:V = π r² h
We have:π = 3.14r = 1.5 fth = 3 ft
Therefore:V = π r² hV = 3.14 * (1.5 ft)² * 3 ftV = 21.2 ft²
here you go
a triangular plot of land has boundary lines 45 meters, 60 meters, and 70 meters long. the 60 meter boundary line runs north-south. Is there a property for the boundary line that runs east-west
Answers
No, there is no property for the boundary line that runs east-west.
Explanation:No, there is no property for the boundary line that runs east-west. This is because if we have a triangle with side lengths 45 meters, 60 meters, and 70 meters, and the 60 meter side runs north-south, then the other two sides must be at an angle to the north-south line. It is not possible for one of the sides to be parallel to the north-south line (east-west) because that would create a rectangle rather than a triangle.
which method is most efficient in solving a system of linear equations when the two equation have x-values with opposite coefficient values
A. GUESS AND CHECK
B. GRAPHING
C. SUBSTITUTION
D. ELIMINATION
Answers
For example, consider the system of equations below
2x+3y = 9
-2x+6y = 18
Adding straight down will have the x terms (2x and -2x) add to 0x which is just 0. The x terms will go away. In this case, the 2 and -2 are opposite coefficient values for the x terms.
helppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
We have then:
x ^ 2 + 20x + 100 = 36
Rewriting:
x ^ 2 + 20x + 64 = 0
The values of the roots are:
x1 = -4
x2 = -16
Remember that the values of the roots are what make the polinome zero
Answer:
x1 = -4
x2 = -16
the gray is a sidewalk and the turquoise is grass. Both are squares. What is the area of the sidewalk?
A) 4 ft2
B) 36 ft2
C) 44 ft2
D) 48 ft2
Answers
Answer:
C 44 ft2 i just took the test .
Step-by-step explanation:
A basketball player scored 2222 times during one game. hehe scored a total of 3030 points, two for each two-point shot and one for each free throw. how many two-point shots did hehe make
Answers
What is the slope of a line perpendicular to the line y=3/4x+1
Answers
The slope of the given line is 3/4. It's simply the value in front of the x. To be more specific, the equation given to us is in the form y = mx+b where m = 3/4 is the slope.
Flip the fraction and then the sign
flip the fraction: 3/4 ----> 4/3
Then flip the sign: 4/3 ----> -4/3
In other words, we take the negative reciprocal
Notice how the original slope 3/4 and the perpendicular slope -4/3 multiply to -1
3, 12, 48, 192, 768, . . .
This sequence has a
A.] common difference of 4
B.] common ratio of 4
C.] common difference of [tex] \frac{1}{4}[/tex]
D.] common ratio of [tex] \frac{1}{4}[/tex]
Answers
The explanation for this would be:
To get the common ratio for get the simplest form of the two numbers, so 12/3 = 4 and 48/12 = 4So we know that their common ratio is 4.
To check:
3 x 4 = 12
12 x 4 = 48
48 x 4 = 192
192 x 4 = 768
*URGENT ALGEBRA 2* Anyone know these answers? Choices provided. Will award brainliest.
Answers
Question 1. Translate y = 2/x 3 units to the left and 4 units up.
Answer:
2
y = -------- + 4 <------- the fourth option
(x + 3)
Explanation:
1) Given function:
y = f(x) = 2 / x
2) Translatiing 3 units to the left is making f(x + 3), so that implies:
y = 2 / (x + 3)
3) Translating 4 units up is making f(x + 3) + 4, so that implies:
2
y = -------- + 4
(x + 3)
Which is the fourth option.
Question 2. simplify
t^2 + 2t - 24
----------------
t^2 - 36
Answer: fourth option
t - 4
------ , with t ≠ - 6 and t ≠ 6.
t + 6
Explanation:
1) Factor the numerator:
t^2 + 2t - 24 = (t + 6) (t - 4)
2) Factor the denominator:
t^2 - 36 = (t + 6) (t - 6)
3) Rewrite the fraction:
(t + 6) (t - 4)
-------------------
(t + 6) (t - 6)
4) Cancel the factor t + 6 which is in both numerator and denominator, which you can do only y t + 6 ≠ 0 => t ≠ -6.
t - 4
-------
t - 6
That is the simplified expression, with the restrictions that t ≠ - 6 and t ≠ 6, because the denominator cannot be 0.
Question 3. Find the product of:
x^2 + 7x + 10 x^2 - 3x - 18
------------------ * ---------------------
x + 3 x^2 + x - 2
Answer: the fhird option:
(x + 5) (x - 6)
------------------
x - 1
with x ≠ -3, x ≠ - 2, and x ≠ 1.
Explanation:
1) Factor x^2 + 7x + 10
x^2 + 7x + 10 = (x + 5) (x + 2)
2) Factor x^2 - 3x - 18
x^2 - 3x - 18 = (x - 6)(x + 3)
3) Factor x^2 + x - 2
x^2 + x - 2 = (x + 2) (x - 1)
4) Rewrite the given expression using the factors:
(x + 5) (x + 2) (x - 6) (x + 3)
--------------------------------------
(x + 3) (x + 2) (x - 1)
5) Cancel the factors that appear on both the numerator and denominator:
(x + 5) (x - 6)
------------------
x - 1
The restrictions are those values of x that make any factor that is or was in the denominator: x ≠ -3, x ≠ - 2, and x ≠ 1.
Question 4. Simplify the complex fraction:
n - 4
------------------
n^2 - 2n - 15
--------------------------
n + 1
-----------
n + 3
Answer: option 4.
n - 4
------------------
(n - 5) ( n + 3)
Explanation
1) Factor n^2 - 2n - 15
n^2 - 2n - 15 = (n - 5)(n + 3)
2) rewrite the expression:
n - 4
---------------------
(n - 5) ( n + 3)
----------------------------
n + 1
----------
n + 3
3) Convert (n + 1) / (n + 3) into its reciprocal (n + 3) / (n + 1), and multiply instead of dividing.
n - 4 n + 3
--------------------- * --------
(n - 5) ( n + 3) ( n + 1)
4) Cancel n + 3
n - 4
------------------
(n - 5) ( n + 3)
That is the simplest form.
Question 5. Find the difference
Answer: second choice
1 - n
--------
n + 4
Explanation:
1) given:
n^2 + 3n + 2 2n
----------------- - -------
n^2 + 6n + 8 n + 4
2) factor the two quadratic trinomials
n^2 + 3n + 2 = (n + 2) ( n + 1)
n^2 + 6n + 8 = (n + 4) (n + 2)
3) Rewrite the expression:
(n + 2) (n + 1) 2n
----------------------- - -------
(n + 4 ) (n + 2) n + 4
4) cancel the factor n + 2
n + 1 2n
----------- - --------
n + 4 n + 4
5) subract the fractions. They have the same denominator.
n + 1 - 2n 1 - n
--------------- = ----------
n + 4 n + 4
And that is the simples form.
Question 6. Problem
Irina paints 1 room in 9 hours
Paulo paints 1 room in 8 hours
How long working together?
Answer:
x / 9 + x / 8 = 1, x ≈ 4.24 hours
Explanation:
1) In the time x, Irina will paint x / 9 parts of the room
2) Paulo will paint (in the same time) x / 8 parts of the same room
3) The total painted is 1 room.
So the equation is:
x / 9 + x / 8 = 1
4) The solution of that equation is:
[8x + 9x ] / (9*8) = 1
=> 8x + 9x = 72
=> 17x = 72
=> x = 72 / 17
=> x ≈ 4.24 hours
gina is traveling to the beach 20 miles away from her house.On Ginas map her house and the beach are 4 inches apart what is the scale used for Ginas map
Answers
Gina is travelling to the beach 20 miles away from her house.
On Ginas map her house and the beach are 4 inches apart
That is a distance of 20 miles is represented by the Ginas map in 4 inches
Therefore, on Ginas map one inch will be = 20/4 miles = 5 miles
So, the scale used for Gina's map is 1 inch = 5 miles
Hope this helps..!!
Thank you :)