The given series ∑[infinity]n=0x−5n9n converges for all x in the interval (-4,14) in the real number system.
To determine the convergence of the given series, we can use the ratio test. Applying the ratio test, we get:
|((x-5(n+1))/9(n+1)) / ((x-5n)/9n)| = |(x-5)/(9(n+1))|.
For the series to converge, we need the limit of the ratio as n approaches infinity to be less than 1 in absolute value. Hence, we have:
lim(n→∞) |(x-5)/(9(n+1))| < 1
|x-5|/9 < 1
|x-5| < 9
This implies -4 < x-5 < 14, or -4 < x < 14. Therefore, the given series converges for all x in the interval (-4,14) in the real number system.
Learn more about interval here:
https://brainly.com/question/29126055
#SPJ11
4k squared = 100 solve for k
Answer:
k = 5
Step-by-step explanation:
4k^2 = 100
4k^2/4 = 100/4
k^2 = 25
k=5
Pls pls pls pls help
Step-by-step explanation:
To prove that two lines are perpendicular, when all we have are those two lines, we can use the Linear Pair Perpendicular Theorem - If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.
Our diagonals intersect at point O, so we'd need to show the two linear angles formed at that intersection point are equal, and we can do that with triangle congruency.
A rhombus is a parallelogram, so we will use what we already know about parallelograms - that the diagonals bisect each other.
It is then easy to show that the triangles ΔAOD and ΔAOB are congruent using the Side-Side-Side postulate, and from that that ∠AOD ≅ ∠AOB.
And now, since ∠AOD and ∠AOB are a linear pair, we use the Linear Pair Perpendicular Theorem - If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.
PROOF
(1) ABCD is a rhombus //Given
(2) AB=AD //definition of rhombus
(3) AO=AO //Common side, reflexive property of equality
(4) BO=OD // A rhombus is a parallelogram, a parallelogram's diagonals bisect each other
(5) △AOD≅△AOB //Side-Side-Side postulate.
(6) ∠AOD ≅ ∠AOB //Corresponding angles in congruent triangles (CPCTC)
(7) AC⊥DB //Linear Pair Perpendicular Theorem
The converse of this is also true: if a parallelogram's diagonals are perpendicular, it is a rhombus.
Find the ratio of 580 ml to 1.12 I to 104 ml
Answer:
580 : 1120 : 104
Step-by-step explanation:
1.12 ml -> 1120 ml
hence,
580 : 1120 : 104
What will be the cost of the paving if cement costs $26.50 per square metre?
Answer:
hey
Step-by-step explanation:
pls help me it is inportant
Answer:
(5.x)+(5.2)
Step-by-step explanation:
Hope it helps you......
Answer:
nah
Step-by-step explanation:
How many liters of 30% salt solution must be added to 6 L of an 80% salt solution to obtain a 50% salt solution
Answer:
9 Liters
Step-by-step explanation:
Let us represent:
The number of liters of the 30% salt solution = x
Number of liters for the 80% solution = 6 Liters
Number of liters for the 50% solution = x + 6 Liters
Hence:
x × 30% + 6 × 80% = (x + 6)50%
0.3x + 4.8 = 0.5x + 3
Collect like terms
4.8 - 3 = 0.5x - 0.3x
1.8 = 0.2x
x = 1.8/0.2
x = 9 Liters
Therefore, the number of liters for the 30% Salt solution = 9 Liters
6 tubs hold 125 gallons in all how much does each run hold
Answer:
125/6= 20.8 gallons
Please Help! Ill give brainliest no fakes PLEASE!!
Answer:
4 and then 15
Step-by-step explanation:
second one: 6:4
last one: 15:10
Plz help me! I need an answer right away
Just for curiosity, which ‘high school/secondary school’ education is harder, the UK or USA?
Answer:
UK
Step-by-step explanation:
(−3⋅10^3 )⋅(4⋅10^6)=???
Answer:
-1.19164 x 10^8
Step-by-step explanation:
Can someone help w/ this math problem plzz
Answer:
its C
Step-by-step explanation:
An account earns simple interest.
$1500 at 4% for 5 years
a. Find the interest earned.
$
b. Find the balance of the account.
Answer:
a) $300 in interest
b) $1800 account total
Step-by-step explanation:
Interest = Principal x Rate x Time
I = 1500(.04)(5)
I = 300
A = P + I
1800 = 1500 + 300
what is the decimal word form of 120.95?
What is the domain of all of these points?
(8, 2), (12,9), (16, 16), (20, 23)
Answer:
8, 12, 16, 20
Step-by-step explanation:
those are the domains
solve the equation 3(x + 1) + 6 = 33.
Answer:
155
Step-by-step explanation:
Select all that apply. Select the formulas that give the amount P in the account after the first period.
Options :
a.) P=1.005Po
b.) P=1.02Po
c.) P=Po(0.02/4)
d.) P=Po(4.02/4)
e.) P=Po(1+ 0.02/4)
Answer:
a.) P=1.005Po
d.) e.) P=Po(1+ 0.02/4)
Step-by-step explanation:
From the compound interest formula:
P = P0(1 + r/n)^t
Rate = 2% = 2/100 = 0.02
n = Number of compounding times per period, quarterly ; n = (12 /3) months
P = P0(1 + 0.02/4)^1
P = p0(1 + 0.02/4)
Simplifying further :
P = P0(1 + 0.005)
P = p0(1.005)
Help Please................
Answer:
split then d the trinangle with the base and the height and do the rectangle as length times width
Step-by-step explanation:
Answer: 1152
Step-by-step explanation:
If the mean of 5 numbers is 10 and the mean of other 15 numbers is 20 , what is the combined mean of both 20 numbers
9514 1404 393
Answer:
17.5
Step-by-step explanation:
The sum of the 5 numbers is 5·10 = 50.
The sum of the 15 numbers is 15·20 = 300.
The sum of all 20 numbers is then 50+300 = 350, so their mean is ...
mean = sum/number = 350/20 = 17.5
The combined mean of the 20 numbers is 17.5.
what r passing marks out of 40
Answer:
36/40 - A, 32/40 - B, 28/40 - C, and 24/40 - D
Step-by-step explanation:
Answer:
18 is ur answer
thank youWhich of the following nets is for a pyramid?
2nd one
hope it helps you
The net of the pyramid is given by figure B
What is the surface area of the pyramid?The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid
Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Given data ,
A net is a two-dimensional representation of a three-dimensional shape that, when folded along the edges, forms the shape of the solid.
In the case of a pyramid, the net consists of a polygonal base and triangular faces that meet at a common vertex.
The number of triangular faces depends on the type of pyramid (triangular, square, pentagonal, etc.).
To learn more about surface area of pyramid click :
https://brainly.com/question/15050758
#SPJ2
I need help it's geometry
Step-by-step explanation:
[tex] \sin(45) = \frac{x}{5} \\ \frac{1}{ \sqrt{2} } = \frac{x}{5} \\ x = \frac{5}{ \sqrt{2} } = 3.535[/tex]
[tex] \sin(45) = \frac{y}{5} \\ y = \frac{5}{ \sqrt{2} } = 3.535[/tex]
Answer:
[tex]\frac{5\sqrt{2} }{2 }[/tex]
Step-by-step explanation:
x=y
45-45-90 equation is x-x- x square root of 2
Help fast please. I will give brainliest.
Answer:
Q5 ) A 80 UNITS²
pls give me brainliest
x y
0 -6
1 -4
2 -2
3 0
The table above represents what type of function?
A.
neither linear nor nonlinear
B.
nonlinear
C.
linear and nonlinear
D.
linear
Answer: let me check
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
0 -6 is a linear and a nonlinear and it keeps on going
can somebody help with this please dont put fake answers i really need to pass this test
Step-by-step explanation:
by using Pythagoras theorem,
h^2= p^2+b^2
or, b^2=h^2- p^2
Answer:
it's 24 cm
30²-18²=
b²=900-324= 576
b²=576
b=24
f(x) = -3x + 3
f(-2) = [?]
Help
is this the answer you're looking for? I'm sorry I'm confused
3 x (5 + 7)
What two words can describe (5 + 7) in the expression above?
O A. quotient and factor
OB.
difference and factor
OC. sum and factor
OD. sum and quotient
The expression contain sum and factor.
The correct option is (C).
What is Expression?Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Given:
3 x(5+7)
In the Above Expression we have two operation Multiplication and Addition.
Also, the Multiplication is also termed as factor.
Hence, the expression contain sum and factor.
Learn more about Expression here:
https://brainly.com/question/14083225
#SPJ2
12 (X + 2) - 4x = 4( 2X + 11 ) -20
Solve for X
Answer:
Step-by-step explanation:
12 (x + 2) - 4x = 4 (2x + 11) - 20
12 + 24 - 4x = 8x + 44 - 20
36 - 4x = 8x + 24
36 - 24 = 8x - 4x
12 = 4x
---- ----
4 4
3 = x
-x = -3
x = 3
-8= -4+x
Solve for x
Answer:
-4 + x = - 8
x = - 8 +4
x = - 4
hope it helps :-
Answer:
-4=x or x=-4
Step-by-step explanation:
Move -4 to the other side by adding 4 on both sides:
-8+4=4-4+x
-4=x or x=-4
Hope this helps!
How many solutions does this system of equations have?
Answer:
One solution.
A system of linear equations has one solution when the graphs intersect at a point.
I hope it's helpful!