i need the fourth term of one and three all I need is the answers so I can quiz my son.
Answers
The formula for the nth term is expressed as
an = (an - 1)^2 - 3
This is a recursive formula
This means that the second term, a2 is
a2 = (a2 - 1)^2 - 3
a2 = (a1)^2 - 3
a2 = 4^2 - 3 = 16 - 3 = 13
a3 = (a3 - 1)^2 - 3
a3 = (a2)^2 - 3
a3 = 13^2 - 3 = 169 - 3 = 166
a4 = (a4 - 1)^2 - 3
a4 = (a3)^2 - 3
a4 = 166^2 - 3 = 27556 - 3 = 27553
Thus,
a4 = 27553
Related Questions
Which steps show how to use the distributive property to evaluate 9 - 32? A. 9(32) = 9(30 + 2) = 9.30 + 9 - 2 = 270 + 18 = 288 0 B. 9(32) = 9(30 + 2) = 9 - 30 + 30 - 2 = 270 + 60 = 330 OC. 9(32) = 9(30 + 2) = 9.30 – 9.2 = 270 – 18 = 252 O D. 9(32) = 9(30 + 2) = 9.30 + 2 = 270 + 2 = 272
Answers
to find the distribution of
[tex]9\cdot32[/tex]rewrite 32 as an addition
[tex]32=30+2[/tex]rewrite the product
[tex]9\cdot(30+2)[/tex]distribute the 9
[tex]\begin{gathered} 9\cdot30=270 \\ 9\cdot2=18 \\ \\ 9\cdot(30+2)=9\cdot30+9\cdot2 \\ 9\cdot(30+2)=270+18 \\ 9\cdot32=288 \end{gathered}[/tex]At the fast food restaurant, an order of fries costs $0.94 and a drink costs $1.04. Howmuch would it cost to get 3 orders of fries and 2 drinks? How much would it cost toget f orders of fries and d drinks?
Answers
Determine the total cost for 3 order of fries and 2 drinks.
[tex]\begin{gathered} T=3\cdot0.94+2\cdot1.04 \\ =2.82+2.08 \\ =4.9 \end{gathered}[/tex]Determine the expression for f orders of fries and d drinks.
[tex]\begin{gathered} T=f\cdot0.94+d\cdot1.04 \\ =0.94f+1.04d \end{gathered}[/tex]So cost of 3 order of fries and 2 drinks is $4.9.
The cost order for f orders of fries and d drinks is 0.94f + 1.04d.
Let E be the event where the sum of two rolled dice is less than 9. List the outcomes in E^c
Answers
The Solution:
Let the outcomes when two dice are tossed be as summarized in the picture attached below:
Derivative of ln(x)cos(x)
Answers
The derivative of the given expression ln(x)cos(x) can be written as (cos(x))/x - sin(x)ln(x).
What is derivative?
In mathematics, the derivative of a function of a real variable measures how sensitive the function's value (or output value) is to variations in its argument (input value). The derivative is the fundamental tool in calculus. A measure of how quickly an object's position changes over time is its velocity, which is the derivative of that object's position with respect to time.
We can solve this derivation using multiplication property of derivatives:
i.e. [tex]\frac{d}{dx}(uv) = u\frac{dv}{dx} + y \frac{du}{dx}[/tex]
In the given question, lets consider ln(x) as u and cos(x) as v
putting the values from question.
[tex]\frac{d}{dx}(ln(x)cos(x)) = ln(x)\frac{d(cos(x))}{dx} + cos(x) \frac{d(ln(x))}{dx}[/tex]
[tex]= ln(x)(-sin(x)) + cos(x)(\frac{1}{x})[/tex]
= (cos(x))/x - sin(x)ln(x)
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Put the following equation of a line into slope-intercept form, simplifying allfractions.2x + 8y = 24
Answers
find the zeros algebraically: f(x)=x^4-8x^3+5x^2+14x
Answers
The given equation is:
x^4-8x^3+5x^2+14x
In this question, we have to find the zeros algebraically. Hence, we need to find the values of x that satisfy the equation.
Note: The roots (values of x) are equal to the power of the equation. Therefore, the given equation will have 4 roots
Therefore,
x^4-8x^3+5x^2+14x = 0
or
x(x^3-8x^2+5x+14) = 0
=> x = 0 and x^3-8x^2+5x+14 = 0
Therefore, the first root is x = 0.
Now,
x^3-8x^2+5x+14 = 0
To simplify that, try putting different values of x (starting from 1 and -1). The value that makes both sides equal to zero would be the solution.
Let's start with (1):
For x = 1
(1)^3 - 8(1)^2 + 5(1) + 14 = 0
1 -8(1) + 5 + 14 = 0
-1 -8 +5 + 14 = 0
- 9 + 19 = 0
10 = 0
It is false, therefore, x = 1 is not the solution.
For x = -1
(-1)^3 - 8(-1)^2 + 5(-1) + 14 = 0
-1 -8(1) - 5 + 14 = 0
-1 -8 -5 + 14 = 0
- 14 + 14 = 0
0 = 0
hence, x = -1 is the second solution.
If x = -1 is the solution, (x + 1) should be the factor of x^3-8x^2+5x+14. Therefore, the whole equation can be divided by factor
x^3-8x^2+5x+14 / (x+1). = x^2 - 9x + 14. (using division)
Now, let's find the roots of x^2 - 9x + 14
x^2 - 9x + 14 = 0
x^2 - 7x - 2x + 14 = 0
x(x - 7) - 2 (x - 7) = 0
(x - 7) (x - 2) = 0
or
x - 7 = 0. and x - 2 = 0
x = 7 and x = 2
Therefore, the zeros of the given equation are, 0, -1, 2 and 7.
3. State whether each sequence is arithmetic or geometric, and then find the explicit and recursive formulas for each sequence.Formulas:
Answers
A sequence is called arithmetic if the difference between two consecutives is a constant
In the first case we see a constant difference of 5
every two consecutives have difference of 5, for example 20-15, 30-25 and so on.
In the second case we see the division between two consecutives is a constant . That is called a GEOMETRIC sequence.
the constant in this case is 18/6 =3
lets return to the 1st case find the explicit
An = Ao +(n-1) d
An means the n term in the sucession
Ao means the first term
d means the constant
with that in mind we replace the values obtained
An= 5 + (n-1) •5
now for the recursive
a1= 5
An = An-1 + 5
Now lets go to the second part, the geometric sequence. Just is needed to replace the values in the ABOVE RIGHT formula
so then
An = A1 •(3)^(n-1)
An = 2• (3)^(n-1)
Explain how to find the point equidistant from all three vertices in the given triangle. Choose the correct answer below. A. Find the intersection of the perpendicular bisectors of each side of the triangle B. Find the intersection of all of the midsegments of the triangle, C. Find the intersection of the angle bisectors of each angle of the triangle, D. Find the midpoint of the line segment that bisects Angle B.
Answers
ANSWER:
The correct option is the following:
C. Find the intersection of the angle bisectors of each angle of the triangle,
EXPLANATION:
The point that equidistant is the point at which the three bisectors of the internal angles of the triangle intersect, and it is the center of the circumference inscribed in the triangle and equidistant from its three sides.
IMPORTANT NOTE:
Any point on the bisector of an angle of a triangle equidistant from the sides that define that angle.
Question 2 (2 points)Find the value of x. If needed, round your answer to the nearest tenth.50°X5Not drawn to scaleX =
Answers
Solution
Find the value of x in the triangle shown below:
Calculate the value of x
Opposite = 5
adjacet = x
[tex]tan\theta=\frac{opp}{adj}[/tex][tex]\begin{gathered} tan50=\frac{5}{x} \\ x=\frac{5}{tan50} \\ x=\frac{5}{1.19175} \\ x=4.1955 \\ x=4.2\text{ \lparen nearest tenth\rparen} \end{gathered}[/tex]Therefore the correct value of x = 4.2
A $40,000 is placed in a scholarship fund that earns an annual interest rate of 4.25% compounded daily find the value in dollars of the account after 2 years assume years have 365 days round your answer to the nearest cent
Answers
SOLUTION
From the question, we want to find the value in dollars of the account after 2 years.
We will usethe formula
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ Where\text{ A = value of the account, amount in dollars = ?} \\ P=principal\text{ money invested = 40,000 dollars } \\ r=annual\text{ interest rate = 4.25\% = }\frac{4.25}{100}=0.0425 \\ n=number\text{ of times compounded = daily = 365} \\ t=time\text{ in years = 2 years } \end{gathered}[/tex]Applying this, we have
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=40,000(1+\frac{0.0425}{365})^{365\times2} \\ A=40,000(1.000116438)^{730} \\ A=40,000\times1.0887116 \\ A=43,548.467179 \\ A=43,548.47\text{ dollars } \end{gathered}[/tex]Hence the answer is 43,548.47 to the nearest cent
41 increased by 4 is what number ?
Answers
The statement
41 increased by 4
The word increase mean adding to the given number 41
Hence,
The statement can be expressed as
[tex]41+4[/tex]Simplifying the result gives
[tex]41+4=45[/tex]Therefore, the answer is
[tex]45[/tex]41 + 4 = (41-1+4=44+1=45)
41 + 4 = 45 (40+5=45)
(41-1=40 4 + 1 = 5 + 40 = 45)
Therefore, 41 increased by 4 (41+4) would be 45. Please correct me if I’m wrong.
The scatter plot shows the median household income x in thousands of dollars, and the number of adults per 1,000 people with bachelors degree y of 50 U.S states. The line y=4.08x+63.13 is a good fit for this data
Answers
So,
The line:
[tex]y=4.08x+63.13[/tex]Is a good fit of the data given.
To predict the number of bachelor's degrees in Mississippi, we replace x by 40.6 and operate:
[tex]\begin{gathered} y=4.08(40.6)+63.13 \\ y=228.778 \end{gathered}[/tex]The number of bachelor's degrees per 1000 people when x=40.6 median income, is predicted as 228.778.
I
Three relationships are described below:
I. The amount of time needed to mow a yard increases as the size of the yard increases.
II. The amount of timeneeded to drive from city A to city B decreases as the speed you are driving increases.
III. The income of a worker who gets paid an hourly wage increases as the number of hours worked increases and
increases as the salary rate increases.
What type of variation describes each relationship?
Answers
The type of variation that describes each relationship include the following:
Direct variation: the amount of time needed to mow a yard increases as the size of the yard increases.Indirect variation: the amount of time needed to drive from city A to city B decreases as the speed you are driving increases.Joint variation: the income of a worker who gets paid an hourly wage increases as the number of hours worked increases and increases as the salary rate increases.What is an indirect variation?An indirect variation simply refers to a type of proportional relationship in which a variable is inversely proportional to another variable. This ultimately implies that, an indirect variation represents two variables that are inversely proportional to each other, which means as one variable increases, the other variable decreases and vice-versa.
What is direct variation?Direct variation refers to a type of proportional relationship in which a variable is directly proportional to another variable. This ultimately implies that, a direct variation represents two variables that are directly proportional to each other, which means as one variable increases, the other variable also increases and vice-versa.
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Graph the line y=1/4x+3 then name the slope and y-intercept by looking at the graph. How do I graph this what are my points and what is m= as well as what is b=?
Answers
Make graph line using the slope and the y-intercept or the point.
m=1/4 and b=3
What is graph ?
graph is a mathematical representation of a networks and it describes that the relationship between lines and points. A graph consists of some points and lines are between them. The length of the lines and position of the points do not matter.
Sol-as per the given question y=1/4x+3
The slope-intercept form y=mx+b where m is the slope and b is the y intercept
y=mx+b
Reorder terms
y=1/4x +3
Use the slope-intercept form to find the slope and y-intercept
Slope=1/4
y-intercept :(0,3)
Any line can be graphed using two points is Select two x
values, and plug them into the equation to find the corresponding Y values.
In record terms -y=1/4 x+3
The table of x and y values are-
X-0,4
Y-3,4
graph the line using the slope and the y-intercept, or the points.
Slope -1/4
y-intercept (0,3)
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I really need help make sure that your answer is 7th grade appropriate
Answers
Examples:
1. Five increased by four times a number
[tex]5+4n[/tex]where n is the number
2.The product of 4, and a number decreased by 7
[tex]4(n-7)[/tex]Jo borrowed $3800 for 8 months from a bank at 5.5% a. how much interest did jo pay the bank for the us of it's money?b. how much did he pay total?
Answers
Let's begin by listing out the given information:
Loan (p) = $3,800
Time (t) = 8 months = 8/12 year
Interest rate (r) = 5.5%
a)
We calculate it thus:
[tex]\begin{gathered} I=\frac{p\times r\times t}{100} \\ I=\frac{3800\times5.5\times\frac{8}{12}}{100}=139.33 \\ I=\text{\$}139.33 \end{gathered}[/tex]b)
The amount paid in total is:
[tex]\begin{gathered} A=p+I \\ A=3800+139.33=3939.33 \\ A=\text{\$}3939.33 \end{gathered}[/tex]Devon is 30 years old than his son, Milan. The sum of both their ages is 56. Using the variables d and m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.How old is Devon?
Answers
Let's set d as the age of Davon and m as the age of Milan.
Devon is 30 years old than his son Milan, it is represented by the equation:
[tex]d=m+30\text{ Equation (1)}[/tex]The sum of both ages is 56, the equation that represents the situation is:
[tex]d+m=56\text{ Equation (2)}[/tex]To find Devon's age, in equation 1, solve for m in terms of d:
[tex]m=d-30[/tex]Now, replace in equation 2 and solve for d:
[tex]\begin{gathered} d+(d-30)=56 \\ 2d-30=56 \\ 2d=56+30 \\ 2d=86 \\ d=\frac{86}{2} \\ d=43 \end{gathered}[/tex]Devon is 43 years old.
given: S is the midpoint of BT ; BO || AT prove:
Answers
"S is the midpoint of BT": this is given.
BO || AT: this is given.
SB = ST: definition of midpoint.
alternate interior
vertical
ΔBOS = ΔTAS: SAS or ASA (both are right).
What is an equation of the line that passes through the point (-4,-6)(−4,−6) and is perpendicular to the line 4x+5y=25?
Answers
First you put the equation into y=mx+b form:
1. move the 4x to the other side
5y=-4x+25
2. divide by 5 on both sides
y=(-4/5)x+5
Next, since the line has to be perpendicular, you take the negative reciprocal of the slope (flip the fraction and put the opposite sign)
1. 5/4
Now, find the y intercept (the b)
1. set up the equation
-6=(5/4)(-4)+b
2. multiply the 5/4 and -4
-6=-5+b
3. move the -5 to the other side (add it)
-1=b
Now, put all the elements together
1. y=(5/4)x-1
Animal is a bird Can fly Tiger Penguin ✓ ✓ Robin ✓ Snail Sparrow ✓ ✓ Pelican ✓ ✓ ✓ Bat Let event A = The animal is a bird. Let event B = The animal can fly. Which outcomes are in A and 8? O A. (robin, sparrow.pelican) B. (penguin, robin, sparrow, pelican) c. robin, sparrow, pelican, bat) D. (penguin, robin, sparrow. pelican, bat)
Answers
Outcome that are in A and B simply means both outcome must be achieved.
Therefore,
[tex]\begin{gathered} \text{Animal can fly and Animal is bird both exist in } \\ A\text{. }\mleft\lbrace\text{Robbin, sparrow, pelican}\mright\rbrace \end{gathered}[/tex]Which ocean animal is closest to a depth of -0.7km?
Answers
Answer:
whales, walruses, porpoises, dolphins, seals, dugongs, manatees, and sea otters
Step-by-step explanation:
have good day
Write a SITUATION that can be represented with this graph. Not an equation.
Answers
We need to think of something that will cool down 10 degrees in 5 hours to be more realistic. You may say that this graph describes the temperature profile of a fermentation broth after it is heated to 82 degrees is left on the tank to cool down to room temperature.
Here are the numbers of times 13 people ate out last month.5, 3, 4, 6, 3, 4, 5, 6, 4, 7, 3, 7, 6Find the modes of this data set.If there is more than one mode, write them separated by commas.If there is no mode, click on "No mode."No modeX?.
Answers
The mode is the number that appears most or occurs most frequently. Therefore, the mode of the data set below can be calculated below
[tex]5,3,4,6,3,4,5,6,4,7,3,7,6[/tex]Let's rearrange the data
[tex]3,3,3,4,4,4,5,5,6,6,6,7,7[/tex]The mode will be
[tex]\mleft\lbrace3,4,6\mright\rbrace[/tex]Help please!!!!!!!!!!!!!!!!!!!!!!!!!Which is the best buy?a. $18.09 for 9 bottles of juiceb. $22.33 for 11 bottles of juice
Answers
Answer:
The correct option is option a.
$18.08 for 9 bottles is the better buy.
Explanation:
The best buy is the item with the lesser price tag.
Let us chech which of the given items has the lesser price tag.
a. $18.08 for 9 bottles of juice
Let us find how much one bottle costs.
1 bottle = 18.08/9
= 2.01
1 bottle of juice costs $2.01 approximately
b. $22.23 for 11 bottles of juice
1 bottle = 22.23/11
= 2.03
1 bottle of juice costs $2.03 approximately.
Comparing these prices per bottle of juice, we realise that the one with $18.08 for 9 bottles is the better buy.
Find the length of the missing side of the triangle using the Pythagorean theorem. (Type an integer or decimal rounded to the nearest tenth as needed.)
Answers
Pythagorean theorem
[tex]\begin{gathered} a^2=b^2+c^2,\text{ where a is the hypotenuse} \\ a^2=(6.5)^2+(4.9)^2 \\ a^2=42.25+24.01 \\ a^2=66.26 \\ a=\sqrt[]{66.26}=8.1^{\prime} \end{gathered}[/tex](Type an integer or decimal rounded to the nearest tenth as needed.)
Integer = 8'
decimal rounded to the nearest tenth as needed = 8.1'
A dwarf seahorse swims 3/4 inch in a minute. How many minutes would take the seahorse to swim 1/3 inch?
A. 1/3 divided by 3/4= 4/9
B. 1/3 times 3/4= 1/4
C. 3/4 divided by 1/3= 9/4
D. 3/4 + 1/3= 13/12
Answers
Answer:
A
Step-by-step explanation:
we have 3/4 in / minute.
so, we divide this by 3/4 to get the time for 1 inch.
and then we multiply by 1/3 to get the time for 1/3 inch.
that combination, dividing by 3/4 and multiplying by 1/3, can be done in any sequence (commutative property of multiplication).
therefore, this can be expressed as 1/3 divided by 3/4. and A is the correct answer.
9×6 can u help me with this
Answers
You have to multiply the numbers:
9x6 =54
Multiply is the same as adding the number 6 times
9+9+9+9+9+9 =54
suppose that you have a savings account with 8500 in it. it pays 7% interest compound as shown below. find the value for the next 4 years
Answers
We want find the compound interest annualy for 4 years, $8500, at 7%'
The formula for the compound amount over one year is;
[tex]A=P(1+\frac{r}{100})[/tex]1st year:
[tex]\begin{gathered} A=8500(1+0.07) \\ A=\text{ \$9095} \end{gathered}[/tex]2nd year:
[tex]\begin{gathered} A=9095(1.07) \\ A=\text{ \$9731.65} \end{gathered}[/tex]3rd year:
[tex]\begin{gathered} A=9731.65(1.07) \\ A=\text{ \$10412.87} \end{gathered}[/tex]4th year:
[tex]\begin{gathered} A=10412.87(1.07) \\ A=\text{ \$11141.77} \end{gathered}[/tex]I NEED HELP ASAP Which of these data sets could best be displayed on a dot plot?721, 722, 722, 723, 724, 724, 724, 725, 727, 728, 73016, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 971.3, 1.9, 2.5, 2.7, 2.7, 3.5, 4.8, 5.3, 7.9, 9.00.012, 0.078, 0.093, 0.147, 0.187
Answers
Take into account that dop plots are usefull for small or moderate sized data sets, and also they are suefull for data with big gaps.
Based on the previous description, you can conclude that the best option for a dot plot is:
16, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 97
in comparisson with the other data sets, the elements of the rest of data sets are closer to each other.
What is the measure of the exterior angle of the triangle? A. 23°B. 149°C. 180°D. 31°
Answers
Solution
The diagram below will be of help
From the image above
We know that the sum of angle in a triangle is 180 degrees
That is
[tex]\begin{gathered} 63+86+y=180 \\ 149+y=180 \\ y=180-149 \\ y=31^{\circ} \end{gathered}[/tex]Now, to find x
We also know that the sum of angle in a straight line is 180 degrees
That is
[tex]y+x=180[/tex]We now solve for x
[tex]\begin{gathered} x=180-y \\ x=180-31 \\ x=149^{\circ} \end{gathered}[/tex]Therefore, the value of x = 149 degrees
Option B