the Following table shows alexandra's investment options over the course of three years. Her initial investment was $1,000 . write one function for each option to describe the value of the investment f(n), in dollars, after n years.
The pattern in the given series of amount in the account are in the form of
arithmetic and geometric progression.
The function for Option 1 is; [tex]\underline{ f(n) = 1,100 + (n - 1) \cdot 100}[/tex]The function for Option 2 is; [tex]\underline{f(n) = 1,100 \times 1.1^{(n - 1)}}[/tex]Reasons:
The given table of values is presented as follows;
[tex]\begin{tabular}{c|c|c|c|}Number of years&1&2&3\\Option 1 (Amount in dollars)&1,100&1,200&1,300\\Option 2 (Amount in dollars)&1,100&1,210&1,331\end{array}\right][/tex]
In Option 1, the amount in dollars for each year has a common difference of d = 100
The first term, a = 1,100
Therefore;
The Option 1 can be represented as an arithmetic progression , A.P. in the
form, tₙ = a + (n - 1)·d as follows;
For the Option 1, we have;
The amount in dollars after n years, [tex]\underline{ f(n) = 1,100 + (n - 1) \cdot 100}[/tex]For Option 2, it is possible to find;
1,331 ÷ 1,210 = 1,210 ÷ 1,100 = 1.1
Therefore;
The terms in the Option 2 have a common ratio of r = 1.1
The Option 2 is a geometric progression, G.P.
The first term in Option 2 is a = 1,100
Which gives, the nth term, tₙ = a·r⁽ⁿ ⁻ ¹⁾
Therefor;
The function for the Option 2 is; [tex]\underline{f(n) = 1,100 \times 1.1^{(n - 1)}}[/tex]Learn more about arithmetic and geometric progression here:
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Need help on HS geometry
Answers:
321°Hope you could get an idea from here.
Doubt clarification - use comment section.
[tex]\\ \tt\Rrightarrow 16x-27=5x+6[/tex]
[tex]\\ \tt\Rrightarrow 16x-5x=6+27[/tex]
[tex]\\ \tt\Rrightarrow 11x=33[/tex]
[tex]\\ \tt\Rrightarrow x=3[/tex]
m<YQR=16(3)-27=48-27=21°Simplify (x^3 + 2x^2 - x) + (4x^3 + x^2 + x)
Answer: 5x^3 + 3x^2
Step-by-step explanation:
Answer:
Step-by-step explanation:
6x2 - 8x - 2
Simplify ————————————
x - 1
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
6x2 - 8x - 2 = 2 • (3x2 - 4x - 1)
Trying to factor by splitting the middle term
3.2 Factoring 3x2 - 4x - 1
The first term is, 3x2 its coefficient is 3 .
The middle term is, -4x its coefficient is -4 .
The last term, "the constant", is -1
Step-1 : Multiply the coefficient of the first term by the constant 3 • -1 = -3
Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -4 .
-3 + 1 = -2
-1 + 3 = 2
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Polynomial Long Division :
3.3 Polynomial Long Division
Dividing : 3x2-4x-1
("Dividend")
By : x-1 ("Divisor")
dividend 3x2 - 4x - 1
- divisor * 3x1 3x2 - 3x
remainder - x - 1
- divisor * -x0 - x + 1
remainder - 2
Quotient : 3x-1
Remainder : -2
Final result :
2 • (3x2 - 4x - 1)
——————————————————
x - 1
See results of polynomial long division:
1. In step #03.03
What is the equation of the line that passes through the points (-4, 2) and (-2, 10)?
Answer:
y=4x+18
Step-by-step explanation:
HOPE THIS HELPS :)
Diego has a skateboard, scooter, bike, and go-cart. He wants to know which vehicle is the fastest. A friend records how far Diego travels on each vehicle in 5 seconds. For each vehicle, Diego travels as fast as he can along a straight, level path.
Answer:
Are there any numbers?
Step-by-step explanation:
Elliott needs 3/4 of a cup of sugar to make a dozen chocolate chip cookies. How many cups of sugar does he
need to make 4 dozen.
Answer:
3 cups
Step-by-step explanation:
3/4 times 4 equals 12/4. divide and get 3.
Find the midpoint of the segment with the following endpoints. (10,6) and (4,9)
Answer:
(7,7.5)
Step-by-step explanation:
midpoint formula:
(10+4)/2=7
(6+9)/2=7.5
(7,7.5)
What is 2+6 100 points the answer is 8 right?
Answer:
yes it is 8
Step-by-step explanation:
Answer:
Step-by-step explanation:
8
how do you simplify this equation?
Answer:
The answer is B --> [tex]\frac{x^{2} }{3x^{2} -1}[/tex]
How I got that:
These are really easy, you're simply looking for numbers that you can factor down. Like here:
I took:
[tex]\frac{4x^{2} }{12x^{2} -4}[/tex]
and saw that I could factor out 4 from the denominator:
[tex]\frac{4x^{2} }{4(3x^{2} -1)}[/tex]
and then I canceled out the common factor (4 because its on both sides):
[tex]\frac{x^{2} }{3x^{2} -1}[/tex]
And there ya go!
~That's All Folks~
-Siascon
Answer: It's B
Step-by-step explanation:
22x2
Simplify ————————
12x2 - 4
4.1 Pull out like factors :
12x2 - 4 = 4 • (3x2 - 1)
What is the slope of any line parallel to the graph of y=8x+20?
Answer:
m = 8
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
When any 2 lines are parallel, they will have the same slope but different y-intercepts.
∴ Our parallel line's slope will be 8.
HELP PLS IM BEING TIMED
A line passes through the points (-5, 2) and (10,-1). Which is the equation of the line?
O y=-3x+1
Oy-x
O y = -5x – 23
O y = 5x + 27
Answer:
The correct answer is none.
Step-by-step explanation:
The correct answer is y = -1/5x + 1
To find the equation of the line, start by finding the slope. You can do this by using the slope formula below.
m(slope) = (y2 - y1)/(x2 - x1)
m = (2 - -1)/(-5 - 10)
m = 3/-15
m = -1/5
Now that we have the slope, we can use it along with either point in the point-slope form to get the equation.
y - y1 = m(x - x1)
y - 2 = -1/5(x + 5)
y - 2 = -1/5x - 1
y = -1/5x + 1
Answer:
It Should be y= -1/5x + 1 but you have not listed it in your options...
Step-by-step explanation:
Which of the following best describes the slope of the line below?
• A. Negative
• B. Undefined
• C. Zero
D. Positive
Answer:
A. Negative
Step-by-step explanation:
This line cannot have a slope of zero or undefined because it's a linear negative line. This line is not positive because it's not heading to the right, it's heading to the left which is the negative side, the slope Rise/Run goes up 1 and left 1, which means the slope for this equation is possibly -1x.
Answer:
Negative
Step-by-step explanation:
We can see that as x increases, y decreases. Therefore, the change in y over the change in x is negative. The line goes down from left to right.
If (-2,11) and (9,22) are two
anchor points on the trend line,
then find the equation of the line.
y = [ ? ]x + [
Answer:
The equation of the line is- y = x + 13
de un grupo de 22 estudiantes hay 13 que practican natación y 10 practican atletismo y 2 que no practican nada . ¿Cuántos practican solo atletismo?
AYUDA¡¡¡
Usando conjuntos de Venn, se encuentra que 7 estudiantes practican solo atletismo.
Los conjuntos son:
Conjunto A: Estudiantes que practican natación.Conjunto B: Estudiantes que practican atletismo.Hay que:
13 que practican natación, o sea, [tex]A = 13[/tex].10 practican atletismo, o sea, [tex]B = 10[/tex].2 que no practican nada, o sea [tex]A \cup B = 22 - 2 = 20[/tex].La cantidad que practica ambos es:
[tex]A \cap B = A + B - A \cup B[/tex]
[tex]A \cap B = 13 + 10 - 20[/tex]
[tex]A \cap B = 3[/tex]
Solo atletismo es:
[tex]B - A \cap B = 10 - 3 = 7[/tex]
7 estudiantes practican solo atletismo.
Más informaciones a cerca de conjuntos de Venn pueden ser obtenidas en https://brainly.com/question/24388608
SOLVE
5x + 2y = 37
y = x + 8
Write the solution below.
Answer:
x=3
y=11
Step-by-step explanation:
5x + 2y = 37
y = x + 8
5x+2(x+8)=37
5x+2x+16=37
7x=21
x=3
y = (3) + 8
y=11
What is the scale factor of the
dilation shown?
Answer:
2
Step-by-step explanation:
Evaluate the following expression if c = 8 and d = -5
3 * (c+d
Hi,
if c = 8 and d = -5:
3*(c + d) <=> 3*(8 + (-5))
= 3*(8 - 5)
= 3*3
= 9
✅^_^
Find EG
Please help
Answer:
EG = 12.2
Step-by-step explanation:
Since HG = HE = 14 then the triangle is isosceles.
HF is a perpendicular bisector of EG , then
EF = FG = 6.1 , so
EG = EF + FG = 6.1 + 6.1 = 12.2
the quotient of a number and 7 is greater than or equal to 20
Answer:
a is greater than or equal to 140
Step-by-step explanation:
Multiply both sides by 7, which cancels out the 7 and turns 20 into 140
what is factoring: problems involving factors of polynomials
Answer: Factoring is essentially the reverse of the distributive property. You are basically trying to simplify the polynomial by taking out common factors. You also may try reducing the power (or the highest exponent) of the polynomial with factoring. I would say that factoring is the breaking down of a bigger polynomial into a product of two expressions that are usually multiplied by each other. One specific use of factoring we see a lot is the quadratic formula.
1. Quadratic Factoring --> [tex]x^2+2x-15[/tex] --> we have an [tex]x^2[/tex] but we want there to only be "[tex]x[/tex]"s. Here we need to constant numbers (integers), that multiply together to get [tex]-15[/tex], and add up to [tex]+2[/tex]. (5 and -3)
- [tex]x^2+2x-15[/tex] ==> [tex]x^2+5x-3x-15[/tex] ==> [tex]x(x+5)-3(x+5)[/tex] ==> [tex](x-3)(x+5)[/tex]
Above: We can see that we factor out [tex]x[/tex] from [tex]x^2+5x[/tex] (This shows that we are aiming to break it down to make it easier to evaluate).
Remember: Factoring does not always mean that the polynomial is in a simpler form. There are many situations where factoring is totally unnecessary and complicates the polynomial even more.
--------------------------------------------------------------------------------------------------------------On a separate note: Distributive Property, if you are unsure or not fully sure on what that means, is when you multiply two expressions together to create one expression. Multiple expressions are combining into one.
Does anybody know how to does this pleaseee helppppp. The first 2 my teacher did them for me but I’m still confused pleaseee helpppp
Answer:
below
Step-by-step explanation:
A triangle can only be a triangle if the two shortest sides add up to be greater than the longest side.
For example on the first one, the segments 1 2 and 3 will not make a triangle as 1 + 2 = 3 and if the two smallest sides of a triangle are equal to the longest side it will not be a triangle at all.
So to make this easy, out of the three numbers given: add the two smallest numbers. This number has to be greater than the third number given, and it cannot be equal.
For question three: 3+9 = 12
And 12 is greater than 11, therefore this can make a triangle.
What is the area of a cross section that is parallel to
face ABCD?
Enter your answer in the box.
cm2
Answer:
1296cm².
Step-by-step explanation:
= 12×36×6÷2 ................
plz check weather correct or notn
What is the area of this figure?
6 in
4 in
1 in
2 in
7 in
6 in
square inches
Answer:
wheres the figure
aaah
good morning
Question 14
Determine if the given lines are parallel or perpendicular or neither.
3y=2-x
y=-1/3x+4
Answer:
The given lines are parallel.
Step-by-step explanation:
3y=2-x
y=-1/3x+4
-------------
y=2/3-1/3x
y=-1/3x+2/3
y=-1/3x+4
----------------
Since the two lines have exact same slopes, it follows that these two lines are parallel.
What are the steps to convert a number from standard notation to scientific notation?
Answer:
Consider a big number 3,400,000. To convert this number into scientific notation:
Place a decimal by counting the steps to the left until the coefficient of the number is between 1 and 9.
Count the number of steps moved. This will be the power of the base 10.
In this case, the coefficient is 3.4 and the 6 steps are moved.
Multiply the coefficient by 106,
Therefore, the answer is 3. 4 x 10 6
Step-by-step explanation:
1. Make a Prediction Write a rule that you can use to find the number of star beads in a bracelet when you know the number of moon beads. Then write a rule that you can use to find the number of moon beads when you know the number of star beads.
Does any one mind helping me on this question I have struggle solving it
-1=0
0.5=4.5
3=3.1
this is the answer
Marhannah must make a costume for the school play. She needs a piece of fabric that’s is 8/3 yards long and 3/2 yards wide. What is the area of the piece of fabric Marhannah needs?
Answer:
Our material is 54" wide. Here is a helpful chart to help you quickly convert linear yards into inches and feet.
How big is one linear yard of fabric?
Yards Length Width
3 108 Inches (9 Feet) 54 Inches (4.5 Feet)
4 144 Inches (12 Feet) 54 Inches (4.5 Feet)
Step-by-step explanation:
C A R R Y
O N
L E A R N I N G
What is the product of 44(4-7)(4)?
-16
O
ОО
-1 -12
-100
8
DONE
Hey there!
44(4 - 7)(4)
= 44(-3)(4)
= -132(4)
= -528
Therefore, your answer is: -528
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Easy peace math problem
Answer:
225/10=441/l
cross multiply
225l=10*441
225l=4410
l=4410/225
l=19.6 liters of gas
Step-by-step explanation:
l=19.6 liters of gas