The sum appears to be
[tex]\displaystyle\sum_{n=0}^\infty(2n+1)x^n[/tex]
I'll assume you want to find out what function this sum converges to.
Let
[tex]f(x)=\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]
with -1 < x < 1. Differentiating gives
[tex]f'(x)=\dfrac1{(1-x)^2}=\displaystyle\sum_{n=0}^\infty nx^{n-1}=\sum_{n=1}^\infty nx^{n-1}=\sum_{n=0}^\infty(n+1)x^n[/tex]
So we have
[tex]\displaystyle\sum_{n=0}^\infty(2n+1)x^n=f'(x)+xf'(x)[/tex]
[tex]\displaystyle\sum_{n=0}^\infty(2n+1)x^n=\frac{1+x}{(1-x)^2}[/tex]
Find the largest prime divisor of $15^6 - 7^6$[tex]Find the largest prime divisor of $15^6 - 7^6$[/tex]
Answer:
Largest prime factor of the given expression is 379.
Step-by-step explanation:
Given the expression:
[tex]15^6 - 7^6[/tex]
To find:
The largest prime factor of the given expression.
Solution:
First of all, let us factorize the given expression.
[tex]15^6 - 7^6\\\Rightarrow (15^3)^2 - (7^3)^2\\\\\text{Using } x^{2} -y^2 = (x+y) (x-y)\\\\\Rightarrow (15^3+7^3)(15^3-7^3)[/tex]
Let us learn two formula:
[tex]x^3+y^3 = (x+y)(x^2+y^2-xy)[/tex]
[tex]x^3-y^3 = (x-y)(x^2+y^2+xy)[/tex]
Applying the above formula in the expression written above:
[tex](15^3+7^3) = (15+7)(15^2+7^2-15\times 7)\\\Rightarrow 22(225+49-105 ) = 2 \times 11 \times 169 \\\Rightarrow 2 \times 11\times 13\times 13\\\Rightarrow 2 \times 11\times 13^2[/tex] ...... (1)
Similarly:
[tex](15^3-7^3) = (15-7)(15^2+7^2+15\times 7)\\\Rightarrow 8(225+49+105 ) = 2^3 \times 379[/tex]........ (2)
Multiplying the expressions from (1) and (2) to get the result:
[tex]\therefore 15^6 - 7^6 = 2^4 \times 11 \times \underline{\bold{379}} \times 13 ^2[/tex]
So, largest prime factor of the given expression is 379.
The largest prime divisor of the expression is 379.
How to solve the divisor?The expression will be factorized. This will be:
= (15³)² - (7³)²
= (15 + 7)³(15 - 7)³
This can be illustrated as:
(15 + 7)³ = 2 × 11 × 13²
(15 - 7)³ = 2³ × 379
In conclusion, the largest prime divisor of the expression is 379.
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please help!!!!! idk how to do this
Answer:
30 seconds.
Step-by-step explanation:
So, we have the equation:
[tex]h(t)=-16t^2+h[/tex]
Where t is the time in seconds and h is the initial height.
A barometer falls from a weather balloon at a height of 14,400 feet. In other words, the initial height is 14,400. Substitute for h:
[tex]h(t)=-16t^2+14400[/tex]
We need to find when the barometer hits the ground. Ground level is 0 feet. Therefore, we can substitute h(t) for 0 and solve for the equation (solve for t) in order to find how long (in seconds) it took for the barometer to fall:
[tex]0=-16t^2+14400\\-14400=-16t^2\\900=t^2\\t=\pm\sqrt{900} \\\text{Time cannot be negative.}\\t=\sqrt{900}\\ t=30 \text{ seconds}[/tex]
Therefore, it took 30 seconds for the barometer to hit the ground when it fell at a height of 14,400 feet.
Edit: Spelling.
A shoe salesperson earns a 5% bonus on weekly sales over $3,000. Consider these functions to answer the following questions. f(x) = x – 3,000 g(x) = 0.05x Part A In your own words, explain what each of the functions represents.
Answer:
g(x)= 0.05x represents the amount of bonus, f(x)=x-3,000 represents weekly sales over $3,000.
Step-by-step explanation:
The function f(x) represents how much money earned by sales person weekly over $3000.
And function g(x) represents the amount of bonus earned by salesperson.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) is called function.
According to the given question.
The percent of bonus earned by salesperson weekly on sales over $3,000 is 5%.
Also, we have two functions.
[tex]f(x) = x - 3000[/tex]
and [tex]g(x) = 0.05x[/tex]
For the function, f(x) if x is the amount of money earned salesperson in a week, then f(x) will represents how much money salesperson earned apart form $3000.
And the function g(x) represents the amount of bonus earned by the salesperson.
Hence, the function f(x) represents how much money earned by sales person weekly over $3000. And function g(x) represents the amount of bonus earned by salesperson.
Find out more information about function here:
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Please answer this question now
Answer:
7.8
Step-by-step explanation:
To do this problem you need to know Pythagorean Theorem which is also known as [tex]a^{2} +b^{2} =c^{2}[/tex].
In this problem 6 would be a, 5 would be b, and d would be c. So to do this we would do 5 squared (which is 25)+ 6 squared which is 36) and you would get 61 and when you do that you will just take the square root of that which is 7.81 and round it to the nearest tenth which is 7.8 and that would be the final answer
Transversal m intersects lines a, b, and c such that m∠1=42° and m∠2=140° and m∠3=138°. Which lines are parallel?
Answer:
Lines a and c.
Step-by-step explanation:
m∠1=42° and m∠3=138°. 42 + 138 = 180, so the two angles form a 180° angle. That means that lines a and c are parallel.
Hope this helps!
Answer:A is parallel to C
Step-by-step explanation:
Statement | Reason
42*+138*=180* |Corresponding angles
There fore A||C aka a parallel to c
42*+140*=180* | Same side int. angles
Therefore A no || B aka A is not parallel to B
138*=140* | Same side int. Angles
Therefore B And C are not parallel and A,B. and C are not parallel
The answer is A||C or A is parallel to C
The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5 . find the original number
Answer:
5/8
Step-by-step explanation:
Let the numerator = n.
Let the denominator = d.
The fraction is
n/d
"The denominator of a rational number is greater than its numerator by 3."
d = n + 3
The fraction is
n/(n + 3)
"If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5."
(n - 3)/(n + 3 + 2) = 1/5
(n - 3)/(n + 5) = 1/5
Cross multiply.
5(n - 3) = 1(n + 5)
5n - 15 = n + 5
4n = 20
n = 5
d = n + 3 = 5 + 3 = 8
n/d = 5/8
The original number is 5/8.
PLEASE help me with this question! No nonsense answers and answer with full solutions please!
Answer: b) {-3, 0.5}
Step-by-step explanation:
The new equation is the original equation plus 6. Move the original graph UP 6 units. The solutions are where it crosses the x-axis.
[tex]\text{Original equation:}\quad f(x)=\dfrac{15}{x}-\dfrac{9}{x^2}\\\\\\\text{New equation:}\quad\dfrac{15}{x}+6=\dfrac{9}{x^2}\\\\\\.\qquad \qquad f(x)= \dfrac{15}{x}-\dfrac{9}{x^2}+6[/tex]
+6 means it is a transformation UP 6 units.
Solutions are where it crosses the x-axis.
The curve now crosses the x-axis at x = -3 and x = 0.5.
f(x) = x2. What is g(x)?
Answer:
A
Step-by-step explanation:
consider the form g(x) = aX^2, where a is negative, means the curve is flip upside down.
-3, shifted down for 3 units.
A certain server works four 6-hour shifts a week at a restaurant and has a base salary of $9.75/ℎ. An average server sells $1400 in a single shift. If the server makes an average of 14% tip of a bill, what is the annual gross income of the server?
Answer:
The annual gross income of the server is $52936
Step-by-step explanation:
The server works four 6-hour shift a week.
the server earns $9.75/h
An average seller sells $1400 in a single shift, and makes 14% tip of a bill.
For the 6-hour shift, the server earns
6 x $9.75 = $58.5 a shift
in a week, the total money made for the four shifts in a week will be
4 x $58.5 = $234
The server makes an average of 14% of a bill, and makes about $1400 in a single shift.
In a single shift he makes a tip of
14% of $1400 = 0.14 x $1400 = $196
in a week he makes 4 x $196 = $784
Total money the server makes in a week is
==> $234 + $784 = $1018
There are 52 weeks in a year.
The server's annual gross income will be
52 x $1018 = $52936
How many real solutions In this problem
Answer:
D
Step-by-step explanation:
Given
y = x² + 1
y = x
Equating gives
x² + 1 = x ( subtract x from both sides )
x² - x + 1 = 0
Consider the discriminant Δ = b² - 4ac
with a = 1, b = - 1 and c = 1
b² - 4ac = (- 1)² - (4 × 1 × 1) = 1 - 4 = - 3
Since b² - 4ac < 0 then there are no real solutions
Find the slope of the line passing through the points D(10, 8) and E(-4, 4).
Answer:
[tex]\frac{2}{7} x[/tex]
Step-by-step explanation:
To find the slope of a line with 2 points we use the following formula.
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
So with the following points,
E(-4,4)
D(10,8)
So 8 is y2 and 4 is y1 8-4 = 4
10 - -4 = 14
Slope: 2/7x
Thus,
the slope of the line is 2/7x.
Hope this helps :)
In the figure, m∠CED = m∠A. Complete the following proportions: ED/ A F= CE/? = CD/?
Answer:
The completed proportions are;
ED/A_F = CE/CA = CF/CD
Step-by-step explanation:
The given m∠CED = m∠A
∴ Angle ∠CDE = Angle ∠A_FC, (corresponding angles)
Angle ∠ECD = Angle ∠ACF (reflexive property)
Triangle ΔDCE is similar to triangle ΔACF (Angle Angle Angle (AAA) similarity)
In triangle ΔDCE and triangle ΔACF
m∠A is bounded by CA and A_F
m∠CED is bounded by CE and ED
∠DCE is bounded by CE and DE
∠C is bounded by CA and CF
Based on the orientation of the two triangles, we have
ED is the corresponding side to A_F, CD is the corresponding side to CF, CE is the corresponding side to CA
Therefore, we have;
ED/A_F = CE/CA = CF/CD.
what are three different whole numbers whose sum and product are equal
Three different whole numbers whose sum and product are equal are 1, 2, and 3.
1 + 2 + 3 = 6
1 x 2 x 3 = 6
As demonstrated above, the sum and product of 1, 2, and 3 is the same.
Hope this helps!! :)
Answer:
1 2 and 3
Step-by-step explanation:
The volume of the Sun is about 1.41 x 10^18 cubic kilometers. The volume of Earth is about 1.09 x 10^12 cubic kilometers. The number of Earths that can fit inside the Sun can be found by dividing the Sun's volume by Earth's volume. Find this quotient and express the answer in scientific notation.
Answer:
1290000
Step-by-step explanation: Given that
The volume of the Sun is about = 1.41 x 10^18 cubic kilometers.
The volume of Earth is about 1.09 x 10^12 cubic kilometers.
The number of Earths that can fit inside the Sun can be found by dividing the Sun's volume by Earth's volume.
= Volume of Sun ÷ Volume of the Earth
= 1.41 x 10^18 cubic km/1.09 x 10^12 cubic km
= 1.41 x 10^18/1.09 x 10^12
=(1.42/1.09)× 10^18-12
= 1.29×10^6
n is 1.29×10^6.
Hence the number of Earth that can be fitted in the Sun is 1290000
Plz ans with steps... Thx!!
Answer:
16
Step-by-step explanation:
Let the 1st part of your answer be x , so the 2nd part will be 40-x . From the given information, we can write the equation: (1/4)x = (3/8) × (40-x) . We can simplify this into (1/4)x = (120-3x)/8 ; 8x = 480-12x ; 8x+12x = 480 ; 20x = 480 ; x = 480/20; x = 24
Therefore, the 1st part = 24
Plug this into your 40-x equation to get: 40 - 24 = 16
OMGGG PLS HELP PLS I WILL GIVE YOU POINTS AND STUFF PLS HELP MEH Figure A is a scale image of Figure B. B: side length x A: side length 10 Figure A maps to Figure B with a scale factor of 0.75. What is the value of x?
try this answer good luck
Answer:
Answer: 1/2
Step-by-step explanation:
Given : Figure B is a scaled copy of Figure A.
We know that the scale factor is the ratio of the corresponding sides of two similar figures.
From , the graph we assume that that one point = one unit of length.
Then, the dimension of one side of figure A = 4 units and the dimension of corresponding side of Figure B = 2.
Then, the scale factor is given by:
k = 2/4 = 1/2
Hence, the scale factor is 1/2
Please help me with this. I am really struggling...
Help is appreicated! (10 points!)
Answer:
5
Step-by-step explanation:
5
5) The solution of (2x - 1)2 = 9 is equal to
d) 21
a) - 1
b) 2
c) - 1,2
d) None of these
6) The GCD of x2 - 2xy + y2
Answer:
Q5 d
Step-by-step explanation:
(2x-1)2=9
4x-2=9
4x=9+2
4x=11
x=2.75
ans: none of these
i will give brainliest.On every sale of goods worth N10,000.00, there is a commission of N550.00. If
an agent delivers N150,000.00, find his commission. pls helllp
Answer:
8250
Step-by-step explanation:
I think
Two cars are traveling north along a highway. The first drives at 40 mph, and the second, which leaves 3 hours later, travels at 60 mph. How long after the second car leaves will it take for the second car to catch the first?
Answer:
Step-by-step explanation:
We will make a table and fill it in according to the information provided. What this question is asking us to find, in the end, is how long did it take the cars to travel the same distance. In other words, how long, t, til car 1's distance = car 2's distance. The table looks like this:
d = r * t
car1
car2
We can fill in the rates right away:
d = r * t
car1 40
car2 60
Now it tells us that car 2 leaves 3 hours after car 1, so logically that means that car 1 has been driving 3 hours longer than car 2:
d = r * t
car1 40 t + 3
car2 60 t
Because distance = rate * time, the distances fill in like this:
d = r * t
car1 40(t + 3) = 40 t+3
car2 60t = 60 t
Going back to the interpretation of the original question, I am looking to solve for t when the distance of car 1 = the distance of car 2. Therefore,
40(t+3) = 60t and
40t + 120 = 60t and
120 = 20t so
t = 6 hours.
What is the domain of the function shown on the graph? A. -10
Answer:
Option (C)
Step-by-step explanation:
Domain of any graph is defined by the x-values or the input values of a function.
Similarly, y-values on the graph of a function define the Range.
In the graph attached, x-values varies from (-∞) to (+∞).
Therefore, Domain of the graphed function will be (-∞, ∞)
Or -∞ < x < ∞
Similarly, y-values of the graph varies from (-∞) to (1)
Therefore, range of the graphed function will be (-∞, 1).
Or -∞ < y < 1
Option (C) will be the answer.
Which ordered pair is a solution of this equation?
Please and thank you
Answer:
Hey there!
-9x-y=-15
9x+y=15
A solution with integer values would be 9(1)+6=15
Thus, x=1 and y=6
(1, 6)
Hope this helps :)
Answer:
(6,1)
Step-by-step explanation:
Question 1
Solve the equation that models the volume of the shipping box, 8(n + 2)(n + 4) = 1,144. If
you get two solutions, are they both reasonable?
Answer:
n = -15 and n = 9. n = -15 is not reasonable because you can't have negative boxes or negative units of measurement.
Step-by-step explanation:
8(n + 2)(n + 4) = 1,144
(n + 2)(n + 4) = 143
n^2 + 2n + 4n + 8 = 143
n^2 + 6n - 135 = 0
(n + 15)(n - 9) = 0
n + 15 = 0
n = -15
n - 9 = 0
n = 9
I got two solutions: n = -15 and n = 9. Only one is reasonable because you cannot have a negative number of boxes or negative weight.
Hope this helps!
Simplify the equation, and set it equal to zero to prepare for factoring.
Multiply the two factors in parentheses using the distributive property:
8(n2 + 2n + 4n + 8) = 1,144
Combine like terms inside the parentheses:
8(n2 + 6n + 8) = 1,144
Multiply the terms inside the parentheses by 8 using the distributive property:
8n2 + 48n + 64 = 1,144
Set the equation equal to zero by subtracting 1,144 from each side:
8n2 + 48n − 1,080 = 0
Factor out the GCF, which is 8:
8n2 + 48n − 1,080 = 0
8(n2 + 6n − 135) = 0
Divide both sides of the equation by 8:
n2 + 6n − 135 = 0
Compare the equation with the standard form ax2 + bx + c = 0, and get a, b, and c:
a = 1, b = 6, c = -135
The leading coefficient of the equation is 1. So, find two numbers that have a sum of 6 and a product of -135:
6 = -9 + 15
-135 = -9 • 15
The two numbers are -9 and 15. Use the two numbers to write the factors of the quadratic expression:
(n − 9)(n + 15) = 0
Use the zero product property, and solve for n:
n − 9 = 0 or n + 15 = 0
n = 9 or n = -15
There are two solutions for n. But since n represents the width of the helmet box, it can’t be negative. Therefore, the only reasonable solution is n = 9
Angle ABC is a straight angle. MAngleDBC = 130° and Ray B E bisects AngleABD. The center of line A C is point B. Two lines extend from point B. One line extends to the left and contains point E. Another line extends up and to the left and contains point D. What is mEBA? °
Answer:
25°
Step-by-step explanation:
Since ∠DBC = 130°, ∠DBC + ∠ABD = 180° (sum of angles on a straight line is 180°). Solving for ∠ABD:
∠DBC + ∠ABD = 180°
130 + ∠ABD = 180°
∠ABD = 180° - 130°
∠ABD = 50°
∠ABD is bisected by line BE, therefore ∠ABD = ∠EBA + ∠DBE (angle addition postulate).
The angle addition postulate states that if w is the interior of xyz then ∠XYZ = ∠XYW + ∠ZYW
Since E is the interior of ∠ABD, then:
∠ABD = ∠EBA + ∠DBE
But ∠EBA = ∠DBE
∠ABD = 2∠EBA
50 = 2∠EBA
∠EBA = 25°
Answer:
The answer is 25 degrees
NEED HELP ASAP!! FIRST ONE TO GET THE ANSWER RIGHT GETS THE MOST BRAINLIEST
Answer:
125
Step-by-step explanation:
Add all the angles then subtract by 360.
Answer:
Vp-by-step explanation:
Can anyone help me with this plz Which pair of triangles can be proved congruent by the SAS Postulate?
Answer: Second choice. Triangle ABX and triangle EDX.
Check out the diagram below. I have color coded the segments that are the same length. The congruent angles are due to the fact we have a pair of vertical angles, which are always the same measure. The green angles are between the red and blue sides for each triangle.
Answer:
Congruent Triangles
Step-by-step explanation:
From the available information, let's concentrate on the fact that lines AX≅EX and lines BX≅DX. This simply means that line AX is equal to line EX and line BX equals DX. since the two lines cross each other to make the vertically opposite angles AXB and DXE equal (AXB≅DXE), then the opposite triangles are congruently sharing two pairs of equal sides and the same.
The congruent triangles are ΔABX and ΔEDX
Please help me with this question ASAP!
Answer:
The fourthStep-by-step explanation:
[tex]x^2+y^2-14x+10y+25=0\\\\x^2-14x\ +\ y^2+10y+25=0\\\\\underline{x^2-14x+49} -49+\underline{y^2+10y+25}=0\\\\\underline{x^2-2\cdot x\cdot7+7^2}-49+\underline{y^2+2\cdot y\cdot5+5^2}=0 \\\\\underline{(x-7)^2}-49+\underline{(y+5)^2}=0\\\\\underline{\underline{(x-7)^2+(y+5)^2=49}}[/tex]
Nancy needs at least 1000 gigabytes of storage to take pictures and videos on her upcoming vacation. She
checks and finds that she has 105 GB available on her phone. She plans on buying additional memory
cards to get the rest of the storage she needs.
The cheapest memory cards she can find each hold 256 GB and cost $10. She wants spend as little
money as possible and still get the storage she needs.
Let C represent the number of memory cards that Nancy buys. 2)what is the least amount of money Nancy can spend to get the storage she needs?
Answer:
The answer to this question can be defined as follows:
In option 1, She buys 4 memory cards.
In option 2, The cost of memory is $40
Step-by-step explanation:
Given:
Available space is = 105 GB
required space = 1000 GB
256 GB memory cost $10.
Find needed memory:
= 1000 GB - 105 GB
= 895 GB
∴ the available memory is 256 GB.
∵ 256 × 4 = 1024 GB
The total memory she have = 1024 + 105 = 1129 GB
And she needs to buy 4 memory cards.
The cost of the four memory cards is= 4 ×10 = $40.
Using proportions, it is found that the least amount of money Nancy can spend to get the storage she needs is of $40.
------------------------------
This question is solved by proportions, using a rule of three.Nancy needs at least 1000 GB, but she only has 105 GB available. Thus, she needs to buy 1000 - 105 = 895 GB.The cheapest cards she can buy have 256 GB. How many of these cards she has to buy?The rule of three is of:
1 card - 256 GB
x cards - 895 GB
Applying cross multiplication:
[tex]256x = 895[/tex]
[tex]x = \frac{895}{256}[/tex]
[tex]x = 3.5[/tex]
Rounding, she has to buy 4 cards.
Each card costs $10, thus, she has to spend $10 x 4 = $40.A similar problem is given at https://brainly.com/question/17594062
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Place the indicated product in the proper location on the grid. (3xy - 1) (4xy + 2)
Answer:
[tex]2(6x^2y^2+xy-1)\\[/tex]
Step-by-step explanation:
We are to find the product of the given expression. Given the expression
(3xy - 1) (4xy + 2), th product is derives by simply opening up the bracket as shown below;
[tex]= (3xy - 1) (4xy + 2)\\\\= 3xy(4xy)+2(3xy)- 1(4xy)-1(2)\\\\= 12x^2y^2 + 6xy-4xy-2\\\\= 12x^2y^2 + 2xy-2\\\\bringing\ out\ the\ common\ factor;\\\\2(6x^2y^2+xy-1)\\\\[/tex]
The expression 2(6x²y²+xy-1) gives the required product.