Given:
The series is
[tex]2x+2x^2+2x^3+...+2x^n[/tex]
To find:
Whether the given series is arithmetic, geometric, both, or neither.
Solution:
We have,
[tex]2x+2x^2+2x^3+...+2x^n[/tex]
Difference between consecutive terms are:
[tex]d_1=a_2-a_1[/tex]
[tex]d_1=2x^2-2x[/tex]
[tex]d_1=2x(x-1)[/tex]
And,
[tex]d_2=a_3-a_2[/tex]
[tex]d_2=2x^3-2x^2[/tex]
[tex]d_2=2x^2(x-1)[/tex]
Here, [tex]d_1\neq d_2[/tex].
So, the given series is not an arithmetic series.
Ratio between consecutive terms are:
[tex]r_1=\dfrac{a_2}{a_1}[/tex]
[tex]r_1=\dfrac{2x^2}{2x}[/tex]
[tex]r_1=x[/tex]
And,
[tex]r_2=\dfrac{a_3}{a_2}[/tex]
[tex]r_2=\dfrac{2x^3}{2x^2}[/tex]
[tex]r_2=x[/tex]
Similarly upto last pair of consecutive terms.
[tex]r_{n-1}=\dfrac{a_n}{a_{n-1}}[/tex]
[tex]r_{n-1}=\dfrac{2x^n}{2x^{n-1}}[/tex]
[tex]r_{n-1}=x[/tex]
Since, [tex]r_1=r_2=...=r_{n-1}[/tex], so the given series have a common ratio.
Therefore, it is a geometric series.
PLEASE HELPpppppppppppppppp
Answer: 140%
Step-by-step explanation:
Cost of the coats = $45 each
Selling price of the coat = $63 each
The percent of the purchase price that is the sales price would be:
= 63/45 × 100
= 7/5 × 100
= 140%
Therefore, the answer is 140%.
When 17 is divided by K ; where k is a positive integer less than 17 the remainder is 3 .What is the remainder when the sum of the beta possible values of Kivided by 17.
Answer:
The remainder is 4.
Step-by-step explanation:
Note: This question is not correctly stated. It is therefore correctly restated before answering the question as follows:
When 17 is divided by k; where k is a positive integer less than 17, the remainder is 3. What is the remainder when the sum of the possible values of k is divided by 17?
The explanation of the answer is now given as follows:
Since k < 17, it implies that the possible values of k must be from between 1 and 16 inclusive.
Between 1 and 16, only 7 or 14 will give a remainder of 3 when either of them is used to divide 17. Therefore, 7 and 14 are the possible values of k.
Therefore, we have:
Sum of the possible values of k = 7 + 14 = 21
Also, we have:
Sum of the possible values of k divided by 17 = 21 / 17 = 1 with a remainder of 4.
Therefore, the remainder is 4 when the sum of the possible values of k is divided by 17.
The machine that Holley operates tightens 40 bolts every 3 minutes. The bolts are delivered to her machine station in boxes containing 1,000 bolts each. Which equation can be used to determine t, the number of minutes it takes Holley's machine to tighten a box of 1,000 bolts at the same tightening rate?
Answer:
75
Step-by-step explanation:
A cube has a side length of 6 cm. What is the volume of the cube, in cubic centimeters
Answer:
V=216cm³
Step-by-step explanation:
V=216cm³
You decide to market your own custom computer software. You must invest $3,255 for computer hardware, and spend $2.90 to buy and package each disk. If each program sells for $13.75, write a system of equations and determine how many disks you must sell to break even.
Answer:
13.75x = 3,255 + 2.90x
Step-by-step explanation:
Given that,
Amount invested on computer hardware = $3,255
Amount invested to buy and package each disk = $2.90
Selling price for each program = $13.75
We need to find the equation that is used to find how many disks you must sell to break even. Let there are n disks that you must sell.
ATQ,
$3,255 is a fixed amount. $2.90 and $13.75 depends on x.
So,
13.75x = 3,255 + 2.90x
We can solve the above equation to find the no. of disks.
13.75x - 2.90x = 3255
10.85x = 3255
x = 300
Hence, you must sell 300 disks to break even.
What time is it exactly 1,440,000 minutes after 10 pm
Answer:
The answer is 11 PM
Step-by-step explanation:
1,440,000 minutes is the same as 24,000 hours. Then, you add that to 10pm of that day and you get 11 pm. It is the same as multiplying 24 x 1000 hrs. it is like adding 1000 days to that since it is 24 hrs in one day. Hope this helped!!
Answer:
11:00 pm
Step-by-step explanation:
1,440,000 minutes, convert it into hours and you get 24,000 hours. Since 24 hours equal a day 24,000 is 1,000 days. Attach 10:00 pm since its exactly 1,000 days after and you get 11:00 pm.
In the worlds coolest freezer sodium gas was cool to temperature of 78.5 below zero and then called 194.65 more what was the new temperature of the sodium gas
Answer:
[tex]-273.15^{\circ}\text{C}[/tex]
Step-by-step explanation:
[tex]T_i[/tex] = Initial temperature of sodium gas = [tex]-78.5^{\circ}\text{C}[/tex]
[tex]\Delta T[/tex] = Change in temperature of sodium gas = [tex]-194.65^{\circ}\text{C}[/tex]
[tex]T_f[/tex] = Final temperature of sodium gas
Change in temperature of gas is given by
[tex]\Delta T=T_f-T_i\\\Rightarrow T_f=\Delta T+T_i\\\Rightarrow T_f=-194.65+(-78.5)\\\Rightarrow \Delta T=-273.15^{\circ}\text{C}[/tex]
The new temperature of sodium gas is [tex]-273.15^{\circ}\text{C}[/tex].
How come nobody answers my questions? Like wth, I'm stuck but everyone else is getting their questions answered left and right.
Answer:
That is a good question and it might be your question you are trying to find the answer and maybe your question looks hard
Hope this help :)
Step-by-step explanation:
If y = 80 when x = 32, find x when y = 100.
Answer:
when y=80 the value of x is 32 and when y=100 what is the value of x so Criss cross 80=32
and 100= x so the answer will be 32*100 divided by 80 is equal to 40 I guess it's 40 the value of x is 40 in my guess
Is -4 a integer yes or no
Answer:
Yes
Step-by-step explanation:
A integer is any number that's not a fraction.
Answer:
yes
Step-by-step explanation:
integer are numbers that aren't a fraction
What is the solution to the equation -6x + 9 – 4x = 14?
[tex] - 6x + 9 - 4x = 14 \\ - 6x - 4x = 14 - 9 \\ - 10x = 5 \\ x = \frac{5}{ - 10} \\ x = - \frac{1}{2} \\ x = - 0.5[/tex]
Need help with question
Point M is the midpoint of point A and point B. Find the coordinates of point B .
A(-7,-10) M( -19/2 , -9/2)
Answer:
coordinate of point b is 12,1 by midpoint formula
Step-by-step explanation:
take mp formula and evaluate by putting value it will give you x again same process then it will give you u
A company loses $5,400 as the result of a manufacturing defect. Each of the 8 owners have agreed to contribute an equal amount, x, to help pay for the losses.
Part A
Which expression shows the total loss after the owners contribute some money?
Answer:
x=$5400:8
$5400:8x = total loss after the owners contribution
The expression shows the total loss after the owners contribute some money is 8x = 5400
Equation
An equation is an expression used to show the relationship between two or more numbers and variables.
Let x represent the amount contributed by each owner as loss.
Since there are 8 owners sharing a loss of $5400, hence:
8x = 5400
x = 675
The expression shows the total loss after the owners contribute some money is 8x = 5400
Find out more on equation at: https://brainly.com/question/13763238
can you help me please?
Answer:
it is a it the first one. 7/13
Answer:
A.
Step-by-step explanation:
The bottom number is the same so leave then and just add the top.
Makes 7/13
A school basketball team has an expense account and a fundraising account. After t weeks, the balance of the expense account is (450−70t) dollars and the balance of the fundraising account is (275+48t) dollars.
a. Write an expression in simplest form that represents the total amount (in dollars) in both accounts after t weeks.
Answer: 707$ because
Step-by-step explanation: if you do the math you can only get this number the wrong and right way
what would be the slope of (1,-2) and (3,0)
Answer:
1
Step-by-step explanation:
Hello :)
So to answer this problem, we can use the rise over run formula.
The rise is the difference of any two y values.
The run is the difference of the x values from the same two y values.
This question gives us 1,-2 and 3,0
We can use them for the formula:
-2 - 0 divided by 1 - 3
-2/-2 = 1
Answer:
[tex]m=1[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (1, -2)
Point (3, 0)
Step 2: Find slope m
Substitute [Slope Formula]: [tex]m=\frac{0+2}{3-1}[/tex]Evaluate Addition/Subtraction: [tex]m=\frac{2}{2}[/tex]Evaluate Division: [tex]m=1[/tex]Help me please. I need helpppppoooooopppppopopppp
Answer:
0
Step-by-step explanation:
The minimum number of cavities a patient had was 0 cavities.
Answer:
0
Step-by-step explanation:
The smallest number that indicates cavity is '0' therefore it is the minimum number of cavities
 Can someone pleaseeee help if you’re correct I’ll give u brainlist
Answer:
p=65
Step-by-step explanation:
180-50=130
130/2=65
A friend purchases items from a website and resells them on her own website. She typically marks up her merchandise 40%. If she purchased an item for 15$, what price should she set for the item?
Answer:
$21
Step-by-step explanation:
Step one:
given
she purchased an item for $15
marks up her merchandise 40%.
let us find 40% of $15
and add the answer to the initial price of the item
Step two:
40/100*15
=0.4*15
=$6
Hence the price should she set for the item is
=15+6
=$21
I have a half-full bottle of water and it has more than 8 ounces in it. What would be the expression
Answer:
The equivalent expression is [tex]\frac{1}{2}\cdot V_{max} > 8\,oz[/tex].
Step-by-step explanation:
The best approach consists in translating the sentence given in the question into mathematical terms until an expression is complete:
(i) I have a half-full bottle of water
Translation: I use a bottle with a maximum volume capacity [tex]V_{max}[/tex], measured in ounces, a half of it is full of water:
[tex]\frac{1}{2}\cdot V_{max}[/tex]
(ii) And it has more than 8 ounces in it
Translation: The volume occupied by the water is greater than 8 ounces. Hence, we get the following inequation:
[tex]\frac{1}{2}\cdot V_{max} > 8\,oz[/tex]
Kyle is making a frame for a rectangular piece of art. The length of the frame is 3 times the width, as shown below.
A rectangle with a length of 3 x and height of x.
If Kyle uses 18 feet of wood to make the frame, what is the length of the frame?
Answer:
D
Step-by-step explanation:
Answer:D
Step-by-step explanation: got it right
A restkaurant worker is able to clean 32 dishes in 8 minutes. How many minutes would it take to clean 58 dishes?
Answer:
14.5
Step-by-step explanation:
Find the unit rate
PLS HELP THIS IS TIMED
What is the length of AC?
A. Square root of 2
B. Square root of 5
C. 3
D. 5
Answer:
B. √5 units
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra II
Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Find points from graph.
Point A (-3, 2)
Point C (-1, 3)
Step 2: Find distance d
Substitute [DF]: [tex]d = \sqrt{(-1+3)^2+(3-2)^2}[/tex]Add/Subtract: [tex]d = \sqrt{(2)^2+(1)^2}[/tex]Exponents: [tex]d = \sqrt{4+1}[/tex]Add: [tex]d = \sqrt{5}[/tex]Find the solution of the system of equations.
- 7x – 4y = -44
7x - 3y = 16
Answer:
{x,y} = {5,8}
Step-by-step explanation:
[1] 7x-3y+5=16
[2] 4y=3x+17
[1] 7x - 3y = 11
[2] -3x + 4y = 17
// Solve equation [2] for the variable y
[2] 4y = 3x + 17
[2] y = 3x/4 + 17/4
// Plug this in for variable y in equation [1]
[1] 7x - 3•(3x/4+17/4) = 11
[1] 19x/4 = 95/4
[1] 19x = 95
// Solve equation [1] for the variable x
[1] 19x = 95
[1] x = 5
// By now we know this much :
x = 5
y = 3x/4+17/4
// Use the x value to solve for y
y = (3/4)(5)+17/4 = 8
Choose the number sentence whose product is 5.85.
A. 1.7 x 3.5
B. 26 x 2.25
C. 4.5 x 2.3
D. 1.3 x 4.5
Answer:
D
1.3 times 4.5 is 5.85
Answer:
D
Step-by-step explanation:
BRAINLYEST please
Find the slope of the line
that goes through the given
points
t
(1,2) (3,-4)
I
1
Answer:
Step-by-step explanation:
y2-y1=
x2-x1
2--4=6(negatives cancel out)
3-1=2
so 6/2 =3
3 is slope
What is the answer to it?
Answer:
The answer is
[tex] - 6x + 17[/tex]
5x^2+2x-3=0 by factorisation method
Answer:
x = - 1, 0.6
Step-by-step explanation:
[tex]5 {x}^{2} + 2x - 3 = 0 \\ \\ 5 {x}^{2} + 5x - 3x - 3 = 0 \\ \\ 5x(x + 1) - 3(x + 1) = 0 \\ \\ (x + 1)(5x - 3) = 0 \\ \\ x + 1 = 0 \: \: or \: 5x - 3 = 0 \\ \\ x = - 1 \: \: or \: \: x = \frac{3}{5} \\ \\ x = - 1 \: \: or \: \: x = 0.6 \\ \\ x = - 1, \: \: 0.6[/tex]
Answer:
X= -1 or X=3/5
Step-by-step explanation:
5x^2+2x-3=0
(x+1)(5x-3)=0
x= -1 or 5x/5=3/5
x=3/5