Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest form. an=-2 an = an-1 -13 an=
Answers
From the recursive rule
[tex]a_n = a_{n-1}-13[/tex]
it follows that
[tex]a_{n-1}=a_{n-2}-13 \implies a_n = a_{n-2} - 2\times13[/tex]
[tex]a_{n-2}=a_{n-3}-13 \implies a_n = a_{n-3} - 3\times13[/tex]
and so on. Notice how the subscript on a on the right side and the coefficient multiplied by 13 add up to n (n - 2 + 2 = n; n - 3 + 3 = n; and so on). If we continue the pattern, we'll end up with
[tex]a_n = a_1 + (n-1)\times13[/tex]
so that the explicit rule for the n-th term in the sequence is
[tex]a_n = -2 + 13(n-1) \implies a_n = \boxed{13n-15}[/tex]
Related Questions
I need helppppp plssssssssss
Answers
Answer:
(x, y) = (9, 17)
Step-by-step explanation:
Any two pairs of equations can be used to form a system of equations that will give appropriate values of x and y. Let's set the upper and lower left expressions equal to the middle one.
2x +3y -20 = 4x +5y -72 . . . . upper left = middle
52 = 2x +2y . . . . . . . . add 72-2x-3y
x + y = 26 . . . . . . . . . . divide by 2
and ...
5x -2y +38 = 4x +5y -72 . . . . lower left = middle
110 = -x +7y . . . . . . . . . . . . . add 72-5x+2y
Now we have two equations in two unknowns that will give us the common values of x and y. Adding these equations eliminates x and gives the value of y:
(x +y) +(-x +7y) = (26) +(110)
8y = 136 . . . . . . . . simplify
y = 17 . . . . . . . . . divide by 8
x = 26 -y = 26 -17 = 9
The values of x and y that make all of these expressions equal are ...
(x, y) = (9, 17)
The value they are equal to is ...
2x +3y -20 = 2(9) +3(17) -20 = 18 +51 -20 = 49
__
Check
upper right = 9 -4(17) +108 = 9 -68 +108 = 49
lower right = 3(9) -17 +39 = 27 -17 +39 = 49
Complete the following statement. Write your answer as a decimal or whole number.
% of $60 = $18
or
Complete the following statement. Write your answer as a decimal or whole number.
% of $60 = $18
or
Complete the following statement. Write your answer as a decimal or whole number.
% of $60 = $18
or
Complete the following statement. Write your answer as a decimal or whole number.
% of $60 = $18
or
Complete the following statement. Write your answer as a decimal or whole number.
% of $60 = $18
or
Complete the following statement. Write your answer as a decimal or whole number.
% of $60 = $18
or
Complete the following statement. Write your answer as a decimal or whole number.
% of $60 = $18
Answers
i need answer please
Answers
Jake used to live 10 miles from school. After he and his family moved, he now lives 18 miles from school. What is the percent of change in distance from Jake’s old house to his new one? Round your answer to the nearest whole number
Answers
Answer:
80%
Step-by-step explanation:
Based on the given conditions: (18 - 10)÷10
Calculate the sum or difference: 8/10
Cross out the common factor: 4/5
Convert to percentage: 80%
Answer: 80%
Answer:
80%
Step-by-step explanation:
Based on the given conditions, formulate: (18-10) ÷ 10
Calculate the sum or difference: 8/10
Cross out the common factor: 4/5
Convert to percentage: 80%
Answer: 80%
Hope this helps
A wooden building has the shape of a rectangular pyramid. The buildings base is 100 meters long and 50 meters wide. The height of each triangular face is 40 meters. How much wood was used to make the entire building?
Answers
Check the picture below.
so let's simply get the area of each of the triangular faces and the base and sum them all up.
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{front and back}}{2\left[ \cfrac{1}{2}(100)(40) \right]}~~ + ~~\stackrel{\textit{left and right}}{2\left[ \cfrac{1}{2}(50)(40) \right]}~~ + ~~\stackrel{base}{(100\cdot 50)}} \\\\\\ 4000~~ + ~~2000~~ + ~~5000\implies 11000~m^2[/tex]
what is -5/2dividedby5/7
Answers
[tex]\frac{ - 5}{2} \: by \: \frac{5}{7} [/tex]
[tex] - 3.5[/tex]
Answer : [tex] - 3.5[/tex]
what is the 10% of 1,500 show all the necessary steps
Answers
[tex] \rightarrow \: \sf \dfrac{10}{100} \times 1500[/tex]
[tex] \\ \\ [/tex]
[tex] \rightarrow \: \sf 10 \times 15[/tex]
[tex] \\ \\ [/tex]
[tex] \rightarrow \: \sf 150[/tex]
0.1 × 1500
The answer would be: 150
Hope this helps :)
Annie has 5 green and 4 purple shirts for a total of 9 shirts. They each have two buttons. How many buttons does she have total?
Answers
Answer:
18 buttons
Step-by-step explanation:
2 buttons per shirt times the number of shirts (9) gives an answer of 18
The cost of 3 scarves is $80.25. What is the unit price?
Answers
Answer:
$26.75 per scarf
Step-by-step explanation:
3 scarves = $80.25 (quite expensive)
1 scarf = $80.25/3
1 scarf = $26.75
Answer:
$8.75 because 26.25 divided by 3 equals 8.75.
Step-by-step explanation:
Amy is trying to determine how many different outfits she can make. She has 4 bottoms 7 tops, 2 belts, and 5 pairs of shoes. Assuming she wears one of each item, how many different outfits can
she make?
Answers
Answer:
Amy puede hacer 4 conjuntos.
Step-by-step explanation:
La solución sería
Se sabe que un conjunto de vestir se compone de camisa o blusa, pantalones, zapatos y cinturones, aunque este ultimo es opcional.
Lo que haremos es esto, empezamos a coger una pieza de cada prenda para armar un conjunto.
Primer conjunto:
1 blusa, 1 pantalón, 1 cinturón, y 1 par de zapatos.
Y esto quedaría así: 3 pantalones, 6 blusas, 1 cinturón y 4 pares de zapatos.
Segundo conjunto:
1 blusa, 1 pantalón, 1 cinturón y 1 par de zapatos.
Esto quedaría así: 2 pantalones, 5 blusas, 0 cinturones, 3 pares de zapatos. Sabemos que el cinturón es opcional, así que podemos continuar.
Tercer conjunto:
1 blusa, 1 pantalón y un par de zapatos.
Esto quedaría así: 1 pantalón, 4 blusas, 0 cinturones y 3 pares de zapatos.
Cuarto conjunto:
1 blusa, 1 pantalón y un par de zapatos.
Esto quedaría así: 0 pantalones, 3 blusas, 0 cinturones y 2 pares de zapatos. Como en un conjunto el pantalón es prioridad, al no tener más pantalones los conjuntos quedarían hasta aquí.
¡Recuerda!
No es lo mismo organizar tu ropa en conjuntos, a que hagas variaciones con ella.
Solve for g:
4g
--- =3j+7
h
Answers
Answer:
g= h(3j+7)
---------
4
Step-by-step explanation:
4g = h(3j + 7)
4g = h*3j+h*7
A triangle has angle measurements of 66°, 66°, and 48°. Is this triangle isosceles?
Answers
Answer:
yes
Step-by-step explanation:
The 2 base angles of an isosceles triangle are congruent.
66° + 66° + 48° = 180° ( sum of angles in a triangle )
Thus the triangle is isosceles with base angles = 66° and vertex = 48°
Problem Situation: Eric is adding water to a 60-gallons pool. a The pool already has 12 gallons of water, and he wants to fill it to at least 27 gallons. The water flows at a rate of 6 gallons per minute. How many minutes, x, will it take for Eric to fill the pool with at least 27 gallons of water? Inequality that represents this situation: 27 < 12 +63 To solve the inequality, you can begin by solving the equation as shown. Drag a diagram to each row of the table to show which number line represents all of the solutions for the inequality and which number line represents all of the solutions for the problem situation
Answers
Answer:
16
Step-by-step explanation:
The number after 15 s 16.
Please help rn
Compare -4 and 1. Which statement is not true?
A. 1 is farther from zero on a number line.
B. 1-4] > [1]
O c. 1 is farther to the right on a number line.
D. 1 has a lower absolute value.
Answers
Answer:
D. 1 has a lower absolute value
Step-by-step explanation:
D is the answer because -4 is negative and can never be more than a positive number like 1.
Answer:
D
Step-by-step explanation:
because 1 have 1 absolute value and -4 have 4 absolute value
since 4 is greater than 1
so 1 have lower absolute value
i will mark brainliest
Answers
Answer:
2 1/2 (2.5)
Step-by-step explanation:
Multiply all the numbers then divide by 1/2
The graph and table shows the relationship between y, the number of words Jean has typed for her essay and x, the number of minutes she has been typing on the computer. A 2-column table with 9 rows. The first column is labeled x with entries 5, 10, 15, 20, 25, 30, 35, 40, 45. The second column is labeled y with entries 271, 464, 820, 965, 1124, 1501, 1718, 2076, 2257. A graph shows the horizontal axis numbered 20 to 80 and the vertical axis numbered 1000 to 3000. A line increases from 0 to 80. According to the line of best fit, about how many words will Jean have typed when she completes 60 minutes of typing? 2,500 2,750 3,000 3,250.
Answers
Answer:
3,000 words
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
just did the test
this is not Math its SCIENCE if you can answer all u get to be brailiest
Answers
Answer:
1a) A chemical compound is a chemical substance composed of many identical molecules composed of atoms from more than one element held together by chemical bonds. A molecule consisting of atoms of only one element is therefore not a compound.
1b)An ionic compound formed by acid-base reactions and without those ions is called a salt. Water is definitely one of the most important inorganic compounds to all living things. It is a compound comprised of two hydrogen atoms and one oxygen atom.
The four major classes of biological macromolecules are carbohydrates, lipids, proteins, and nucleic acids.
2a)Regulates body temperature. Moistens tissues in the eyes, nose and mouth. Protects body organs and tissues. Carries nutrients and oxygen to cells.
2b)If a cell is seriously deprived of water,
this lack of water would most likely affect
the cell's enzymes because:
• The cytoplasm and plasma
membrane would not function
properly
Both the plant and animal cell needs
water in order to perform their basic
functions which include transport of
materials, waste distribution, production
of genetic information, and many more.
As a result of this, we can see that there
would be a serious problem if any
of these cells are deprived of water
which would lead to the cytoplasm and
plasma membrane to partially shut
down because they would not be able to
engage in protein synthesis and other
important functions.
3a)Carbohydrates provides energy rich for organic compounds made of elements carbon, hydrogen and oxygen. The lipids contain the element nitrogen. The carbohydrates contain the only elements carbon, hydrogen, and oxygen.
3b)Organic nitrogen occurs in many forms, including amino acids, proteins, nucleic acids, nucleotides, and urea.
3c)A carbohydrate has only Carbon, Hydrogen and Oxygen, with the hydrogen and oxygen in the ratio 2:1. A protein is made of amino acids. ... So without nitrogen atoms the compound can not be a protein.
Finding the measure of each angle indicated
Answers
Answer:
50
Step-by-step explanation:
Because if the tringles are equal they'll be the same amount (110) 50+60= 110
Help its a Math problem !! i am confused
Answers
Answer: D
Step-by-step explanation:
If you look at the quadratic formula, we see that b=5, a=5, and c=3.
So ax^2 + bx + c = 0 -> 5x^2 + 5x + 3 = 0
Question is in the picture. Please answer
You don't have to explain in full detail if you don't want I just need the answer and a short explanation
Answers
Answer:
[tex]tan(A) = \frac{4}{3}[/tex]
Step-by-step explanation:
Here we see tan(B) has opposite side of 12 and adjacent of 9
using the formula:
[tex]tan(A) = \frac{opposite }{adjacent}[/tex]
[tex]tan(A) = \frac{12}{9}[/tex]
[tex]tan(A) = \frac{4}{3}[/tex]
Answer:
[tex]\textsf{tan(A)}=\frac{4}{3}[/tex]
Step-by-step explanation:
The trig ratio for tan is: [tex]\textsf{tan}(x)=\mathsf{\frac{O}{A}}[/tex] where
[tex]x[/tex] is the angle O = side OPPOSITE to the angleA = side ADJACENT to the angleFor angle A:
O = 12
A = 9
[tex]\implies \textsf{tan(A)}=\frac{12}{9}\\\\\implies \textsf{tan(A)}=\frac{4}{3}[/tex]
Consider the information in the previous questions (Henry only has quarters, nickels, dimes and pennies). Is it mathematically possible for Henry to have exactly 23 pennies if he has a total of $2.41? Defend your conclusion with an equation for the sum of the coins and two or more complete sentences explaining your conclusion.
Answers
Answer:
NoStep-by-step explanation:
The total amount is $2.41.
If the are 23 pennies, then the amount excluding the pennies is:
$2.41 - $0.23 = $2.18This amount comprises quarters, nickels and dimes.
Each of them is multiple of 5:
Quarter = $0.25Nickel = $0.05Dime = $0.10Any amount made by the combinations of these has to be multiple of 5 cents. But the sum is $2.18, which is not multiple of 5 cents.
It means Henry can't make it.
im having trouble solving this. y=5(x-3)
Answers
Hi there!!
If you need X to be solved then the answer is X=Y over 5+3 and if your looking for the answer for Y then the answer is Y=5x−15
When you are solving for X you will need to use the distributive property so you can multiply 5 by X-3.
Y=5x-15. Once you've done that then you need to swap sides so all of the variables are on the same side as each other (they need to be on the left side) 5x-15=Y.
Then you need to add 15 to both of the sides to make it look like this ->5x=Y+15
When that's done you then need to divide both sides by 5 so it then looks like this when done.
5x over 5= Y+15 over 5
When you divide this by 5, it then undoes the multiplication by 5.
X= Y+15 over 5
Finally, you need to divide Y+15 by 5
X=Y over 5 plus 3
When solving for Y, all you will need to do is use the distributive property to multiply 5 by X-3.
I REALLY HOPE THIS HELPED YOU OUT AND THAT I DIDN'T WASTE YOUR TIME WITH A WRONG ANSWER . BUT IF THIS WAS CORRECT THEN YOU ARE VERY WELCOME
help me with this please
Answers
Answer:
a. length: 20-2x; width: 12-2x; height: x
b. V = 4x^3 -64x^2 +240x
c. cubic trinomial
d. 262.7 cubic inches maximum for a 2.4 inch square
e. 15 × 7 × 2.5 inches for 262.5 in³ volume
Step-by-step explanation:
a.If the square cut from each corner has side length x, the dimensions are ...
height: xwidth: 12 -2xlength: 20 -2x__
b.The volume is the product of length, width, and height.
V = LWH
V = (20 -2x)(12-2x)(x) = 4(x-10)(x-6)x = 4(x^2 -16x +60)x
V = 4x^3 -64x^2 +240x
__
c.The volume function is a cubic trinomial.
__
d.The maximum volume will be found where the derivative of the volume function is zero.
V' = 12x^2 -128x +240 = 0
x^2 -32/3x +20 = 0 . . . . divide by 12
(x -16/3)^2 = 76/9 . . . . . complete the square
x = (16 -√76)/3 ≈ 2.4 . . . . size of the square
V = 4(2.4)(10 -2.4)(6 -2.4) ≈ 262.7 . . . cubic inches
The maximum box volume is about 262.7 cubic inches when the square is about 2.4 inches on each side.
__
e.A graphing calculator shows there to be two solutions for a volume of 262.5 cubic inches. The rational solution is x = 2.5 inches. The box dimensions would be ...
length = 20 -2(2.5) = 15 incheswidth = 12 -2(2.5) = 7 inchesheight = 2.5 inchesPLZ HELP!!
Solve by substitution
y = -5x
y + 4x = -1
Explain PLZ
Answers
Answer:
x= 1
Step-by-step explanation:
The value of y = -5x
Plug it in the equation of y + 4x = -1
So it becomes, -5x + 4x = -1
Combine like terms which are -5x and 4x which equals to -x
Eliminate the negative sign because x cannot be negative. Apply that to -1. It becomes 1.
Hope you find this helpful!
Answer:
Step-by-step explanation:
Equation 1: y = -5x
Equation 2: y + 4x = -1
Step 1. Substitute y in equation 2 using equation 1
You would get, -5x + 4x = -1
Step 2. Combine like terms
-x = -1
Step 3. Cross out the negatives
x = 1
Step 4. Substitute x in Equation 1 to get y
y = -5(1)
y = -5
Hope this helps :)
Have a great day!
there are six red marbles and 11 orange marbles in a bag. You randomly choose one of the marbles. What is the probability of choosing a red marble?
Answers
Answer:
The probability of choosing a red marble is 35%.
Step-by-step explanation:
Total marbles: 17
Red marbles: 6Orange marbles: 11[tex]\frac{6}{17} = 0.35[/tex]
Napoleon's route through the alps involved a climb of 6km and a descent of 4km. His army travelled twice as fast downhill as it did uphill, the whole journey took 8 hours. How long did it take to reach the top?
Answers
Answer:
6 hours.
Step-by-step explanation:
since that is true we can use trial and error. if every km took an hour it would take six hours up and 4 hours down but they said they were twice as fast going down so that means it would take 2 hours going down. 6 add 2 is 8 which is our total meaning that 6 hours is the right answer
Is the square root of 2times 10 the same as 2 square root 10
Answers
Answer:
no
Step-by-step explanation:
√(2*10= √20= 4.47
2*√10= 6.32
Answer:
No.
Step-by-step explanation:
[tex]=\sqrt{2*10}\\\\=2\sqrt{5}[/tex]
[tex]=2\sqrt{10} \\\\=2\sqrt{10}[/tex]
2√5≠2√10
M is the midpoint of segment CD. Given M(-2,2) and C(2,8), find the coordinates of D.
Answers
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{2}~,~\stackrel{y_1}{8})\qquad D(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x + 2}{2}~~~ ,~~~ \cfrac{ y + 8}{2} \right)~~ = ~~\stackrel{\stackrel{M}{\downarrow }}{(-2~~,~~2)}\implies \begin{cases} \cfrac{x+2}{2}=-2\\[1em] x+2=-4\\ \boxed{x=-6}\\[-0.5em] \hrulefill\\ \cfrac{y+8}{2}=2\\[1em] y+8=4\\ \boxed{y=-4} \end{cases}[/tex]
Your freezer produces 8 ice cubes every two hours. Your friends freezer produces 24 ice cubes every 5 hours what is the ratios?
Answers
If the image of (x,-3) is (-3,4) under the reflection in y=x , find the value of x.
Answers
Step-by-step explanation:
4
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