Construct an explicit rule in function notation for the arithmetic sequence represented in the table. Then determine the value of the given term, and explain what it means. Darnell starts saving the same amount from each week′s paycheck. The table shows the total balance f(n) of his savings account over time in weeks. Time (weeks) n 1 2 3 4 Savings account balance ($) f(n) 260 360 460 560 Determine the value of f(11) and tell what it represents in this situation. f(n) = + (n − 1) f(11) = After 11 weeks, Darnell′s savings account will have a total of $ .
Answer:
After 11 weeks, Darnell′s savings account will have a total of $8,360.
Step-by-step explanation:
The data provided is as follows:
n: 1 2 3 4
f (n): 260 360 460 560
Consider the data for f (n).
The series f (n) follows an arithmetic sequence with a common difference of 100 and first term as 260.
The nth term of an arithmetic sequence is:
[tex]a_{n}=\frac{n}{2}[2a+(n-1)d][/tex]
Compute the value of f (11) as follows:
[tex]f(11)=\frac{11}{2}[(2\times260)+(11-1)\times 100][/tex]
[tex]=5.5\times[520+1000]\\\\=5.5\times 1520\\\\=8360[/tex]
Thus, after 11 weeks, Darnell′s savings account will have a total of $8,360.
Write an equation of the line in STANDARD FORM with a slope of 3 and passes through the point (6,-2) in standard form.
Standard form:
Ax + By = C
First make it into slope-intercept form first:
y = mx + b
Find b by substituting the given to their respective positions:
-2 = 3(6) + b
-2 = 18 + b
-2 - 18 = b
-20 = b
Now the complete version is:
y = 3x - 20
Arrange the equation:
y = 3x - 20
-3x + y = -20
Easy :)
The length of a rectangle is 3.7 inches when rounded to the nearest tenth of an inch. Select all of the following that could be the actual length of the rectangle.
Answer:
poop
Step-by-step explanation:
2 1⁄4 × 1 1⁄2 × 5⁄3 =
please help me
The answer is:
5 5/8
I got this by multiplying 2 1/4 and 1 1/2 first and i got 3 3/8, then multiplied that number with 5/3
5. What is the y-intercept of the given
graph?
y-intercept:
Answer:
1
Step-by-step explanation:
Max and Maddy race. Max runs at a speed of 2mph. Maddy runs at a speed of 3mph. If Max takes 3 hours, what is Maddy's speed?
Plz answer!
Answer:
The question has the answer in it.. Maddy's speed.. which is 3 MPH :/ but... if you need to find the thing that isn't known... Maddy's time.. here is how..
Step-by-step explanation:
Max takes 3 hours at 2 mph.. soo 3x2=6 miles that max traveled
Maddy runs at 3 mph so .. 6 miles / 3MPH =2 hours, Maddy takes 2 hours
Can any one help me ??
Answer:
A
Step-by-step explanation:
would a boxplot of the data 113, 116, 116, 116, 118, 118, 119, 119, 122, 124, 124, 124 allow you to find the mean and the median?
I really need help....
..
Answer:
show the whole number line plz
Step-by-step explanation:
Which is greater -3 or -5
Answer: -3
Step-by-step explanation:because -3 looks like it is smaller, but when a number is negative, the smaller the number, the greater the value actually is.
Pls help me I don't know what to do here
Answer:
3/9
1 x 3
1 x 9
Step-by-step explanation:
What's b/2-14=8 Equal ?
Answer:
1. add 14 to both sides
b/2 = 8E + 14
2. multiply both sides by 2
b = (8E + 14) x 2
3. regroup terms
b = 2(8E + 14)
Hope this helped :)
Pls help me with this question
Answer:
option C, x=1
Step-by-step explanation:
[tex]2^{9x-3} = 8^{3-x}[/tex]
[tex]2^{9x-3} = (2^3)^{3-x}[/tex]
[tex]2^{9x-3} = 2^{9-3x}[/tex]
cut 2 from LHS and RHS you will get,
9x-3 = 9-3x
9x + 3x = 9 + 3
12x = 12
x = 12/12
x = 1
therefore, option C is the correct option
hope it helps you!
Answer:
[tex] \huge{ \boxed{ \bold{ \tt{x = 1}}}}[/tex]
Option C is correct.
Step-by-step explanation:
[tex] \text{First ,\: let's \: know \: about \: exponential \: equation} : [/tex]
Exponential EquationAn equation in which variables appears as an exponent of a base is known as exponential equation. The following axioms are useful while solving the exponential equations :
If [tex] \sf{ {a}^{x} = {a}^{b} }[/tex] , then x = bIf aˣ = 1 , then aˣ = a⁰ and x = 0Thus , while solving an exponential equation, we should simplify the equation till the equation is obtained in the form [tex] \sf{ {a}^{x} = {a}^{b}} [/tex] or aˣ = 1 .
Now, let's start to solve :
[tex] \sf{ {2}^{(9x - 3)} = {8}^{( 3 - x)}} [/tex]
➸ [tex] \sf{ {2}^{9x - 3} = {2}^{3(3 - x)} }[/tex]
➸ [tex] \sf{ {2}^{9x - 3} = {2}^{9 - 3x}} [/tex]
➸ [tex] \sf{ \cancel{2} ^{ \: 9x - 3} = \cancel{2} ^{ \: 9 - 3x} }[/tex]
➸ [tex] \sf{9x - 3 = 9 - 3x}[/tex]
➸ [tex] \sf{9x + 3x = 9 + 3}[/tex]
➸ [tex] \sf{12x = 12}[/tex]
➸ [tex] \sf{ \frac{12x}{12} = \frac{12}{12}} [/tex]
➸ [tex] \boxed{ \sf{x = 1}}[/tex]
The value of x is 1 .
Hope I helped!
Best regards! :D
~[tex] \text{TheAnimeGirl}[/tex]
Pool #1 is a rectangle that is 14 feet wide. The length is (14– 8)2ft.
The dimensions of the pool are: Length=________ ft Width=_________ft
Answer: the length is 6 feet. The width is 2 feet
Step-by-step explanation:
The garden pool is rectangular in shape.
Let L represent the length of the rectangular garden.
Let W represent the width of the rectangular garden.
The area of a rectangle is expressed as L× W. The area of the rectangular garden pond is 12ft^2. It means that
L× W = 12 - - - - - - - - - - 1
The length of the pool needs to be 2ft more than twice that width. This means that
L = 2W + 2 - - - - - - - - - - - 2
Substituting equation 2 into equation 1, it becomes
W(2W + 2) = 12
2W^2 + 2W = 12
2W^2 + 2W - 12 = 0
W^2 + W - 6 = 0
W^2 + 3W - 2W - 6 = 0
W(W + 3) - 2(W + 3) = 0
W - 2 = 0 or W + 3 = 0
W = 2 or W = - 3
Since the Width cannot be negative, then the width is 2 feet
Substituting W = 2 into equation 2. It becomes
L = 2×2 + 2 = 6 feet
If A ⊂ B, then A ∩ B = A ∪ B. a) sometimes b) always c) never
The Answer is Never- Hope this helps and have a great day!
Explanation:
We are given that set A⊂B .
This means that set A is properly contained in set B.
i.e. A≠B
This means that there are some elements in set B which are not in set A.
Now we have to show whether the following property A∩B=A∪B
always, sometimes or never hold.
As A is a proper set of B.
This means that: A∩B=A ( Since A is a smaller set)
Also, A∪B=B (Since B is a bigger set)
Hence, A∩B ≠ A∪B (Since A≠ B)
Credit to -virtuematane
Two shops, Lidal and Oldi, sell the same brand of toilet rolls but with different package sizes. Calculate the price per 36 rolls for each shop. Write which shop is the best value for money in the comment box. lidals deal is 9 £3.51 oldi deal is 4 £1.52
Answer: Oldi gives the best value of money.
Step-by-step explanation:
Lidal's deal : 9 rolls for £3.51
Oldi's deal : 4 rolls for £1.52
Cost per roll = [tex]\dfrac{\text{total cost}}{\text{Number of rolls}}[/tex]
So,
For Lidal, Cost per roll = [tex]\pounds\dfrac{3.51}{9}=\pounds0.39[/tex]
For Oldi', Cost per roll = [tex]\pounds\dfrac{1.52}{4}=\pounds0.38[/tex]
Clearly, [tex]\pounds 0.39> \pounds 0.38[/tex]
Hence, Oldi gives the best value of money.
Check all of the polynomial functions that have 2 as a root.
h(m) = 8 – m3
f(g) = g3 – 2g2 + g
f(a) = a3 – 4a2 + a + 6
f(x) = x3 – x2 – 4
Answer:
Explained below
Step-by-step explanation:
Polynomial Roots
If x=a is a root of f(x), then f(a)=0
We will test the following functions to check if a=2 is a root.
[tex]h(m)=8-m^3[/tex][tex]h(2)=8-2^3=8-8=0[/tex]
Thus m=2 is a root of h
[tex]f(g)=g^3-2g^2+g[/tex][tex]f(2)=2^3-2\cdot 2^2+2[/tex]
[tex]f(2)=8-2\cdot 4+2=8-8+2=2[/tex]
Thus g=2 is not a root of f
[tex]f(a) = a^3 - 4a^2 + a + 6[/tex][tex]f(2) = 2^3 - 4\cdot 2^2 + 2 + 6[/tex]
[tex]f(2) = 8-16+8=0[/tex]
Thus a=2 is a root of f
[tex]f(x) = x^3 - x^2 - 4[/tex][tex]f(2)=2^3 - 2^2 - 4[/tex]
[tex]f(2)=8 - 4 - 4=0[/tex]
Thus x=2 is a root of f
Answer:
answers are A, C, and D
Step-by-step explanation:
THIS IS CORRECT
Dominic bought a new video game that was on sale for 35% off. If the original price is 29.95, what will the amount be that Dominic pays?
Answer:
19.47
Step-by-step explanation:
f (x) =x^2 - 2x + 9
g (x) = -3x -14
F + 3!=0, g = (F^2 + 5 F + 20)/(9 (F + 3)), x = -14/(F + 3)
Step-by-step explanation:
PLEASE HELP! I WILL MARK THE BRAINLIEST!
A coordinate plane with a line passing through (negative 3, 0), (0, negative 2) and (3, negative 4).
What is the equation of the graphed line written in standard form?
Answer:
2x+3y=-6
Step-by-step explanation:
Solve this problem please :)
Mr. Peters uses a phone card to call relatives in France. It costs him 48 cents to talk for 12 minutes. What is the call rate for the phone card?
Answer:
The ratio is 1:4
Step-by-step explanation:
For every minute of talking, it costs him 4 cents, and so on.
please help fast! i will give brainliest
Answer:
0.39
Step-by-step explanation:
Answer:
1.87
Step-by-step explanation:
Which set of coordinate pairs do NOT represent a linear function?
(−4, −12), (−3, −10), (−2, −8), (−1, −6)
(−4, −17), (−3, −10), (−2, 5), (−1, 2)
(1, −7), (2, −10), (3, −13), (4, −16)
(1, 1), (2, 4), (3, 7), (4, 10)
Answer:
(-4, -17), (-3, -10), (-2,5), (-1,2)
All the coordinates are represent linear function.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The coordinates are,
⇒ (-4, -12), (-3,-10), (-2, -8), (-1,-6)
⇒ (-4, -17), (-3, -10), (-2,5), (-1,2)
⇒ (1, -7), (2, -10), (3, -13), (4, -16)
⇒ (1, 1), (2, 4), (3, 7), (4, 10)
Now,
We know that;
A relation between a set of inputs having exactly one output each is called a linear function.
Clearly, All the coordinate have exactly one output for every input.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ6
Find the equation of the perpendicular bisect of the given segment by following these steps
1. Determine the slope of the given segment
Answer:
3/2
Explanation: Just did this on Edge
5. Suppose a bunny's second hop is 8% higher than her first hop. Is the
statement below true or false? If the statement is false, correct it.
"The bunny's second hop is 108% of her first hop."
Select the interval where f is negative
Answer:
The negative regions of a function are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero). y-values that are on the x-axis are neither positive nor negative. The x-axis is where y = 0.
Step-by-step explanation:
hope this helps :)
c. How many doughnuts are in 7.80 dozen doughnuts
Answer:
93.6 becasue there are 12 donuts in a dozen. So you multiply 12 by 7.80.
i need help right now and asap this is the question and if u answer i will give brainliest and whatever it is i will give it anyway here it is
Philosophers during the Enlightenment of the 1600s and 1700s
a were most concerned with faith and religion.
b were disdainful of art and science.
c used emotion as a guiding principle.
d used reason to try to improve people’s lives.
Answer:
Sorry if I'm late!!!
D. Used reason to improve people's lives
Explanation:
The enlightenment was a time when philosophers challenged the teachings of the catholic church.
whats 100+100 try to guess :)
Answer:
100+100=200
Step-by-step explanation:
hope it helps :)
Answer:
200
Step-by-step explanation:
100 + 100 = 200